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Journal articles on the topic 'Heat transfer problems'

Author: Grafiati
Published: 6 September 2023

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1

Orlande, Helcio R. B. "Inverse Heat Transfer Problems." Heat Transfer Engineering 32, no. 9 (August 2011): 715–17. http://dx.doi.org/10.1080/01457632.2011.525128.

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2

Emery, A. F. "Solving stochastic heat transfer problems." Engineering Analysis with Boundary Elements 28, no. 3 (March 2004): 279–91. http://dx.doi.org/10.1016/s0955-7997(03)00058-4.

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3

Brunetkin, А. I. "Integrated approach to solving the fluid dynamics and heat transfer problems." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 2 (December 15, 2014): 108–15. http://dx.doi.org/10.15276/opu.2.44.2014.21.

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4

ITAGAKI, Haruaki. "Heat Transfer Problems in Space Systems." SHINKU 38, no. 6 (1995): 574–80. http://dx.doi.org/10.3131/jvsj.38.574.

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5

Orlande, Helcio R. B., Marcelo J. Colaco, George S. Dulikravich, Flavio Vianna, Wellington da Silva, Henrique Fonseca, and Olivier Fudym. "STATE ESTIMATION PROBLEMS IN HEAT TRANSFER." International Journal for Uncertainty Quantification 2, no. 3 (2012): 239–58. http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2012003582.

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6

Fu, Bai-Shan, Liao Yi, and Jun Zhou. "Dilution refrigerator and its heat transfer problems." Acta Physica Sinica 70, no. 23 (2021): 230202. http://dx.doi.org/10.7498/aps.70.20211760.

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In the research of cryogenic physics and quantum information science, it is essential to maintain a steady low temperature of millikelvin regime continuously. Dilution refrigerator is a widely used refrigeration device to achieve extremely low temperature. It utilizes the phase separation effect of superfluid <sup>4</sup>He and its isotope <sup>3</sup>He mixed solution at ultra-low temperatures. The performance of heat exchanger is the key factor to determine the performance of continuous cycle refrigerating machine. At extremely low temperatures, there appears a huge interfacial thermal resistance between helium and metal (Kapitza resistance), and the problem of heat exchange can be effectively solved by using the porous sintered metal particles to increase the contact area. Therefore, it is of significance to study the heat exchange between metal particles and liquid helium at extremely low temperature and to develop the relevant high-performance sintered Ag powder heat exchanger.
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7

Kozdoba, L. A. "Problems and Methods of Heat-Transfer Theory." Heat Transfer Research 30, no. 4-6 (1999): 385–99. http://dx.doi.org/10.1615/heattransres.v30.i4-6.200.

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8

Colaço, Marcelo J., Helcio R. B. Orlande, and George S. Dulikravich. "Inverse and optimization problems in heat transfer." Journal of the Brazilian Society of Mechanical Sciences and Engineering 28, no. 1 (March 2006): 1–24. http://dx.doi.org/10.1590/s1678-58782006000100001.

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9

Bai-Shan, Fu, LiaoYi, and Zhou Jun. "Dilution refrigerator and its heat transfer problems." Acta Physica Sinica 70, no. 23 (2021): 230202. http://dx.doi.org/10.7498/aps.71.20211760.

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10

Jordan, A., S. Khaldi, M. Benmouna, and A. Borucki. "Study of non-linear heat transfer problems." Revue de Physique Appliquée 22, no. 1 (1987): 101–5. http://dx.doi.org/10.1051/rphysap:01987002201010100.

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11

Ltaief, Hatem, Edgar Gabriel, and Marc Garbey. "Fault tolerant algorithms for heat transfer problems." Journal of Parallel and Distributed Computing 68, no. 5 (May 2008): 663–77. http://dx.doi.org/10.1016/j.jpdc.2007.09.004.

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12

De Mey, G., B. Bogusławski, and A. Kos. "Unstable Inverse Heat Transfer Problems in Microelectronics." Acta Physica Polonica A 123, no. 4 (April 2013): 637–41. http://dx.doi.org/10.12693/aphyspola.123.637.

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13

Dorfman, Abram, and Zachary Renner. "Conjugate Problems in Convective Heat Transfer: Review." Mathematical Problems in Engineering 2009 (2009): 1–27. http://dx.doi.org/10.1155/2009/927350.

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A review of conjugate convective heat transfer problems solved during the early and current time of development of this modern approach is presented. The discussion is based on analytical solutions of selected typical relatively simple conjugate problems including steady-state and transient processes, thermal material treatment, and heat and mass transfer in drying. This brief survey is accompanied by the list of almost two hundred publications considering application of different more and less complex analytical and numerical conjugate models for simulating technology processes and industrial devices from aerospace systems to food production. The references are combined in the groups of works studying similar problems so that each of the groups corresponds to one of selected analytical solutions considered in detail. Such structure of review gives the reader the understanding of early and current situation in conjugate convective heat transfer modeling and makes possible to use the information presented as an introduction to this area on the one hand, and to find more complicated publications of interest on the other hand.
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14

Singh, I. V., and P. K. Jain. "Parallel EFG algorithm for heat transfer problems." Advances in Engineering Software 36, no. 8 (August 2005): 554–60. http://dx.doi.org/10.1016/j.advengsoft.2005.01.009.

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15

Şahin, Ahmet Z., Davut Kavranoğlu, and Maamar Bettayeb. "Model reduction in numerical heat transfer problems." Applied Mathematics and Computation 69, no. 2-3 (May 1995): 209–25. http://dx.doi.org/10.1016/0096-3003(94)00128-q.

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16

Ikegawa, Masahiro, Masayuki Kaiho, and Atsushi Hayasaka. "Advanced numerical simulation of heat transfer problems." International Journal for Numerical Methods in Fluids 47, no. 6-7 (2005): 561–74. http://dx.doi.org/10.1002/fld.831.

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17

Zhao, Duan, Xiao-Jun Yang, and H. M. Srivastava. "On the fractal heat transfer problems with local fractional calculus." Thermal Science 19, no. 5 (2015): 1867–71. http://dx.doi.org/10.2298/tsci150821132z.

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This article investigates several fractal heat transfer problems from the local fractional calculus viewpoint. At low and high excess temperatures, the linear and nonlinear heat-transfer equations are presented. The non-homogeneous linear and nonlinear oscillator equations in fractal heat transfer are discussed. The results are adopted to present the behaviors of the heat transfer in fractal media.
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18

Flik, M. I. "Heat Transfer in Superconducting Films." Applied Mechanics Reviews 44, no. 3 (March 1, 1991): 93–108. http://dx.doi.org/10.1115/1.3119498.

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Thin films that are superconducting above liquid-nitrogen temperature possess promising applications in electronics and sensor technology. The design, the characterization and the processing of devices based on the high-temperature superconductors pose new fundamental heat transfer problems. This article reviews thermal conduction, thermal radiation and thermal stability phenomena in superconducting films. The understanding of these thermal phenomena requires solid-state physics and materials science, in addition to heat transfer and thermodynamics. Future research opportunities are pointed out for thermal problems in superconducting films.
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19

Wen, Yan, Na Li, and Bin Liu. "Modeling and Solving Problems of Heat Transfer of Cement Clinker." Advanced Materials Research 361-363 (October 2011): 1557–62. http://dx.doi.org/10.4028/www.scientific.net/amr.361-363.1557.

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Based on the analysis of heat transfer characteristics of the cement clinker, the porous media’s seepage heat transfer theory is introduced into researching of clinker heat transfer according to its porous media characteristics, and then the control model of cement clinker is built up. Furthermore, this project solves the model by using the finite difference method. At last, the inherent heat transfer law of cement clinker is obtained through simulation.
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20

Corzo, Santiago Francisco, Damian Enrique Ramajo, and Norberto Marcelo Nigro. "High-Rayleigh heat transfer flow." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 9 (September 4, 2017): 1928–54. http://dx.doi.org/10.1108/hff-05-2016-0176.

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Purpose The purpose of this paper is to assess the Boussinesq approach for a wide range of Ra (10 × 6 to 10 × 11) in two-dimensional (square cavity) and three-dimensional (cubic cavity) problems for air- and liquid-filled domains. Design/methodology/approach The thermal behavior in “differentially heated cavities” filled with air (low and medium Rayleigh) and water (high Rayleigh) is solved using computational fluid dynamics (CFDs) (OpenFOAM) with a non-compressible (Boussinesq) and compressible approach (real water properties from the IAPWS database). Findings The results from the wide range of Rayleigh numbers allowed for the establishment of the limitation of the Boussinesq approach in problems where the fluid has significant density changes within the operation temperature range and especially when the dependence of density with temperature is not linear. For these cases, the symmetry behavior predicted by Boussinesq is far from the compressible results, thus inducing a transient heat imbalance and leading to a higher mean temperature. Research limitations/implications The main limitation of the present research can be found in the shortage of experimental data for very high Rayleigh problems. Practical implications Practical implications of the current research could be use of the Boussinesq approach by carefully observing its limitations, especially for sensible problems such as the study of pressure vessels, nuclear reactors, etc. Originality/value The originality of this paper lies in addressing the limitations of the Boussinesq approach for high Rayleigh water systems. This fluid is commonly used in numerous industrial equipment. This work presents valuable conclusions about the limitations of the currently used models to carry out industrial simulations.
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21

Abdelhamid, Talaat, Ammar H. Elsheikh, Olatunji Mumini Omisore, N. A. Saeed, T. Muthuramalingam, Ronglinag Chen, and Md Mahbub Alam. "Reconstruction of the heat transfer coefficients and heat fluxes in heat conduction problems." Mathematics and Computers in Simulation 187 (September 2021): 134–54. http://dx.doi.org/10.1016/j.matcom.2021.02.011.

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22

Hajrulla, Shkelqim, Arban Uka, and Taylan Demir. "Simulations and Results for the Heat Transfer Problem." European Journal of Engineering Science and Technology 6, no. 1 (June 12, 2023): 1–9. http://dx.doi.org/10.33422/ejest.v6i1.986.

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In many studies of the heat transfer problems, many scientifics have studied the heat transfer problems by solving partial differential equations without any use of approximations or finding the solutions with experimental data. In this paper, we analyze the heat transfer problem using a heat source in a closed environment and how it transfers in the neighboring sections. We refer to mathematical concept to make possible the simplification of the complexity that associates such thermodynamic problems. We will discuss such a problem as a discrete one, easily computable, rather than treating it as a continuous one. We have reduced this problem into solving a simple system of linear equations and differential equations. In many cases differential equations are hard and difficult to solve. So, we use numerical methods to approximate the differential equations to algebraic equations and solve them. We will compare different algorithms used and show which one of them performs better under our test conditions. The program will simulate the heat transfer of a single heat source in a closed environment. The results of the simulations will be presented in graphs and demonstrated in visual settings. In the end, we will provide our conclusions on the performance of the numerical methods. We achieve the purpose of this study, which is to analyze the heat generation analysis and heat transport in three-dimensional space as to the neighboring sides of a closed environment.
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23

Dyban, E. P., and Eleonora Ya Epik. "Heat Transfer Problems of Bypass Laminar-Turbulent Transition." Heat Transfer Research 29, no. 1-3 (1998): 54–65. http://dx.doi.org/10.1615/heattransres.v29.i1-3.80.

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24

Shekriladze, I. G. "Feedback Problems in Forced-Convective Condensation Heat Transfer." Heat Transfer Research 30, no. 7-8 (1999): 422–30. http://dx.doi.org/10.1615/heattransres.v30.i7-8.10.

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25

Leontiev, A. I. "Heat and Mass Transfer Problems for Film Cooling." Journal of Heat Transfer 121, no. 3 (August 1, 1999): 509–27. http://dx.doi.org/10.1115/1.2826012.

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In the paper, a review of calculation methods and of experimental results for heat transfer under film cooling is presented. The effects of arrangement of film cooling, longitudinal pressure gradient, nonisothermality and compressibility of the gas, injection of a foreign gas, surface roughness, swirling of flow, and turbulent pulsations of the main gas flow on the effectiveness of film cooling are considered. A generalized correlation for the effectiveness of film cooling, is proposed, which makes it possible to take into account the influence of the above factors. It is shown, that in determination of the heat transfer coefficient in the region of film cooling, it is necessary to take into account the influence of injected gas on the development of the thermal boundary layer. A method of calculation for combined cooling (film, porous or transpiration and convective), which accounts for effect of longitudinal heat conductivity of the wall on the film cooling effectiveness is proposed. An estimation of profile losses on a gas turbine blade is given for the cases of film and porous or transpiration cooling.
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26

Khan, Rahmat. "Approximation of solutions of nonlinear heat transfer problems." Electronic Journal of Qualitative Theory of Differential Equations, no. 52 (2009): 1–13. http://dx.doi.org/10.14232/ejqtde.2009.1.52.

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27

Xue, Yanni, and Haitian Yang. "Interval Estimation of Convection-Diffusion Heat Transfer Problems." Numerical Heat Transfer, Part B: Fundamentals 64, no. 3 (May 4, 2013): 263–73. http://dx.doi.org/10.1080/10407790.2013.797316.

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28

Divo, Eduardo, and Alain J. Kassab. "A meshless method for conjugate heat transfer problems." Engineering Analysis with Boundary Elements 29, no. 2 (February 2005): 136–49. http://dx.doi.org/10.1016/j.enganabound.2004.10.001.

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29

Magalhães, Elisan, Bruno Anselmo, Ana Lima e Silva, and Sandro Lima e Silva. "Time Traveling Regularization for Inverse Heat Transfer Problems." Energies 11, no. 3 (February 27, 2018): 507. http://dx.doi.org/10.3390/en11030507.

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30

Errera, M. P., and G. Turpin. "Temporal multiscale strategies for conjugate heat transfer problems." Journal of Coupled Systems and Multiscale Dynamics 1, no. 1 (April 1, 2013): 89–98. http://dx.doi.org/10.1166/jcsmd.2013.1005.

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31

Zhang, Yi, Bin Huang, and Dong Xu Li. "Finite Element Analysis of the Heat Transfer Problems of PCMs." Materials Science Forum 743-744 (January 2013): 216–21. http://dx.doi.org/10.4028/www.scientific.net/msf.743-744.216.

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Finite element method (FEM) was used for analyzing the heat transfer problems of the PCMs and phase change gypsum board. The simulation results showed that the heat transfer rate of composite PCMs (phase change materials) is higher than the PCMs, the mixture of diatomite improved the heat transfer performance of PCMs. Compared with blank gypsum board,the cold side temperature of phase change gypsum board was decreased, and the temperature rise rate of the cold side was also delayed. The cold side temperature difference between gypsum board and phase change gypsum board was decreasing as the ongoing of heat transfer process.
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32

Hajrulla, Shkelqim, Arban Uka, Loubna Ali, and Taylan Demir. "Numerical Methods and Approximations for The Heat Transfer Problem." Proceedings of The International Conference on Academic Research in Science, Technology and Engineering 1, no. 1 (May 9, 2023): 21–31. http://dx.doi.org/10.33422/icarste.v1i1.14.

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In many studies of heat transfer problems, many researchers have studied heat transfer problems by solving partial differential equations without using approximations or finding solutions with experimental data. This paper analyzes the heat transfer problem using a heat source in a closed environment and how it transfers in the neighboring sections. Referring to mathematical concepts, this work makes possible the simplification of the complexity that associates with such thermodynamic problems. In this framework, the research group discusses such a problem as a discrete one, easily computable, rather than treating it as a continuous one. The reduction of this problem to the solution of a simple system of linear equations and differential equations gives us the possibility to obtain the desired results regarding heat distribution. In many cases, differential equations are hard and difficult to solve. So, we deal with numerical methods to approximate the differential equations to algebraic equations and solve them. Comparing the different algorithms used and showing which of them works best in our testing conditions gives us the possibility of testing and comparing the results and the proper performance. The program will simulate the heat transfer of a single heat source in a closed environment. The results of the simulations will be presented in graphs and demonstrated in visual settings. In the end, our research will provide conclusions on the performance of the numerical methods. The purpose of this article is to study and analyze heat generation and heat transport in three-dimensional space with respect to neighboring sides of a closed environment.
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33

Dreitser, G. A., N. V. Paramonov, A. S. Neverov, A. S. Myakochin, I. V. Podporin, L. S. Yanovskii, A. V. Sergeev, et al. "Integrated study of scientific and applied problems on heat transfer enhancement in tubular heat transfer apparatuses." Journal of Engineering Physics and Thermophysics 65, no. 1 (July 1993): 638–43. http://dx.doi.org/10.1007/bf00862421.

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34

Chen, Han-Taw, and Xin-Yi Wu. "Estimation of Heat Transfer Coefficient in Two-Dimensional Inverse Heat Conduction Problems." Numerical Heat Transfer, Part B: Fundamentals 50, no. 4 (August 2006): 375–94. http://dx.doi.org/10.1080/10407790600859791.

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35

Kudinov, V. A., A. V. Eremin, and E. V. Stefanyuk. "Analytical Solutions of Heat-Conduction Problems with Time-Varying Heat-Transfer Coefficients." Journal of Engineering Physics and Thermophysics 88, no. 3 (May 2015): 688–98. http://dx.doi.org/10.1007/s10891-015-1238-y.

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36

Yu, Yang, Xiao Chuan Luo, and Yuan Wang. "Application of Inverse Heat Conduction Problems in the Slab Solidification Process." Applied Mechanics and Materials 395-396 (September 2013): 1135–41. http://dx.doi.org/10.4028/www.scientific.net/amm.395-396.1135.

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The surface heat transfer coefficient is obtained by the calculation of water-flowing in the second cooling zone of continuous casting; the parameters of this formula are determined by the engineering experiment methods. This paper adopts a new method-numerical calculation method to obtain these parameters. Firstly, the paper uses the method of solving inverse heat conduction problems to calculate the surface heat flux and the surface heat transfer coefficient. Secondly, by using the least square method, the parameters in the formula between the surface heat transfer coefficient and water-flowing are identified. Finally, a plant steel data is used to do some simulation experiments. The results of this simulation prove this numerical method feasibility and effectiveness.
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37

Michiyoshi, I. "Boiling Heat Transfer in Liquid Metals." Applied Mechanics Reviews 41, no. 3 (March 1, 1988): 129–49. http://dx.doi.org/10.1115/1.3151887.

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This article presents the state-of-the-art review of boiling heat transfer in various liquid metals paying attention to research papers published in the last 15 years. Particular emphasis is laid on the incipient boiling superheat, diagnosis of natural and forced convection boiling, nucleate pool boiling heat transfer in mercury, sodium, potassium, NaK, lithium, and so on at sub- and near atmospheric pressure, effect of liquid level on liquid metal boiling, subcooling effect due to hydrostatic head on liquid metal boiling, effect of magnetic field on liquid metal boiling, pool boiling crisis under various conditions and intermittent boiling of liquid metal, two-phase flow heat transfer, and natural and forced convection film boiling in saturated and subcooled liquid metals. In conclusion, there still remain some ambiguous and unsolved problems which are pointed out in this article. Further studies are of course required to clarify and solve them in future with both theoretical and experimental approaches.
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38

Vikulov, A. G. "Mathematical simulation of heat transfer in spacecraft." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 2 (June 30, 2017): 61–78. http://dx.doi.org/10.38013/2542-0542-2017-2-61-78.

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We implemented a systemic scientific approach to thermal vacuum development of spacecraft, which integrates the problems of thermal calculations, thermal vacuum tests and accuracy evaluation for mathematical models of heat transfer by means of solving identification problems. As a result, the following factors increase the efficiency of spacecraft ground testing: reducing the duration of thermal vacuum tests, making autonomous thermal vacuum testing of components possible, increasing the accuracy of thermal calculations
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39

Mishuris, Gennady, and Michał Wróbel. "Coupled FEM-BEM Approach for Axisymetrical Heat Transfer Problems." Defect and Diffusion Forum 273-276 (February 2008): 740–45. http://dx.doi.org/10.4028/www.scientific.net/ddf.273-276.740.

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This work deals with a stationary axisymmetrical heat transfer problem in a combined domain. This domain consists of half-space joined with a bounded cylinder. An important feature of the problem is the possible flux singularity along the edge points of the transmission surface. Domain decomposition is used to separate the subdomains. The solution for an auxiliary mixed boundary value problem in the half space is found analytically by means of Hankel integral transform. This allows us to reduce the main problem in the infinite domain to another problem defined in the bounded subdomain. In turn, the new problem contains a nonlocal boundary conditions along the transmission surface. These conditions incorporate all basic information about the infinite sub-domain (material properties, internal sources etc.). The problem is solved then by means of the Finite Element Method. In fact it might be considered as a coupled FEM-BEM approach. We use standard MATLAB PDE toolbox for the FEM analysis. As it is not possible for this package to introduce directly a non-classical boundary condition, we construct an appropriate iterative procedure and show the fast convergence of the main problem solution. The possible solution singularity is taken into account and the corresponding intensity coefficient of the heat flux is computed with a high accuracy. Numerical examples dealing with heat transfer between closed reservoir (filled with some substance) and the infinite foundation are discussed.
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40

Scott, S. N., J. A. Templeton, P. D. Hough, J. R. Ruthruff, M. V. Rosario, and J. P. Peterson. "Statistical validation for heat transfer problems: a case study." International Journal of Computational Methods and Experimental Measurements 3, no. 2 (June 30, 2015): 101–20. http://dx.doi.org/10.2495/cmem-v3-n2-101-120.

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41

Majchrzak, Ewa, Jolanta Dziatkiewicz, and Łukasz Turchan. "Sensitivity Analysis and Inverse Problems in Microscale Heat Transfer." Defect and Diffusion Forum 362 (April 2015): 209–23. http://dx.doi.org/10.4028/www.scientific.net/ddf.362.209.

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In the paper the selected problems related to the modeling of microscale heat transfer are presented. In particular, thermal processes occurring in thin metal films exposed to short-pulse laser are described by two-temperature hyperbolic model supplemented by appropriate boundary and initial conditions. Sensitivity analysis of electrons and phonons temperatures with respect to the microscopic parameters is discussed and also the inverse problems connected with the identification of relaxation times and coupling factor are presented. In the final part of the paper the examples of computations are shown.
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42

Abdullayev, Akmaljon, Kholsaid Kholturayev, and Nigora Safarbayeva. "Exact method to solve of linear heat transfer problems." E3S Web of Conferences 264 (2021): 02059. http://dx.doi.org/10.1051/e3sconf/202126402059.

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When approximating multidimensional partial differential equations, the values of the grid functions from neighboring layers are taken from the previous time layer or approximation. As a result, along with the approximation discrepancy, an additional discrepancy of the numerical solution is formed. To reduce this discrepancy when solving a stationary elliptic equation, parabolization is carried out, and the resulting equation is solved by the method of successive approximations. This discrepancy is eliminated in the approximate analytical method proposed below for solving two-dimensional equations of parabolic and elliptic types, and an exact solution of the system of finite difference equations for a fixed time is obtained. To solve problems with a boundary condition of the first kind on the first coordinate and arbitrary combinations of the first, second and third kinds of boundary conditions on the second coordinate, it is proposed to use the method of straight lines on the first coordinate and ordinary sweep method on the second coordinate. Approximating the equations on the first coordinate, a matrix equation is built relative to the grid functions. Using eigenvalues and vectors of the three-diagonal transition matrix, linear combinations of grid functions are compiled, where the coefficients are the elements of the eigenvectors of the three-diagonal transition matrix. Boundary conditions, and for a parabolic equation, initial conditions are formed for a given combination of grid functions. The resulting one-dimensional differential-difference equations are solved by the ordinary sweep method. From the resulting solution, proceed to the initial grid functions. The method provides a second order of approximation accuracy on coordinates. And the approximation accuracy in time when solving the parabolic equation can be increased to the second order using the central difference in time. The method is used to solve heat transfer problems when the boundary conditions are expressed by smooth and discontinuous functions of a stationary and non-stationary nature, and the right-hand side of the equation represents a moving source or outflow of heat.
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43

Pyatkov, Sergey Grigorievich. "INVERSE PROBLEMS IN THE HEAT AND MASS TRANSFER THEORY." Yugra State University Bulletin 13, no. 4 (December 15, 2017): 61–78. http://dx.doi.org/10.17816/byusu20170461-78.

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This article is a survey of the recent results obtained preferably by the author and its coauthors and devoted to the study of inverse problem for some mathematical models, in particular those describing heat and mass transfer and convection-diffusion processes. They are defined by second and higher order parabolic equations and systems. We examine the following two types of overdetermination conditions: a solution is specified on some collection of spatial manifolds (or at separate points) or some collection of integrals of a solution with weight is prescribed. We study an inverse problem of recovering a right-hand side (the source function) or the coefficients of equations characterizing the medium. The unknowns (coefficients and the right-hand side) depend on time and a part of the space variables. We expose existence and uniqueness theorems, stability estimates for solutions. The main results in the linear case, i.e., we recover the source function, are global in time while they are local in time in the general case. The main function spaces used are the Sobolev spaces.
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44

Mahanta, P., and Subhash C. Mishra. "Modified Collapsed Dimension Method for Radiative Heat Transfer Problems." Journal of Thermophysics and Heat Transfer 15, no. 2 (April 2001): 246–48. http://dx.doi.org/10.2514/2.6601.

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45

XUE, B. Y., S. C. WU, W. H. ZHANG, and G. R. LIU. "A SMOOTHED FEM (S-FEM) FOR HEAT TRANSFER PROBLEMS." International Journal of Computational Methods 10, no. 01 (February 2013): 1340001. http://dx.doi.org/10.1142/s021987621340001x.

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By smoothing, via various ways, the compatible strain fields of the standard finite element method (FEM) using the gradient smoothing technique, a family of smoothed FEMs (S-FEMs) has been developed recently. The S-FEM possesses the advantages of both mesh-free methods and the standard FEM and works well with triangular and tetrahedral background cells and elements. Intensive theoretical investigations have shown that the S-FEM models can achieve numerical solutions for many important properties, such as the upper bound solution in strain energy, free from volumetric locking, insensitive to the distortion of the background cells, super-accuracy and super-convergence in displacement or stress solutions or both. Engineering problems, including complex heat transfer problems, have also been analyzed with better accuracy and efficiency. This paper presents the general formulation of the S-FEM for thermal problems in one, two and three dimensions. To examine our formulation, some computational results are compared with those obtained using other established means.
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46

Kaipio, Jari P., and Colin Fox. "The Bayesian Framework for Inverse Problems in Heat Transfer." Heat Transfer Engineering 32, no. 9 (August 2011): 718–53. http://dx.doi.org/10.1080/01457632.2011.525137.

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Rukolaine, S. A. "Regularization of inverse boundary design radiative heat transfer problems." Journal of Quantitative Spectroscopy and Radiative Transfer 104, no. 1 (March 2007): 171–95. http://dx.doi.org/10.1016/j.jqsrt.2006.09.001.

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Moore, Travis J., and Matthew R. Jones. "Solving nonlinear heat transfer problems using variation of parameters." International Journal of Thermal Sciences 93 (July 2015): 29–35. http://dx.doi.org/10.1016/j.ijthermalsci.2015.02.002.

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Hawthorn, D. "Heat transfer: Solving scaling problems at the design stage." Chemical Engineering Research and Design 87, no. 2 (February 2009): 193–99. http://dx.doi.org/10.1016/j.cherd.2008.08.011.

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Kassab, Alain J., and Scott Chesla. "An iterative CVBEM solution of nonlinear heat transfer problems." Engineering Analysis with Boundary Elements 11, no. 1 (January 1993): 67–75. http://dx.doi.org/10.1016/0955-7997(93)90080-5.

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