Journal articles: 'Boundary heat flux'

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Huang, Weichao, Jiahao Li, and Ding Liu. "Research on Unsteady Inverse Heat Conduction Based on Dynamic Matrix Control." Energies 16, no. 11 (May 30, 2023): 4420. http://dx.doi.org/10.3390/en16114420.

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For the unsteady multi-boundary inverse heat conduction problem, a real-time solution method for boundary heat flux based on dynamic matrix control is proposed in the paper. The method solves the heat flux at the boundary in real-time by measuring the temperature information at the measurement points of the heat transfer system. A two-dimensional direct heat conduction model of the heat transfer system is established in the paper, and is solved by the finite difference method to obtain the temperature information of the measurement points under any heat flux boundary. Then, the correspondence between the heat flux of boundary and the temperature information is presented by means of a step-response model. The regularization parameters are introduced into the method to improve the stability of the inversion process, and the effect of real-time inversion on the heat flux of the boundary is achieved through rolling optimization. The experimental results show that the proposed method can achieve real-time inversion of the heat fluxes of the two-dimensional boundary with good accuracy.

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Miao, Wenbo, Xiaoli Cheng, Bangcheng Ai, and Yonghui Dong. "Surface Slip Effect on Thermal Environment of Hypersonic Non-Equilibrium Flows." International Journal of Computational Methods 12, no. 04 (August 2015): 1540008. http://dx.doi.org/10.1142/s0219876215400083.

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Boundary slip effect caused by low gas density has an important influence on the thermal environment of the vehicles. Numerical studies on the boundary slip effect and accommodation for moment and energy have been carried out in this paper. The simulations considering slip boundary and surface catalysis are validated with Arc-jet test data. Mechanism and rules of impact on surface heat flux by different boundary slip level (Knudsen number from 0.0028 to 0.05) has been investigated in typical hypersonic flow conditions. The results show that mechanisms of boundary slip effect on mass diffusion heat flux and convective heat flux are different; slip boundary diminishes the convective heat, whereas enhances the mass diffusion heat flux. Smaller moment and energy accommodation coefficient is equivalent to more rarefaction. As Knudsen number goes up, the influences of accommodation on heatflux are enhanced, it mainly affects the convective heat flux.

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Wang, Fu Qiang. "Ray-Thermal Sequential Coupled Heat Transfer ANALYSIS of Porous Media Receiver for Solar Dish Collector." Applied Mechanics and Materials 442 (October 2013): 169–75. http://dx.doi.org/10.4028/www.scientific.net/amm.442.169.

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For the sake of reflecting the concentrated heat flux distribution boundary condition as genuine as possible during simulation, the sequential coupled optical-thermal heat transfer analysis is introduced for porous media receiver. During the sequential coupled numerical analysis, the non-uniform heat flux distribution on the fluid entrance surface of porous media receiver is obtained by Monte-Carlo ray tracing method. Finite element method (FEM) is adopted to solve energy equation using the calculated heat flux distribution as the third boundary condition. The dimensionless temperature distribution comparisons between uniform and non-uniform heat flux distribution boundary conditions, various porosities, and different solar dish concentrator tracking errors are investigated in this research.

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Wen, Jun, and M. M. Khonsari. "Analytical Formulation for the Temperature Profile by Duhamel’s Theorem in Bodies Subjected to an Oscillatory Heat Source." Journal of Heat Transfer 129, no. 2 (July 5, 2005): 236–40. http://dx.doi.org/10.1115/1.2424236.

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An analytical technique is presented for treating heat conduction problems involving a body experiencing oscillating heat flux on its boundary. The boundary heat flux is treated as a combination of many point heat sources, each of which emits heat intermittently based on the motion of the flux. The working function of the intermittent heat source with respect to time is evaluated by using the Fourier series and temperature profile of each point heat source is derived by using the Duhamel’s theorem. Finally, by superposition of the temperature fields over all the point heat sources, the temperature profile due to the original moving heat flux is determined. Prediction results and verification using finite element method are presented for an oscillatory heat flux in a rectangular domain.

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Alghamdi, A. "Inverse Estimation of Boundary Heat Flux for Heat Conduction Model." Journal of King Abdulaziz University-Engineering Sciences 21, no. 1 (2010): 73–95. http://dx.doi.org/10.4197/eng.21-1.5.

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Taylor, Robert P., Philip H. Love, Hugh W. Coleman, and M. H. Hosni. "Step heat flux effects on turbulent boundary-layer heat transfer." Journal of Thermophysics and Heat Transfer 4, no. 1 (January 1990): 121–23. http://dx.doi.org/10.2514/3.29175.

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Dewar, W. K., and R. X. Huang. "Fluid flow in loops driven by freshwater and heat fluxes." Journal of Fluid Mechanics 297 (August 25, 1995): 153–91. http://dx.doi.org/10.1017/s0022112095003041.

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Thermohaline convection in a salt water loop is discussed. Fluid temperature is affected by relaxation on the loop surface and fluid salinity by a freshwater flux through the loop surface. In addition, other boundary conditions on salinity, such as the equivalent virtual salt flux or salinity relaxation condition, are examined and the dynamic role of diffusion in thermohaline convection is analysed.Both analytical and numerical analyses indicate that the system behaviour depends sensitively on the nature of the salinity boundary condition. For the saline-only loop model, analysis indicates that perturbations are advected by the mean flow, and flow stability is independent of the strength of the boundary forcing. In the full thermohaline loop problem, the virtual salt flux formulation accurately mirrors the freshwater flux results when the system is in the thermal mode. However, these formulations can differ substantially when the system is in the haline mode, especially in the strongly forced, weakly diffusive limit.For both types of loop configuration, salinity profiles governed by freshwater flux have scales determined by the internal parameters, while virtual salt flux profiles necessarily reflect the lengthscales of applied boundary conditions. Negative salinities can also appear under virtual salt flux owing to the inaccuracies inherent in the approximation, while freshwater flux ensures positive-definite salinity values.Our analysis supports the use of the physically more accurate freshwater flux boundary conditions when simulating thermohaline circulation.

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8

Voglar, Jure. "Physical Model of a Single Bubble Growth during Nucleate Pool Boiling." Fluids 7, no. 3 (February 27, 2022): 90. http://dx.doi.org/10.3390/fluids7030090.

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A simplified physical model of a single bubble growth during nucleate pool boiling was developed. The model was able to correlate the experimentally observed data of the bubble’s growth time and its radius evolution with the use of the appropriate input parameters. The calculated values of separated heat fluxes from the heater wall, thermal boundary layer, and to the bulk liquid gave us a new insight into the complex mechanisms of the nucleate pool boiling process. The thermal boundary layer was found to supply the majority of the heat to the growing bubble. The heat flux from the thermal boundary layer to the bubble was found to be close to the Zuber’s critical heat flux limit (890 kW/m2). This heat flux was substantially larger than the input heater wall heat flux of 50 kW/m2. The thermal boundary layer acts as a reservoir of energy to be released to the growing bubble, which is filled during the waiting time of the bubble growth cycle. Therefore, the thickness of the thermal boundary layer was found to have a major effect on the bubble’s growth time.

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9

Ji, Xuan, Nora Bailey, Daniel Fabrycky, Edwin S. Kite, Jonathan H. Jiang, and Dorian S. Abbot. "Inner Habitable Zone Boundary for Eccentric Exoplanets." Astrophysical Journal Letters 943, no. 1 (January 1, 2023): L1. http://dx.doi.org/10.3847/2041-8213/acaf62.

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Abstract The climate of a planet can be strongly affected by its eccentricity due to variations in the stellar flux. There are two limits for the dependence of the inner habitable zone boundary (IHZ) on eccentricity: (1) the mean stellar flux approximation ( S IHZ ∝ 1 − e 2 ), in which the temperature is approximately constant throughout the orbit, and (2) the maximum stellar flux approximation (S IHZ ∝ (1 − e)2), in which the temperature adjusts instantaneously to the stellar flux. Which limit is appropriate is determined by the dimensionless parameter Π = C BP , where C is the heat capacity of the planet, P is the orbital period, and B = ∂ Ω ∂ T s , where Ω is the outgoing long-wave radiation and T s is the surface temperature. We use the Buckingham Π theorem to derive an analytical function for the IHZ in terms of eccentricity and Π. We then build a time-dependent energy balance model to resolve the surface temperature evolution and constrain our analytical result. We find that Π must be greater than about ∼1 for the mean stellar flux approximation to be nearly exact and less than about ∼0.01 for the maximum stellar flux approximation to be nearly exact. In addition to assuming a constant heat capacity, we also consider the effective heat capacity including latent heat (evaporation and precipitation). We find that for planets with an Earthlike ocean, the IHZ should follow the mean stellar flux limit for all eccentricities. This work will aid in the prioritization of potentially habitable exoplanets with nonzero eccentricity for follow-up characterization.

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Juliano, Thomas J., Jonathan Poggie, Kevin M. Porter, Roger L. Kimmel, Joseph S. Jewell, and David W. Adamczak. "HIFIRE-5b Heat Flux and Boundary-Layer Transition." Journal of Spacecraft and Rockets 55, no. 6 (November 2018): 1315–28. http://dx.doi.org/10.2514/1.a34147.

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Seager, Richard, Yochanan Kushnir, and Mark A. Cane. "On Heat Flux Boundary Conditions for Ocean Models." Journal of Physical Oceanography 25, no. 12 (December 1995): 3219–30. http://dx.doi.org/10.1175/1520-0485(1995)025<3219:ohfbcf>2.0.co;2.

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12

Kim, Sin, Kyung Jin Lee, Yung Joo Ko, Bum Jin Chung, Kyung Youn Kim, and Min Chan Kim. "Direct estimation of time-dependent boundary heat flux." International Communications in Heat and Mass Transfer 31, no. 2 (March 2004): 273–80. http://dx.doi.org/10.1016/s0735-1933(03)00232-x.

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13

Vader, D. T., F. P. Incropera, and R. Viskanta. "Convective Nucleate Boiling on a Heated Surface Cooled by an Impinging, Planar Jet of Water." Journal of Heat Transfer 114, no. 1 (February 1, 1992): 152–60. http://dx.doi.org/10.1115/1.2911241.

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Convective nucleate boiling has been studied on a flat, upward facing, constant heat flux surface cooled by a planar, impinging water jet. Surface temperature distributions are presented for jet velocities between 1.8 and 4.5 m/s, fluid temperatures of 30, 40, and 50°C, and heat fluxes between 0.25 and 2.5 MW/m2. Although the critical Reynolds number, Rex*,c, is independent of heat flux for q” < q”ONB, boiling incipience strongly affects the transition to a turbulent boundary layer. As the heat flux increases, vapor bubbles of 1 mm diameter first appear at the point of maximum surface temperature, which also marks the onset of boundary layer turbulence. The leading edge of these bubbles moves toward the stagnation line and Rex*,c decreases with further increases in heat flux. Acceleration in the stagnation region stabilizes the flow, however, so that boundary layer turbulence is restricted to x/wj ≳ 1.6. With increasing heat flux, vigorous nucleate boiling covers more of the heater and surface temperature variations decrease.

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14

Xu, Mingtian. "Slip boundary condition of heat flux in Knudsen layers." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2161 (January 8, 2014): 20130578. http://dx.doi.org/10.1098/rspa.2013.0578.

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In a Knudsen layer with thickness comparable to the mean free path, collisions between heat carriers and solid walls play an important role in nanoscale heat transports. An interesting question is that whether these collisions also induce the slip of heat flow similar to the velocity slip condition of the rarefied gases on solid walls. In this work based on the discrete Boltzmann transport equation, the slip boundary condition of heat flux on solid walls in the Knudsen layer is established. This result is exemplified by the slip boundary condition of heat flux in nanowires, which has been proposed in a phenomenological way.

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15

Petrushevsky, V., and S. Cohen. "Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation." Journal of Heat Transfer 121, no. 3 (August 1, 1999): 708–11. http://dx.doi.org/10.1115/1.2826037.

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A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

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16

Hristov, Jordan. "Semi-derivative integral method to transient heat conduction time-dependent heat flux boundary conditions." Thermal Science 25, Spec. issue 2 (2021): 303–8. http://dx.doi.org/10.2298/tsci21s2303h.

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Transient heat conduction in semi-infinite medium with a time dependent heat flux as boundary condition has been solved by a semi-derivative integral-balance method. Two versions boundary fluxes have been considered: power-law and exponential.

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17

El Omari, Kamal, and Yves Le Guer. "Laminar mixing and heat transfer for constant heat flux boundary condition." Heat and Mass Transfer 48, no. 8 (January 25, 2012): 1285–96. http://dx.doi.org/10.1007/s00231-012-0976-z.

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18

Arzel, Olivier, Thierry Huck, and Alain Colin de Verdière. "The Different Nature of the Interdecadal Variability of the Thermohaline Circulation under Mixed and Flux Boundary Conditions." Journal of Physical Oceanography 36, no. 9 (September 1, 2006): 1703–18. http://dx.doi.org/10.1175/jpo2938.1.

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Abstract The differences between the interdecadal variability under mixed and constant flux boundary conditions are investigated using a coarse-resolution ocean model in an idealized flat-bottom single-hemisphere basin. Objective features are determined that allow one type of oscillation to be distinguished versus the other. First, by performing a linear stability analysis of the steady state obtained under restoring boundary conditions, it is shown that the interdecadal variability under constant flux and mixed boundary conditions arises, respectively, from the instability of a linear mode around the mean stratification and circulation and from departure from the initial state. Based on the budgets of density variance, it is shown next that the two types of oscillations have different energy sources: Under the constant-flux boundary condition (the thermal mode), the downgradient meridional eddy heat flux in the western boundary current regions sustains interdecadal variability, whereas under mixed boundary conditions (the salinity mode), a positive feedback between convective adjustment and restoring surface heat flux is at the heart of the existence of the decadal oscillation. Furthermore, the positive correlations between temperature and salinity anomalies in the forcing layer are shown to dominate the forcing of density variance. In addition, the vertical structure of perturbations reveals vertical phase lags at different depths in all tracer fields under constant flux, while under mixed boundary conditions only the temperature anomalies show a strong dipolar structure. The authors propose that these differences will allow one to identify which type of oscillation, if any, is at play in the more exhaustive climate models.

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Kim, Min-Seong, Byung-Hyuk Kwon, Tae-Young Goo, and Sueng-Pil Jung. "Dropsonde-Based Heat Fluxes and Mixed Layer Height over the Sea Surface near the Korean Peninsula." Remote Sensing 15, no. 1 (December 21, 2022): 25. http://dx.doi.org/10.3390/rs15010025.

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Dropsonde-based sensible heat flux, latent heat flux, and buoyancy flux were estimated over the sea around the Korean Peninsula in 2021. During a preceding severe weather (SW) mission, a total of 243 dropsondes were released from a National Institute of Meteorological Sciences (NIMS) Atmospheric Research Aircraft (NARA). The heat fluxes were indirectly validated by comparison with model-based heat fluxes. The sensible heat flux calculated by the bulk transfer method depended entirely on the temperature difference between the sea level and atmosphere, whereas the latent heat flux was mainly affected by wind speed. Boundary layer heights above 800 m are closely related to buoyancy flux, which is greater in regions with higher sea surface temperatures. Furthermore, the utility of the dropsonde was confirmed in the marine atmospheric boundary layer (MABL) growth, which is difficult to observe in situ and, a relationship was proposed for estimating MABL based on mean meteorological data over the sea level.

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Briozzo, Adriana C., and Domingo A. Tarzia. "Exact Solutions for Nonclassical Stefan Problems." International Journal of Differential Equations 2010 (2010): 1–19. http://dx.doi.org/10.1155/2010/868059.

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We consider one-phase nonclassical unidimensional Stefan problems for a source functionFwhich depends on the heat flux, or the temperature on the fixed facex=0. In the first case, we assume a temperature boundary condition, and in the second case we assume a heat flux boundary condition or a convective boundary condition at the fixed face. Exact solutions of a similarity type are obtained in all cases.

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Shakunthala, S., and M. M. Nandeppanavar. "Boundary Layer Flow and Cattaneo-Christov Heat Flux of a Nonlinear Stretching Sheet with a Suspended CNT." Nanoscience & Nanotechnology-Asia 9, no. 4 (November 25, 2019): 494–503. http://dx.doi.org/10.2174/2210681208666180821142231.

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Background: In this article the Boundary layer flow and Cattaneo-Christov Heat flux of nonlinear stretching sheet in a suspended carbon nanotube is analyzed. Methods: The governing classical PDE’s are changing into ODE’s using the similarity transformation method. This boundary value problem is solved by using numerical method known as Runge-Kutta fourth order method with effective shooting technique. Presently in this analysis , the flow, velocity and heat transfer characteristics for different heat transferphysical parameters such as nanofluid (ϕ), suction parameter (N>0), heat flux parameter (β) and Prandtl number (Pr) are studied for two cases i.e., single Wall Carbon Nanotube (SWCNT) and Multiwall Carbon Nanotube (MWCNT) respectively. Results: Our results are in good agreement within a limiting condition comparing with previously published results. This study signifies that practical applications in science and engineering fields for example in functional ceramics, nano metals for energy and environmental applications. Conclusion: A theoretical study of boundary layer flow and Catteneo-Christove heat flux is carried out. In this study some of the important findings are collected as follows: 1. The result of nanoparticle volume fraction f and suction parameter N shows that, as increasing f it increases the flow, velocity and temperature while as increasing N which increases the flow and temperature but decreases the velocity at boundary layer. 2. A comparison result is plotted which is an excellent agreement with previously published results. 3. As increasing the Prandtl number and relaxation time of heat flux parameter in the thermal boundary layer which decreases the temperature of thermal boundary layer. 4. Effect of relaxation time of heat flux is same for both local skin friction and local nusselt number i.e. increasing.

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Zhou, Zhifeng, Zhichao Zhang, Zhenxun Gao, Ke Xu, and Chun-Hian Lee. "Numerical Investigation on Mechanisms of MHD Heat Flux Mitigation in Hypersonic Flows." Aerospace 9, no. 10 (September 25, 2022): 548. http://dx.doi.org/10.3390/aerospace9100548.

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Numerical simulations of hypersonic magnetohydrodynamics (MHD) flow over a typical sphere–cone blunt body are carried out based on the assumption of a low magnetic Reynolds number. The effects of an external dipole magnetic field on the surface heat flux are analyzed in detail, and multiple mechanisms of the MHD heat flux mitigation are revealed systematically for the first time. The following is found: (1) The external magnetic field can effectively reduce the stagnation point heat flux, and the increase in the boundary layer thickness due to the effect of counter-flow Lorentz force, which is equivalent to adding an adverse pressure gradient, is the main reason. (2) In the head region of the blunt body, the relative surface heat flux shows a complex trend of rising and falling because there are two mechanisms which could produce the opposite effects on the surface heat flux. One is that the counter-flow Lorentz force results in an increase in the boundary layer thickness, and the other is that the Joule heating increases the static temperature behind the shock wave. (3) In the shoulder region of the blunt body, the Lorentz force component, normal to streamline, could change the flow direction of the fluid elements, causing the streamline to deviate from the wall or even separate, thus affecting the surface heat flux. (4) In the large area downstream of the blunt body, the surface heat flux could still be reduced by more than 30% due to the “upstream historical effect”.

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Kupiec, Krzysztof, and Monika Gwadera. "Heat Balance of Horizontal Ground Heat Exchangers." Ecological Chemistry and Engineering S 25, no. 4 (December 1, 2018): 537–48. http://dx.doi.org/10.1515/eces-2018-0035.

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Abstract This work refers to the modelling of heat transfer in horizontal ground heat exchangers. For different conditions of collecting heat from the ground and different boundary condition profiles of temperature in the ground were found, and temporal variations of heat flux transferred between the ground surface and its interior were determined. It was taken into account that this flux results from several different mechanisms of heat transfer: convective, radiative, and that connected with moisture evaporation. It was calculated that ground temperature at great depths is greater than the average annual ambient temperature.

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Ozawa, H., and S. J. Laurence. "Experimental investigation of the shock-induced flow over a wall-mounted cylinder." Journal of Fluid Mechanics 849 (June 26, 2018): 1009–42. http://dx.doi.org/10.1017/jfm.2018.433.

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The unsteady aerodynamic and aerothermal phenomena resulting from the interaction between a shock-induced supersonic boundary-layer flow and a wall-mounted cylinder are investigated. Experiments were conducted in a shock tube at three different post-shock unit Reynolds numbers and a single Mach number to investigate the effects of differing ratios of inviscid and viscous temporal scales on the flow development. Two cylinder heights were studied: ‘large’ and ‘small’ protuberances based on calculated boundary-layer thicknesses. Heat-flux measurements on the shock-tube wall were performed using an ultra-fast-response temperature sensitive paint and verified by independent thermocouple measurements. High-speed schlieren provided visualizations of the inviscid flow phenomena. The unsteady shock-wave/boundary-layer interaction ahead of the cylinder resulted in high transient heat loading on the wall and caused transition to turbulence of the incoming laminar boundary layer. Once this incoming boundary layer had naturally transitioned, the region of enhanced heat flux collapsed back towards the cylinder; during this process, heat transfer in the immediate wake increased significantly. The overall heat flux upstream of the cylinder was higher for the large protuberance, whereas the downstream heat flux was generally higher for the small protuberance. In the case of the large protuberance, the viscous scaling appeared to best collapse the upstream heat-flux development for the three different unit Reynolds numbers, though the agreement downstream was less satisfactory. Neither the viscous nor the inviscid scaling appeared to adequately collapse the development for the small protuberance.

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Taler, Jan, Dawid Taler, and Andrzej Kowal. "Measurements of absorbed heat flux and water-side heat transfer coefficient in water wall tubes." Archives of Thermodynamics 32, no. 1 (April 1, 2011): 77–88. http://dx.doi.org/10.2478/v10173-011-0004-6.

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Measurements of absorbed heat flux and water-side heat transfer coefficient in water wall tubes The tubular type instrument (flux tube) was developed to identify boundary conditions in water wall tubes of steam boilers. The meter is constructed from a short length of eccentric tube containing four thermocouples on the fire side below the inner and outer surfaces of the tube. The fifth thermocouple is located at the rear of the tube on the casing side of the water-wall tube. The boundary conditions on the outer and inner surfaces of the water flux-tube are determined based on temperature measurements at the interior locations. Four K-type sheathed thermocouples of 1 mm in diameter, are inserted into holes, which are parallel to the tube axis. The non-linear least squares problem is solved numerically using the Levenberg-Marquardt method. The heat transfer conditions in adjacent boiler tubes have no impact on the temperature distribution in the flux tubes.

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Wang, Haitao, and Qiang Fu. "Experimental Evaluation of Thermoelectric Generator Performance under Different Heat Conduction Boundary Conditions." Journal of Physics: Conference Series 2463, no. 1 (March 1, 2023): 012015. http://dx.doi.org/10.1088/1742-6596/2463/1/012015.

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Abstract Heat conduction boundary conditions play a crucial role in the performance of thermoelectric generators (TEG). The TEG output voltage and power were measured under constant temperature boundary and heat flux conditions to evaluate the TEG performance under different heat conduction boundary conditions. External loading pressure and thermal interface material (TIM) were applied to reduce the interfacial thermal contact resistance. In our measurement setup, a fast-response electronic load was used for the rapid current-voltage scan, which can eliminate the thermal drift caused by the Peltier effect. A guard heater arrangement is used to minimize heat loss. In constant temperature boundary conditions, reducing the thermal contact resistance can increase the effective temperature drop across the TEG module and significantly improve the output voltage and power. But in the constant heat flux conditions, since the heat flux flow through the TEG is unchanged, the temperature drop across the TEG was unaffected by the thermal contact resistance. As a result, the TEG performance was lightly influenced by the thermal contact resistance.

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Ryabenko, A. S., K. A. Sklyarov, and O. A. Kutsigina. "Determination of the Temperature in a Homogeneous Half-Plane with an Inclined Rectilinear Crack Approaching the Boundary of the Half-Plane According to the Magnitude of the Heat Flux Through the Boundary of the Half-Plane and the Magnitude of the Temperature and Heat Flux Jumps on the Crack." Russian Journal of Building Construction and Architecture, no. 2(58) (May 15, 2023): 15–24. http://dx.doi.org/10.36622/vstu.2023.2.58.002.

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Statement of the problem. The study is devoted to determining the temperature in a homogeneous half-plane with a finite rectilinear crack approaching the boundary of the half-plane, provided that the magnitude of the heat flux through the boundary of the half-plane as well as the jumps in temperature and heat flux on the crack are known. Results. A mathematical model is set forth that describes the stationary distribution of heat in a homogeneous half-plane with a rectilinear crack approaching the boundary of the half-plane, for the case when the magnitude of the heat flux through the boundary of the half-plane and the jumps in temperature and heat flux on the crack are known. The mathematical correctness of the proposed model is proved; a technique for constructing a solution to the model, as well as a whole class of related problems, is shown; a formula for representing the solution of the model is obtained. Conclusions. The formula obtained in the article can be used to study the temperature distribution in a material with a crack, including in the vicinity of a crack, as well as to determine what effect the presence of a crack has on the heat distribution.

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Kim, Sung Jin, and Duckjong Kim. "Thermal Interaction at the Interface Between a Porous Medium and an Impermeable Wall." Journal of Heat Transfer 123, no. 3 (January 1, 2001): 527–33. http://dx.doi.org/10.1115/1.1370504.

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The present work investigates a heat transfer phenomenon at the interface between a porous medium and an impermeable wall subject to a constant heat flux at the bottom. Currently, two possible thermal boundary conditions (which are called the First Approach and the Second Approach) at the interface are used interchangeably for the thermal analysis of convection in a channel filled with a porous medium. The focus of this paper is to determine which of these thermal boundary conditions is more appropriate in accurately predicting the heat transfer characteristics in a porous channel. To this end, we numerically examine the heat transfer at the interface between a microchannel heat sink (an ideally organized porous medium) and a finite-thickness substrate. From the examination, it is clarified that the heat flux distribution at the interface is not uniform for an impermeable wall with finite thickness. This means that a non-uniform distribution of the heat flux (First Approach) is physically reasonable. When the First Approach is applied to the thermal boundary condition, an additional boundary condition based on the local thermal equilibrium assumption at the interface is used. This additional boundary condition is applicable except in the case of a very thin impermeable wall. Hence, for practical situations, the First Approach with a local thermal equilibrium assumption at the interface is suggested as an appropriate thermal boundary condition. In order to confirm our suggestion, convective flows both in a microchannel heat sink and in a sintered porous channel subject to a constant heat flux condition are analyzed by using the two Approaches separately as a thermal boundary condition at the interface. The analytically obtained thermal resistance of the microchannel heat sink and the numerically obtained overall Nusselt number for the sintered porous channel are shown to be in close agreement with available experimental results when our suggestion for the thermal boundary condition at the interface is applied.

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Terra-Nova, Filipe, and Hagay Amit. "Magnetic boundary layers in numerical dynamos with heterogeneous outer boundary heat flux." Physics of the Earth and Planetary Interiors 309 (December 2020): 106589. http://dx.doi.org/10.1016/j.pepi.2020.106589.

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Tran, L. T., and D. B. Taulbee. "Prediction of Unsteady Rotor-Surface Pressure and Heat Transfer From Wake Passings." Journal of Turbomachinery 114, no. 4 (October 1, 1992): 807–17. http://dx.doi.org/10.1115/1.2928034.

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The research described in this paper is a numerical investigation of the effects of unsteady flow on gas turbine heat transfer, particularly on a rotor blade surface. The unsteady flow in a rotor blade passage and the unsteady heat transfer on the blade surface as a result of wake/blade interaction are modeled by the inviscid flow/boundary layer approach. The Euler equations that govern the inviscid flow are solved using a time-accurate marching scheme. The unsteady flow in the blade passage is induced by periodically moving a wake model across the passage inlet. Unsteady flow solutions in the passage provide pressure gradients and boundary conditions for the boundary-layer equations that govern the viscous flow adjacent to the blade surface. Numerical solutions of the unsteady turbulent boundary layer yield surface heat flux values that can then be compared to experimental data. Comparisons with experimental data show that unsteady heat flux on the blade suction surface is well predicted, but the predictions of unsteady heat flux on the blade pressure surface do not agree.

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Li, JunYang, Ming Yu, Dong Sun, PengXin Liu, and XianXu Yuan. "Wall heat transfer in high-enthalpy hypersonic turbulent boundary layers." Physics of Fluids 34, no. 8 (August 2022): 085102. http://dx.doi.org/10.1063/5.0100416.

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In this paper, we investigate the differences in wall heat transfer between the low- and high-enthalpy turbulent boundary layers by exploiting direct numerical simulation databases of hypersonic turbulent boundary layers at the free-stream Mach number of 4.5 and the friction Reynolds number of 800. For that purpose, we refine the integral formula of decomposing the wall heat flux proposed by Sun et al. [“A decomposition formula for the wall heat flux of a compressible boundary layer,” Adv. Aerodyn. 4, 1–13 (2022)], enabling us to scrutinize the contribution of different physical processes. Statistical results show that the mean wall heat transfer is primarily contributed by the heat conduction, the turbulent heat transfer, viscous dissipation of mean kinetic energy, and turbulent kinetic energy production. Among these processes, the contribution of the turbulent heat flux in the high-enthalpy case is 10% higher than that in the low-enthalpy case. Such discrepancy is caused by the turbulent–chemistry interaction consisting of velocity and species mass fraction fluctuations. Coherent structures in the conditionally averaged fields related to this process reveal that the sweep in the viscous sublayer and ejection in the logarithmic layer bringing the hot fluid downward and upward, respectively, significantly alter the distribution of the species mass fraction. The wall heat flux fluctuations are slightly enhanced in the high-enthalpy flows, which is ascribed to be the intensification of traveling wave packets.

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McGrath-Spangler, E. L., A. S. Denning, K. D. Corbin, and I. T. Baker. "Implementation of a boundary layer heat flux parameterization into the Regional Atmospheric Modeling System (RAMS)." Atmospheric Chemistry and Physics Discussions 8, no. 4 (July 25, 2008): 14311–46. http://dx.doi.org/10.5194/acpd-8-14311-2008.

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Abstract. The response of atmospheric carbon dioxide to a given amount of surface flux is inversely proportional to the depth of the boundary layer. Overshooting thermals that entrain free tropospheric air down into the boundary layer modify the characteristics and depth of the lower layer through the insertion of energy and mass. This alters the surface energy budget by changing the Bowen ratio and thereby altering the vegetative response and the surface boundary conditions. Although overshooting thermals are important in the physical world, their effects are unresolved in most regional models. A parameterization to include the effects of boundary layer entrainment was introduced into a coupled ecosystem-atmosphere model (SiB-RAMS). The parameterization is based on a downward heat flux at the top of the boundary layer that is proportional to the heat flux at the surface. Results with the parameterization show that the boundary layer simulated is deeper, warmer, and drier than when the parameterization is turned off. These results alter the vegetative stress factors thereby changing the carbon flux from the surface. The combination of this and the deeper boundary layer change the concentration of carbon dioxide in the boundary layer.

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WELLS, M. G., R. W. GRIFFITHS, and J. S. TURNER. "Competition between distributed and localized buoyancy fluxes in a confined volume." Journal of Fluid Mechanics 391 (July 25, 1999): 319–36. http://dx.doi.org/10.1017/s0022112099005248.

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We investigate the convection and density stratification that form when buoyancy fluxes are simultaneously applied to a finite volume in both a turbulent buoyant plume from a small source and as a uniform heat flux from a horizontal boundary. The turbulent plume tends to produce a stable density stratification, whereas the distributed flux from a boundary tends to force vigorous overturning and vertical mixing. Experiments show that steady, partially mixed and partially stratified states can exist when the plume buoyancy flux is greater than the distributed flux.When the two fluxes originate from the same boundary, the steady state involves a balance between the rate at which the mixed layer deepens due to encroachment and vertical advection of the stratified water far from the plume due to the plume volume flux acquired by entrainment. There is a monotonic relationship between the normalized mixed layer depth and flux ratio R (boundary flux/plume flux) for 0<R<1, and the whole tank overturns for R>1. The stable density gradient in the stratified region is primarily due to the buoyancy from the plume but is strengthened by a stabilizing temperature gradient resulting from entrainment of heat into the plume from the mixed layer. This result may be relevant to the upper oceans of high latitude where there is commonly a destabilizing heat flux from the sea surface as well as more localized and intense deep convection from the surface.For the case of fluxes from a plume on one boundary and a uniform heat flux from the opposite boundary the shape of the density profile is that given by the Baines & Turner (1969) ‘filling-box’ mechanism, with the gradient reduced by a factor (1 + R) due to the heating. Thus, when R<−1 there is no stratified region and the whole water column overturns. When 0>R>−1, the constant depth of the convecting layer is determined by a balance between buoyancy and turbulent kinetic energy in the outflow layer from the plume.

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Zhao, Peipei, Lipo Wang, and Nilanjan Chakraborty. "Analysis of the flame–wall interaction in premixed turbulent combustion." Journal of Fluid Mechanics 848 (June 1, 2018): 193–218. http://dx.doi.org/10.1017/jfm.2018.356.

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The present work focuses on the flame–wall interaction (FWI) based on direct numerical simulations (DNS) of a head-on premixed flame quenching configuration at the statistically stationary state. The effects of FWI on the turbulent flame temperature, wall heat flux, flame dynamics and flow structures were investigated. In turbulent head-on quenching, particularly for high turbulence intensity, the distorted flames generally consist of the head-on flame part and the entrained flame part. The flame properties are jointly influenced by turbulence, heat generation from chemical reactions and heat loss to the cold wall boundary. For the present FWI configuration, as the wall is approached, the ‘influence zone’ can be identified as the region within which the flame temperature, scalar gradient and flame dilatation start to decrease, whereas the wall heat flux tends to increase. As the distance to the wall drops below the flame-quenching distance, approximately where the wall heat flux reaches its maximum value, chemical reactions become negligibly weak inside the ‘quenching zone’. A simplified counter-flow model is also proposed. With the reasonably proposed relation between the flame speed and the flame temperature, the model solutions match well with the DNS results, both qualitatively and quantitatively. Moreover, near-wall statistics of some important flame properties, including the flame dilatation, reaction progress variable gradient, tangential strain rate and curvature were analysed in detail under different wall boundary conditions.

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A. K. Satapathy, P. K. Kar. "REWETTING OF AN INFINITE SLAB WITH BOUNDARY HEAT FLUX." Numerical Heat Transfer, Part A: Applications 37, no. 1 (January 14, 2000): 87–99. http://dx.doi.org/10.1080/104077800274433.

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Saidi, Arash, and Jungho Kim. "Heat flux sensor with minimal impact on boundary conditions." Experimental Thermal and Fluid Science 28, no. 8 (October 2004): 903–8. http://dx.doi.org/10.1016/j.expthermflusci.2004.01.004.

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Mahrt, L. "Heat Flux in the Strong-Wind Nocturnal Boundary Layer." Boundary-Layer Meteorology 163, no. 2 (November 24, 2016): 161–77. http://dx.doi.org/10.1007/s10546-016-0219-9.

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Abd-el-Malek, Mina B., Fayez H. Michael, and Samy M. A. El-Mansi. "Group method analysis of two-dimensional plate in heat flux." International Journal of Mathematics and Mathematical Sciences 2003, no. 22 (2003): 1369–82. http://dx.doi.org/10.1155/s0161171203206335.

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The group transformation theoretic approach is applied to present an analytic study of the temperature distribution in a triangular plate,Ω, placed in the field of heat flux, along one boundary, in a form of polynomial functions of any degree n. The Laplace's equation has been reduced to second-order linear ordinary differential equation with an appropriate boundary conditions. Exact solution has been obtained for general shape ofΩand different boundary conditions.

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Eichinger, W. E., H. E. Holder, R. Knight, J. Nichols, D. I. Cooper, L. E. Hipps, W. P. Kustas, and J. H. Prueger. "Lidar Measurement of Boundary Layer Evolution to Determine Sensible Heat Fluxes." Journal of Hydrometeorology 6, no. 6 (December 1, 2005): 840–53. http://dx.doi.org/10.1175/jhm461.1.

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Abstract The Soil Moisture–Atmosphere Coupling Experiment (SMACEX) was conducted in the Walnut Creek watershed near Ames, Iowa, over the period from 15 June to 11 July 2002. A main focus of SMACEX is the investigation of the interactions between the atmospheric boundary layer, surface moisture, and canopy. A vertically staring elastic lidar was used to provide a high-time-resolution continuous record of the boundary layer height at the edge between a soybean and cornfield. The height and thickness of the entrainment zone are used to estimate the surface sensible heat flux using the Batchvarova–Gryning boundary layer model. Flux estimates made over 6 days are compared to conventional eddy correlation measurements. The calculated values of the sensible heat flux were found to be well correlated (R2 = 0.79, with a slope of 0.95) when compared to eddy correlation measurements in the area. The standard error of the flux estimates was 21.4 W m−2 (31% rms difference between this method and surface measurements), which is somewhat higher than a predicted uncertainty of 16%. The major sources of error were from the estimates of the vertical potential temperature gradient and an assumption that the entrainment parameter A was equal to the ratio of the entrainment flux and the surface heat flux.

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Hennemuth, Barbara, and Hans-Jürgen Kirtzel. "Towards operational determination of boundary layer height using sodar/RASS soundings and surface heat flux data." Meteorologische Zeitschrift 17, no. 3 (June 23, 2008): 283–96. http://dx.doi.org/10.1127/0941-2948/2008/0289.

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Kim, Min-Seong, and Byung Hyuk Kwon. "Estimation of Sensible Heat Flux and Atmospheric Boundary Layer Height Using an Unmanned Aerial Vehicle." Atmosphere 10, no. 7 (June 30, 2019): 363. http://dx.doi.org/10.3390/atmos10070363.

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In this work, sensible heat flux estimated using a bulk transfer method was validated with a three-dimensional ultrasonic anemometer or surface layer scintillometer at various sites. Results indicate that it remains challenging to obtain temperature and wind speed at an appropriate reference height. To overcome this, alternative observations using an unmanned aerial vehicle (UAV) were considered. UAV-based wind speed and sensible heat flux were indirectly estimated and atmospheric boundary layer (ABL) height was then derived using the sensible heat flux data. UAV-observed air temperature was measured by attaching a temperature sensor 40 cm above the rotary-wing of the UAV, and UAV-based wind speed was estimated using attitude data (pitch, roll, and yaw angles) recorded using the UAV’s inertial measurement unit. UAV-based wind speed was close to the automatic weather system-observed wind speed, within an error range of approximately 10%. UAV-based sensible heat flux estimated from the bulk transfer method corresponded with sensible heat flux determined using the eddy correlation method, within an error of approximately 20%. A linear relationship was observed between the normalized UAV-based sensible heat flux and radiosonde-based normalized ABL height.

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Kumar, Hitesh. "Heat transfer over a stretching porous sheet subjected to power law heat flux in presence of heat source." Thermal Science 15, suppl. 2 (2011): 187–94. http://dx.doi.org/10.2298/tsci100331074k.

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In the present investigation the boundary layer steady flow and heat transfer of a viscous incompressible fluid due to a stretching porous sheet in presence of heat source are studied. The equations of motion and heat transfer are reduced to non-linear ordinary differential equations and the exact solutions are obtained in the form of confluent hypergeometric function (Kummer?s Function) for prescribed heat flux, when the wall is at prescribed second order power law heat flux or the prescribed heat flux at the stretching porous wall varies as the square of the distance from the origin. The effects of the various parameters entering into the problem on the temperature distribution and recovery temperature are discussed.

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Childs, P. R. N., J. R. Greenwood, and C. A. Long. "Heat flux measurement techniques." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 213, no. 7 (July 1, 1999): 655–77. http://dx.doi.org/10.1177/095440629921300702.

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Heat flux measurement is used in the field of fluid mechanics and heat transfer to quantify the transfer of heat within systems. Several techniques are in common use, including: differential temperature sensors such as thermopile, layered resistance temperature devices or thermocouples and Gardon gauges; calorimetric methods involving a heat balance analysis and transient monitoring of a representative temperature, using, for example, thin-film temperature sensors or temperature sensitive liquid crystals; energy supply or removal methods using, for example, a heater to generate a thermal balance; and, finally, by measurement of mass transfer which can be linked to heat transfer using the analogy between the two. No one method is suitable to all applications because of the differing considerations of accuracy, sensitivity, size, cost and robustness. Recent developments including the widespread availability and application of thin-film deposition techniques for metals and ceramics, allied with advances in microtechnology, have expanded the range of devices available for heat flux measurement. This paper reviews the various types of heat flux sensors available, as well as unique designs for specific applications. Critical to the use of a heat flux measurement technique is accurate calibration. Use of unmatched materials disturbs the local heat flux and also the local convective boundary layer, producing a potential error that must be compensated for. The various techniques in common use for calibration are described. A guide to the appropriate selection of a heat flux measurement technique is provided according to the demands of response, sensitivity, temperature of operation, heat flux intensity, manufacturing constraints, commercial availability, cost, thermal disturbance and acceleration capability for vibrating, rotating and reciprocating applications.

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Pais, Enno. "IDENTIFICATION OF MEMORY KERNELS IN HEAT FLOW MEASURING HEAT FLUX AT THE ENDS OF THE BAR." Mathematical Modelling and Analysis 15, no. 4 (November 15, 2010): 473–90. http://dx.doi.org/10.3846/1392-6292.2010.15.473-490.

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An inverse problem to determine time‐ and space‐dependent relaxation kernels of internal energy and heat flux with first kind boundary conditions by means of heat flux measurements is considered. The case when observations of the heat flux are made at the ends of the bar with thermal memory was not studied before. Existence and uniqueness of a solution to the inverse problem are proved. The financial support of Estonian Science Foundation is gratefully acknowledged (Grant nr. 7728).

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Franc¸a, Francis H. R., Ofodike A. Ezekoye, and John R. Howell. "Inverse Boundary Design Combining Radiation and Convection Heat Transfer." Journal of Heat Transfer 123, no. 5 (February 20, 2001): 884–91. http://dx.doi.org/10.1115/1.1388298.

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This work investigates inverse boundary design for radiation, convection and conduction combined-mode heat transfer. The problem consists of finding the heat flux distribution on a heater that satisfies both the temperature and the heat flux prescribed on a design surface of an enclosure formed by two finite parallel plates. A gray participating medium flows in laminar regime between the walls, which are gray, diffuse emitters and absorbers. All the thermal properties are uniform. This problem is described by an ill-conditioned system of non-linear equations. The solution is obtained by regularizing the system of equations by means of truncated singular value decomposition (TSVD).

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Zhao, Yatian, Zhiyuan Shao, and Hongkang Liu. "Aerodisk Effect on Hypersonic Boundary Layer Transition and Heat Transfer of HIFiRE-5 Vehicle." Aerospace 9, no. 12 (November 23, 2022): 742. http://dx.doi.org/10.3390/aerospace9120742.

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The substantial aerodynamic drag and severe aerothermal loads, which are closely related to boundary layer transition, challenge the design of hypersonic vehicles and could be relieved by active methods aimed at drag and heat flux reduction, such as aerodisk. However, the research of aerodisk effects on transitional flows is still not abundant. Based on the improved k-ω-γ transition model, this study investigates the influence of the aerodisk with various lengths on hypersonic boundary layer transition and surface heat flux distribution over HIFiRE-5 configuration under various angles of attack. Certain meaningful analysis and results are obtained: (i) The existence of aerodisk is found to directly trigger separation-induced transition, moving the transition onset near the centerline upstream and widening the transition region; (ii) The maximum wall heat flux could be effectively reduced by aerodisk up to 52.1% and the maximum surface pressure can even be reduced up to 80.4%. The transition shapes are identical, while the variety of growth rates of intermittency are non-monotonous with the increase in aerodisk length. The dilation of region with high heat flux boundary layer is regarded as an inevitable compromise to reducing maximum heat flux and maximum surface pressure. (iii) With the angle of attack rising, first, the transition is postponed and subsequently advanced on the windward surface, which is in contrast to the continuously extending transition region on the leeward surface. This numerical study aims to explore the effects of aerodisk on hypersonic boundary layer transition, enrich the study of hypersonic flow field characteristics and active thermal protection system considering realistic boundary layer transition, and provide references for the excogitation and utilization of hypersonic vehicle aerodisk.

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Emery, A. F., and T. D. Fadale. "The Effect of Imprecisions in Thermal Sensor Location and Boundary Conditions on Optimal Sensor Location and Experimental Accuracy." Journal of Heat Transfer 119, no. 4 (November 1, 1997): 661–65. http://dx.doi.org/10.1115/1.2824169.

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Optimal sensor locations and the information content obtained when estimating thermal parameters using the inverse method are significantly affected by uncertainties in sensor position and in the system parameters. This paper describes the effects of these uncertainties. It is shown that the effect of sensor location uncertainties can be reduced by placing temperature sensors in locations of minimum heat flux. In transient experiments, the uncertainties in the boundary conditions have the greatest effect at points of high heat flux and cause the optimal sensor locations to move from the boundary with the highest convective heat transfer coefficient to the boundary with the lowest in an abrupt manner.

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Mound, Jon E., and Christopher J. Davies. "Heat transfer in rapidly rotating convection with heterogeneous thermal boundary conditions." Journal of Fluid Mechanics 828 (September 5, 2017): 601–29. http://dx.doi.org/10.1017/jfm.2017.539.

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Convection in the metallic cores of terrestrial planets is likely to be subjected to lateral variations in heat flux through the outer boundary imposed by creeping flow in the overlying silicate mantles. Boundary anomalies can significantly influence global diagnostics of core convection when the Rayleigh number, $Ra$, is weakly supercritical; however, little is known about the strongly supercritical regime appropriate for planets. We perform numerical simulations of rapidly rotating convection in a spherical shell geometry and impose two patterns of boundary heat flow heterogeneity: a hemispherical $Y_{1}^{1}$ spherical harmonic pattern; and one derived from seismic tomography of the Earth’s lower mantle. We consider Ekman numbers $10^{-4}\leqslant E\leqslant 10^{-6}$, flux-based Rayleigh numbers up to ${\sim}800$ times critical, and a Prandtl number of unity. The amplitude of the lateral variation in heat flux is characterised by $q_{L}^{\ast }=0$, 2.3, 5.0, the peak-to-peak amplitude of the outer boundary heat flux divided by its mean. We find that the Nusselt number, $Nu$, can be increased by up to ${\sim}25\,\%$ relative to the equivalent homogeneous case due to boundary-induced correlations between the radial velocity and temperature anomalies near the top of the shell. The $Nu$ enhancement tends to become greater as the amplitude and length scale of the boundary heterogeneity are increased and as the system becomes more supercritical. This $Ra$ dependence can steepen the $Nu\propto Ra^{\unicode[STIX]{x1D6FE}}$ scaling in the rotationally dominated regime, with $\unicode[STIX]{x1D6FE}$ for our most extreme case approximately 20 % greater than the equivalent homogeneous scaling. Therefore, it may be important to consider boundary heterogeneity when extrapolating numerical results to planetary conditions.

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Vreugdenhil, Catherine A., Ross W. Griffiths, and Bishakhdatta Gayen. "Geostrophic and chimney regimes in rotating horizontal convection with imposed heat flux." Journal of Fluid Mechanics 823 (June 15, 2017): 57–99. http://dx.doi.org/10.1017/jfm.2017.249.

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Convection in a rotating rectangular basin with differential thermal forcing at one horizontal boundary is examined using laboratory experiments. The experiments have an imposed heat flux boundary condition, are at large values of the flux Rayleigh number ($Ra_{F}\sim O(10^{13}{-}10^{14})$ based on the box length $L$), use water with Prandtl number $Pr\approx 4$ and have a small depth to length aspect ratio. The results show the conditions for transition from non-rotating horizontal convection governed by an inertial–buoyancy balance in the thermal boundary layer, to circulation governed by geostrophic flow in the boundary layer. The geostrophic balance constrains mean flow and reduces the heat transport as Nusselt number $Nu\sim (Ra_{F}Ro)^{1/6}$, where $Ro=B^{1/2}/f^{3/2}L$ is the convective Rossby number, $B$ is the imposed buoyancy flux and $f$ is the Coriolis parameter. Thus flow in the geostrophic boundary layer regime is governed by the relative roles of horizontal convective accelerations and Coriolis accelerations, or buoyancy and rotation, in the boundary layer. Experimental evidence suggests that for more rapid rotation there is another transition to a regime in which the momentum budget is dominated by fluctuating vertical accelerations in a region of vortical plumes, which we refer to as a ‘chimney’ following related discussion of regions of deep convection in the ocean. Coupling of the chimney convection in the region of destabilising boundary flux to the diffusive boundary layer of horizontal convection in the region of stabilising boundary flux gives heat transport independent of rotation in this ‘inertial chimney’ regime, and the new scaling $Nu\sim Ra_{F}^{1/4}$. Scaling analysis predicts the transition conditions observed in the experiments, as well as a further ‘geostrophic chimney’ regime in which the vertical plumes are controlled by local geostrophy. When $Ro<10^{-1}$, the convection is also observed to produce a set of large basin-scale gyres at all depths in the time-averaged flow.

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Stoll, Rob, and Fernando Porté-Agel. "Surface Heterogeneity Effects on Regional-Scale Fluxes in Stable Boundary Layers: Surface Temperature Transitions." Journal of the Atmospheric Sciences 66, no. 2 (February 1, 2009): 412–31. http://dx.doi.org/10.1175/2008jas2668.1.

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Abstract Large-eddy simulation, with recently developed dynamic subgrid-scale models, is used to study the effect of heterogeneous surface temperature distributions on regional-scale turbulent fluxes in the stable boundary layer (SBL). Simulations are performed of a continuously turbulent SBL with surface heterogeneity added in the form of streamwise transitions in surface temperature. Temperature differences between patches of 6 and 3 K are explored with patch length scales ranging from one-half to twice the equivalent homogeneous boundary layer height. The surface temperature heterogeneity has important effects on the mean wind speed and potential temperature profiles as well as on the surface heat flux distribution. Increasing the difference between the patch temperatures results in decreased magnitude of the average surface heat flux, with a corresponding increase in the mean potential temperature in the boundary layer. The simulation results are also used to test existing models for average surface fluxes over heterogeneous terrain. The tested models fail to fully represent the average turbulent heat flux, with models that break the domain into homogeneous subareas grossly underestimating the heat flux magnitude over patches with relatively colder surface temperatures. Motivated by these results, a new parameterization based on local similarity theory is proposed. The new formulation is found to correct the bias over the cold patches, resulting in improved average surface heat flux calculations.

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Journal articles on the topic 'Boundary heat flux'

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