THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

ANALYTICAL SOLUTION OF CONJUGATE TURBULENT FORCED CONVECTION BOUNDARY LAYER FLOW OVER PLATES

ABSTRACT
A conjugate (coupled) forced convection heat transfer from a heated conducting plate under turbulent boundary layer flow is considered. A heated plate of finite thickness is cooled under turbulent forced convection boundary layer flow. Because the conduction and convection boundary layer flow is coupled (conjugated) in the problem, a semi-analytical solution based on Differential Transform Method (DTM) is presented for solving the non-linear integro-differential equation occurring in the problem. The main conclusion is that in the conjugate heat transfer case the temperature distribution of the plate is flatter than the one in the non-conjugate case. This feature is more pronounced under turbulent flow when compared with the laminar flow.
KEYWORDS
PAPER SUBMITTED: 2014-01-15
PAPER REVISED: 2014-05-14
PAPER ACCEPTED: 2014-05-23
PUBLISHED ONLINE: 2014-06-15
DOI REFERENCE: https://doi.org/10.2298/TSCI140115062J
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 5, PAGES [1499 - 1507]
REFERENCES
  1. Perelman, Y.L., On conjugate problems of heat transfer, Int. J. Heat Mass Transfer, vol. 3, pp. 293-303, 1961.
  2. Luikov, A.V., Aleksashenko, V.A., and Aleksashenko, A.A., Analytical methods of solution of conjugate problems in convective heat transfer, Int. J. Heat Mass Transfer, vol. 14, pp. 1047-1056, 1971.
  3. Treviño, C., and Liñan, A., External heating of a flat plate in a convective flow, Int. J. Heat Mass Transfer, vol. 27, pp. 1067-1073, 1984.
  4. Sohal, M. S., and Howel, J. R., Determination of plate temperature in case of combined conduction, convection and radiation heat exchange, Int. J. Heat Mass Transfer, vol. 16, pp. 2055-2066, 1973.
  5. Karvinen, R., Some new results for conjugated heat transfer in a flat plate, International Journal of Heat and Mass Transfer, Int. J. Heat Mass Transfer, vol. 21,, pp. 1261-1264.
  6. Kanna, P.R. and Das, M.K., Conjugate forced convection heat transfer from a flat plate by laminar plane wall jet flow, Int. J. Heat Mass Transfer, vol. 48, pp. 2896-2910, 2005.
  7. Hajmohammadi, M. R., Poozesh, S. Nourazar, S. S., and Habibi Manesh, A., Optimal architecture of heat generating pieces in a fin, J. Mech. Sci. and Tech., vol. 27, pp. 1143-1149, 2013.
  8. Alebrahim, A. Bejan, A., Constructal Trees of Circular Fins for Conductive and Convective Heat Transfer, Int. J. Heat MassTransfer, vol. 42, pp. 3585-359, 1999.
  9. Pouzesh, A., Hajmohammadi, M. R., Poozesh, S., Investigations on the internal shape of constructal cavities intruding a heat generating body, Thermal Science, DOI: 10.2298/TSCI120427164P 2012.
  10. Hajmohammadi, M. R., Poozesh, S., Campo, A., and Nourazar, S. S., Valuable reconsideration in the constructal design of cavities, Energy Conv. and Management, vol. 66, pp. 33-40, 2013.
  11. Hajmohammadi, M. R., Poozesh, S., and Hosseini, R., Radiation effect on constructal design analysis of a T-Y-shaped assembly of fins, J. Therm.Sci. & Tech., vol. 7, pp. 677-692, 2012.
  12. Nagasue, H., Steady state heat transfer with axial conduction in laminar flow in a circular tube with a specified temperature or heat flux wall, Int. J. Heat Mass Transfer, vol. 24, no. 11, pp. 1823-1832, 1981.
  13. Chiu, W.K., Richards, C.J., and Jaluria, Y., Experimental and numerical study of conjugate heat transfer in a horizontal channel heated from below, J. Heat Transfer, ASME, vol. 123, no. 4, pp. 688-694, 2001.
  14. Karvinen, R., Transient conjugated heat transfer to laminar flow in a tube or channel, Int. J. Heat Mass Transfer, vol. 31, no. 6, pp. 1326-1328, 1988.
  15. Escandón, J.P., Bautista, O., Méndez, F., and Bautista, E., Theoretical conjugate heat transfer analysis in a parallel flat plate micro-channel, Int. J. Thermal Sciences, vol. 50, pp. 1022-1030, 2011.
  16. Hajmohammadi, M. R., Moulod, M., Joneydi Shariatzadeh O., and Campo, A., Effect of a thick plate on the excess temperature of iso-heat flux heat sources cooled by laminar forced convection flow; Conjugate analysis, Numerical Heat Transfer, Part A, vol. 66, pp. 205-216, 2014.
  17. Hajmohammadi, M. R., Salimpour, M. R., Saber, M., and Campo, A., Detailed analysis for the cooling performance enhancement of a heat source under a thick plate, Eng. Conv. and Management, vol. 76 pp. 691-700, 2013.
  18. Hajmohammadi, M. R., Campo, A., Nourazar, S.S. and Ostad, A. M., Improvement of forced convection cooling due to the attachment of heat sources to a conducting thick plate, J Heat Transf. Trans. ASME, vol. 135, pp. 124504-1, 2013.
  19. Lindstedt, M., and Karvinen, R., Conjugate heat transfer in a plate - One surface at constant temperature and the other cooled by forced or natural convection, Int. J. Heat Mass Transfer, vol. 66, pp. 489-495, 2013.
  20. Dorfman, A., and Renner, Z., Conjugate Problems in Convective Heat Transfer: Review, Mathematical Problems in Engineering, doi:10.1155/2009/927350.
  21. Karvinen, R., Use of Analytical Expressions of Convection in Conjugated Heat Transfer Problems J. Heat Transfer, vol. 134, pp. 031007 (9 pages), 2012.
  22. Sofiane, T., Toufik, B., Numerical Study of The Conjugate Heat Transfer In A Horizontal Pipe Heated by Joulean Effect, Thermal Science, vol. 16, pp. 53-67, 2012.
  23. Rachid, S., Said, A., and Boumédiene, B., Computational analysis of transient turbulent flow and conjugate heat transfer characteristics in a solar collector panel with internal, rectangular fins and baffles, Thermal Science, vol. 14, pp. 221-234, 2010.
  24. Kumar, T., Alagumurthi, N., Palaniradja, K., Conjugated heat transfer analysis of gas turbine vanes using maccormack's technique, Thermal Science, vol. 12, pp. 65-73, 2008.
  25. Mamun, A.A., Chowdhury, Z.R., Azim, M.A., and Molla, M.M., MHD-conjugate heat transfer analysis for a vertical flat plate in presence of viscous dissipation and heat generation, Int. Comm. Heat Mass Transfer, vol. 35, pp. 1275-1280, 2008.
  26. Mobedi, M., Conjugate natural convection in a square cavity with finite thickness horizontal walls, Int. Comm. Heat Mass Transfer, vol. 35, pp. 503-513, 2008.
  27. Karuppa, R. and Srikanth, G., Shell side numerical analysis of a shell and tube heat exchanger considering the effects of baffle inclination angle on fluid flow using CFD, Thermal Science, vol. 16, pp. 1165-1174, 2012.
  28. Dinarvand, S. Abbassi, A., Hosseini, R., Pop, I., Homotopy analysis method for mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder, Thermal Science, DOI: 10.2298/TSCI120225165D
  29. Rashidi, M.M., and Erfani, E., New analytical method for solving Burgers' and nonlinear heat transfer equations and comparison with HAM, Computer Physics Communications, vol. 180, no. 9, pp. 1539-1544, 2009.
  30. Hetmaniok, E., Nowak I., Słota, D., Wituła, R., and Zielonka, A., Solution of the inverse heat conduction problem with Neumann boundary condition by using the homotopy perturbation method, Thermal Science, vol. 17, pp. 643-650, 2013.
  31. He, J. H., A Note on the Homotopy Perturbation Method, Thermal Science, vol. 14, pp. 565-568, 2010.
  32. Khaleghi, H., Ganji, D. D., and Sadighi, A., Application of variational iteration and homotopy-perturbation methods to nonlinear heat transfer equations with variable coefficients, Numerical Heat Transfer Part A, vol. 52, pp. 25-42, 2007.
  33. Zhou, J. K., Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
  34. Moradia, A., Alsaedib, A., and Hayat, T., Investigation of heat transfer and viscous dissipation effects on the jeffery-hamel flow of nanofluids, Thermal Science, DOI: 10.2298/TSCI120410208M
  35. Hajmohammadi, M. R., Nourazar, S. S. and Habibi Manesh, A., Semi-analytical treatments of conjugate heat transfer, Journal of Mechanical Engineering Science, vol. 227, pp. 492-503, 2012.
  36. Yaghoobi, H., and Torabi, M., The application of differential transformation method to nonlinear equations arising in heat transfer, Int. Comm. Heat Mass Transfer, vol. 38, pp. 815-820, 2011.
  37. Hajmohammadi, M. R., and S. S. Nourazar, Conjugate forced convection heat transfer from a heated flat plate of finite thickness and temperature-dependent thermal conductivity, Heat Transfer Engineering, vol. 35 pp. 863-874, 2014.
  38. Bejan, A., Convection Heat Transfer, 3rd ed., Wiley, 2004.

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence