Abstract.
The present study is devoted to investigate the influences of viscous dissipation on buoyancy induced flow over a horizontal or a vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface temperature (PT) or with prescribed variable surface heat flux (PHF) for the horizontal plate case. While, the similarity solutions are obtained with prescribed variable surface heat flux for the vertical plate case. Different similar transformations, for each case, are used. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Nusselt number associated with temperature distributions and excess surface temperature associated with heat flux distributions which are entered in tables have been presented for different values of the power-law index n and the exponent λ as well as Eckert number.
Similar content being viewed by others
References
Chen HT; Chen CK (1988) Free convection of non-Newtonian fluids along a vertical plate embedded in a porous medium. Trans ASME J Heat Transfer 110: 257–260
Nakayama A; Koyama H (1991) Buoyancy induced flow of non-Newtonian fluids over a non-isothermal body of arbitrary shape in a fluid saturated porous medium. Appl Sci Res 48: 55–70
Fand RM; Steinberger TE; Cheng P (1986) Natural convection heat transfer from a horizontal cylinder embedded in a porous medium. Int J Heat Mass Transfer 29: 119–133
Gebhart B (1962) Effects of viscous dissipation in natural convection. J Fluid Mech 14: 225–235
Gebhart B; Mollendorf J (1969) Viscous dissipation in external natural convection flows. J Fluid Mech 38: 97–107
Fand RM; Brucker J (1983) A correlation for heat transfer by natural convection from horizontal cylinders that accounts for viscous dissipation. Int J Heat Mass Transfer 26: 709–726
Nakayama A; Pop I (1989) Free convection over a non-isothermal body in a porous medium with viscous dissipation. Int comm Heat Mass Trans 16: 173–180
Hady FM; Ibrahim FS (1997) Forced convection heat transfer on a flat plate embedded in porous media for power-law fluids. Trans Porous Media 28: 125–134
Nakayama A (1993) A similarity solution for free convection from a point heat source embedded in a non-Newtonian fluid saturated porous medium. Trans ASME J Heat Trans 115: 510–513
Yang YT; Wang SJ (1996) Free convection heat transfer of non-Newtonian fluids over axisymmetric and two dimensional bodies of arbitrary shape embedded in a fluid saturated porous medium. Int J Heat Mass Transfer 39: 203–210
Hossain MA; Nakayama A; Pop I (1995) Conjugate free convection of non-Newtonian fluids about a vertical cylindrical fin in porous media. Waerme und Stoffuebertragung 30: 149–153
Gorla RSR; Shanmugam K; Kumari M (1997) Nonsimilar solutions for mixed convection in non-Newtonian fluids along horizontal surfaces in porous media. Trans Porous Media 28: 319–334
Murthy PVSN; Singh P (1997) Effects of viscous dissipation on a non-Darcy natural convection regime. Int J Heat Mass Transfer 40: 1251–1260
Mehta KN; Rao KN (1994) Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal horizontal plate embedded in a porous medium. Int J Eng Sci 32: 521–525
Mehta KN; Rao KN (1994) Buoyancy-induced flow of non-Newtonian fluids in a porous medium past a vertical flat plate with non-uniform surface heat flux. Int J Eng Sci 32: 297–302
Christopher RH; Middleman S (1965) Power-law flow through a packed tube. I & EC Fundamentals 4: 422–426
Dharmadhikari RV; Kale DD (1985) Flow of non-Newtonian fluids through porous media. Chem Eng Sci 40: 527–529
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
El-Amin, M.F., El-Hakiem, M.A. & Mansour, M.A. Effects of viscous dissipation on a power-law fluid over plate embedded in a porous medium. Heat and Mass Transfer 39, 807–813 (2003). https://doi.org/10.1007/s00231-003-0415-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00231-003-0415-2