THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

Authors of this Paper

External Links

online first only

Heat conduction in rectangular solids with internal heat generation

ABSTRACT
A representative steady-state heat conduction problem in rectangular solids with uniformly distributed heat generation has been investigated analytically. An analytical solution is provided by solving a nonhomogeneous partial differential equation. A simple and accurate model is proposed to predict the dimensionless shape factor parameter for the first time. The dimensionless shape factor is obtained in the light of the solution of Poisson equation with constant wall temperature boundary conditions. The area-mean temperature is found by integration on the rectangular cross-section. The model is very concise and nice for quick real world approximations, and it provides acceptable accuracy for engineering practice.
KEYWORDS
PAPER SUBMITTED: 2020-04-15
PAPER REVISED: 2020-07-24
PAPER ACCEPTED: 2020-08-24
PUBLISHED ONLINE: 2020-09-06
DOI REFERENCE: https://doi.org/10.2298/TSCI200415235D
REFERENCES
  1. Rogié, B., et al., Practical analytical modeling of 3D multi-layer Printed Wired Board with buried volumetric heating sources, International Journal of Thermal Sciences, 129 (2018), pp. 404-415
  2. Xu, G. Y., Wang, J. B., Analytical solution of time fractional Cattaneo heat equation for finite slab under pulse heat flux, Applied Mathematics and Mechanics, 39 (2018), 10, pp. 1465-1476
  3. Forslund, R., et al., Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters, Applied Mathematical Modelling, 66 (2019), pp. 227-240
  4. França, M. V., Orlande, H. R. B., Estimation of parameters of the dual-phase-lag model for heat conduction in metal-oxide-semiconductor field-effect transistors, International Communications in Heat and Mass Transfer, 92 (2018), pp. 107-111
  5. Shen, Y., et al., Effect of non-condensable gas on heat conduction in steam sterilization process, Thermal Science, 23 (2019), 4, pp. 2489-2494
  6. Haji-Sheikh, A., Beck, J. V., Temperature solution in multi-dimensional multi-layer bodies, International Journal of Heat and Mass Transfer, 45 (2002), 9, pp. 1865-1877
  7. Aviles-Ramos, C., et al., Exact solution of heat conduction in composite materials and application to inverse problems, Journal of Heat Transfer, 120 (1998), 3, pp. 592-599
  8. Beck, J. V., et al., Verification solution for partial heating of rectangular solids, International Journal of Heat and Mass Transfer, 47 (2004), 19-20, pp. 4243-4255
  9. Beck, J. V., Cole, K. D., Improving convergence of summations in heat conduction, International Journal of Heat and Mass Transfer, 50 (2007), 1-2, pp. 257-268
  10. Beck, J. V., et al., Conduction in rectangular plates with boundary temperatures specified, International Journal of Heat and Mass Transfer, 51 (2008), 19-20, pp. 4676-4690
  11. Wang, X. Y., Local fractional functional decomposition method for solving local fractional Poisson equation in steady heat-conduction problem, Thermal Science, 20 (2016), Suppl. 3, pp. S785-S788
  12. Laraqi, N., et al., Simple and accurate correlations for some problems of heat conduction with nonhomogeneous boundary conditions, Thermal Science, 21 (2017), 1A, pp. 125-132
  13. Gao, F., Yang, X. J., Local fractional Euler's method for the steady heat-conduction problem, Thermal Science, 20 (2016), Suppl. 3, pp. S735-S738
  14. Ei Maakoul, A., et al., A general approach to solve heat conduction problems with internal heat sources using resistance and quadrupole concepts, International Journal of Heat and Mass Transfer, 129 (2019), pp. 793-800
  15. Deng, S. X., Ge, X. X., Local fractional Helmholtz simulation for heat conduction in fractal media, Thermal Science, 23 (2019), 3A, pp. 1671-1675
  16. Yilmazer, A., Kocar, C., Heat conduction in convectively cooled eccentric spherical annuli: A boundary integral moment method, Thermal Science, 21 (2017), 5, pp. 2255-2266
  17. Uddin, M. J., et al., Two parameter scaling group for unsteady convective magnetohydrodynamic flow, Alexandria Engineering Journal, 55 (2016), 2, pp. 829-835
  18. Kountouriotis, Z., et al., Development lengths in Newtonian Poiseuille flows with wall slip, Applied Mathematics and Computation, 291 (2016), pp. 98-114
  19. Siddiqui, O. K., et al., Assessment of thermo-fluid analogies for different flow configurations: the effect of Prandtl number, and laminar-to-turbulent flow regimes, International Journal of Thermal Sciences, 129 (2018), pp. 145-170
  20. Wiwatanapataphee, B., et al., Oscillating pressure-driven slip flow and heat transfer through an elliptical microchannel, Advances in Difference Equations, 2019 (2019), ID 342
  21. Wei, C., Wang, H., Solutions of the heat-conduction model described by fractional Emden-Fowler type equation, Thermal Science, 21 (2017), Suppl. 1, pp. S113—S120
  22. Perkowski, D. M., et al., Axisymmetric stationary heat conduction problem for half-space with temperature-dependent properties, Thermal Science, 24 (2020), 3B, pp. 2137-2150
  23. Tian, Y. Symmetry reduction a promising method for heat conduction equations, Thermal Science, 23 (2019), 4, pp. 2219-2227
  24. Harfash, A. J., Resonant penetrative convection in porous media with an internal heat source/sink effect, Applied Mathematics and Computation, 281 (2016), pp. 323-342
  25. Bennett, C. A., Hohmann, R. P., Methods for calculating shear stress at the wall for single-phase flow in tubular, annular, plate, and shell-side heat exchanger geometries, Heat Transfer Engineering, 38 (2017), 9, pp. 829-840
  26. Monsivais, I., et al., Conjugate thermal creep flow in a thin microchannel, International Journal of Thermal Sciences, 124 (2018), pp. 227-239
  27. Li, B. T., et al., Generating optimal heat conduction paths based on bionic growth simulation, International Communications in Heat and Mass Transfer, 83 (2017), pp. 55-63
  28. Mohsenyzadeh, M., et al., A numerical approach for the solution of a class of singular boundary value problems arising in physiology, Advances in Difference Equations, 2015 (2015), ID 231
  29. Maitama, S., Zhao, W. D., Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets, Advances in Difference Equations, 2019 (2019), ID 127
  30. Wang, B. X., et al., Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations, Advances in Difference Equations, 2019 (2019), ID 411
  31. Carslaw, H. S., Jaeger, J. C., Conduction of Heat in Solids, 2nd ed., Oxford University Press, London, 1959
  32. Arpaci, V. S., Conduction Heat Transfer, Addison-Wesley, Reading, MA, USA, 1966
  33. Özişik, M. N., Heat Conduction, 2nd ed., John Wiley and Sons, New York, USA, 1993
  34. Schneider, P. J., Conduction Heat Transfer, Addison-Wesley, Reading, MA, USA, 1955
  35. Bejan, A., Heat Transfer, John Wiley and Sons, New York, USA, 1993
  36. Kakaç, S., et al., Heat Conduction, CRC Press, Boca Raton, USA, 2018
  37. Cole, K. D., Yen, D. H. Y., Green's functions temperature and heat flux in the rectangle, International Journal of Heat and Mass Transfer, 44 (2001), 20, pp. 3883-3894
  38. Crittenden, P. E., Cole, K. D., Fast-converging steady-state heat conduction in the rectangular parallelepiped, International Journal of Heat and Mass Transfer, 45 (2002), 17, pp. 3585-3596
  39. Hayat, T., et al., Jeffrey fluid flow due to curved stretching surface with Cattaneo-Christov heat flux, Applied Mathematics and Mechanics, 39 (2018), 8, pp. 1173-1186
  40. Duan, Z. P., Pressure drop for subsonic gas flow in microchannels and nanochannels, Nanoscale and Microscale Thermophysical Engineering, 16 (2012), 2, pp. 117-132
  41. Incropera, F. P., et al., Fundamentals of Heat and Mass Transfer. 6th ed., John Wiley and Sons, New York, USA, 2007
  42. Duan, Z. P., et al., Pressure drop of microchannel plate fin heat sinks, Micromachines, 10 (2019), 2, ID 80
  43. Ma, H., et al., Fluid flow and entropy generation analysis of Al2O3-water nanofluid in microchannel plate fin heat sinks, Entropy, 21 (2019), 8, ID 739
  44. Hadad, Y., et al., Performance analysis and shape optimization of a water-cooled impingement micro-channel heat sink including manifolds, International Journal of Thermal Sciences, 148 (2020), ID 106145