Natural Convection in Wavy-Wall Cavities Filled with Power-Law Fluid

Authors: Cha’o-Kuang Chen, Ching-Chang Cho

Abstract:

This paper investigates the natural convection heat transfer performance in a complex-wavy-wall cavity filled with power-law fluid. In performing the simulations, the continuity, Cauchy momentum and energy equations are solved subject to the Boussinesq approximation using a finite volume method. The simulations focus specifically on the effects of the flow behavior index in the power-law model and the Rayleigh number on the flow streamlines, isothermal contours and mean Nusselt number within the cavity. The results show that pseudoplastic fluids have a better heat transfer performance than Newtonian or dilatant fluids. Moreover, it is shown that for Rayleigh numbers greater than Ra=10³, the mean Nusselt number has a significantly increase as the flow behavior index is decreased.

Keywords: Non-Newtonian fluid, Power-law fluid, Natural convection, Heat transfer enhancement, Cavity, Wavy wall.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337375

References:

[1] S. Ostrach, "Natural convection in enclosures,” J. Heat Transf.-Trans. ASME, vol. 110, pp. 1175-1190, 1988.
[2] S. Mahmud, P.K. Das, N. Hyder, and A.K.M.S., Islam, "Free convection in an enclosure with vertical wavy walls,” Int. J. Therm. Sci., vol. 41, pp. 440-446, 2002.
[3] H.F. Oztop, E. Abu-Nada, Y. Varol, and A. Chmkha, "Natural convection in wavy enclosures with volumetric heat sources,” Int. J. Therm. Sci., vol. 50, pp. 502-514, 2011.
[4] C.C. Cho, C.L. Chen, and C.K. Chen, "Natural convection heat transfer performance in complex-wavy-wall enclosed cavity filled with nanofluid,” Int. J. Therm. Sci., vol. 60, pp. 255-263, 2012.
[5] G.B. Kim, J.M. Hyun, and H.S. Kwak, "Transient buoyant convection of a power-law non-Newtonian fluid in an enclosure,” Int. J. Heat Mass Transf., vol. 46, pp. 3605-3617, 2003.
[6] M. Lamsaadi, M. Naimi, and M. Hasnaoui, "Natural convection heat transfer in shallow horizontal rectangular enclosures uniformly heated from the side and filled with non-Newtonian power law fluids,” Energy Conv. Manag., vol. 47, pp. 2535-2551, 2006.
[7] M. Lamsaadi, M. Naimi, M. Hasnaoui, and M. Mamou, ”Natural convection in a titled rectangular slot containing non-Newtonian power-law fluids and subject to a longitudinal thermal gradient,” Numer. Heat Tranf. A-Appl., vol. 50, pp. 561-583, 2006.
[8] O. Turan, A. Sachdeva, N. Chakraborty, and R.J. Poole, "Laminar natural convection of power-law fluids in a square enclosure with differentially heated side walls subjected to constant temperatures,” J. Non-Newton. Fluid Mech., vol. 166, pp. 1049-1063, 2011.
[9] L. Khezzar, D. Siginer, and I. Vinogradov, "Natural convection of power law fluids in inclined cavities,” Int. J. Therm. Sci., vol. 53, pp. 8-17, 2012.
[10] C.C. Cho, C.L. Chen, and C.K. Chen, "Electrokinetically-driven non-Newtonian fluid flow in rough microchannel with complex-wavy surface,” J. Non-Newton. Fluid Mech., vol. 173-174, pp. 13-20, 2012.
[11] P.D. Thomas, and J.F. Middlecoff, "Direct control of the grid point distribution in meshes generated by elliptic equations,” AIAA J., vol. 18, pp. 652-656, 1980.
[12] S. V. Patankar, "Numerical Heat Transfer and Fluid Flow,” New York:McGraw-Hill, 1980.