Natural Convection of Non-Newtonian Fluids About a Horizontal Surface in a Porous Medium

Abstract

The problem of natural convection of a non-Newtonian power-law fluid about a horizontal impermeable surface in the porous medium is considered, where the plate is assumed with a nonuniform heat flux distribution. The present study is based on the boundary layer approximation and only suitable for a high Rayleigh number. Similarity solutions are obtained by using the fourth-order Runge-Kutta method and the Nachtsheim-Swigert iteration scheme. The effects of the nonuniform wall heat flux qw(x) and the new power-law index n on the heat transfer characteristics are discussed.

Natural Convective Boundary Layer Flow Over a Vertical Cone Embedded in a Porous Medium Saturated with a Nanofluid

“…Gorla and co-workers [7,8] solved the nonsimilar problem of free convective heat transfer from a vertical plate embedded in a saturated porous medium with an arbitrarily varying surface temperature or heat flux. Chen and Chen [9] and Mehta and Rao [10] presented similarity solutions for free convection of non-Newtonian fluids over horizontal surfaces in porous media. Nakayama and Koyama [11] studied the natural convection over a non-isothermal body of arbitrary geometry placed in a porous medium.…”

Magnetohydrodynamic free convection of non-Newtonian power-law fluids over a uniformly heated horizontal plate

“…The non-Newtonian behavior of these fluids mostly exhibits itself by a shear-dependent viscosity. Due to the growing use of such fluids, the phenomenon of natural-convection has been widely investigated for the flow of these types of fluid on vertical [8][9][10][11][12], inclined [13], and horizontal surfaces [14][15][16][17][18]. Different studies have been reported on the steady natural-convection flow of power-law fluids over vertical surfaces with constant temperature [8], constant wall heat flux [9,10], and under mixed thermal boundary conditions [11].…”

“…A similarity solution of natural-convection of non-Newtonian power-law fluid about a horizontal impermeable surface with a non-uniform heat flux distribution in the porous medium has been reported in [14]. In addition, Gorla and Kumari [15] have investigated free convection problem for the horizontal plate subject to variable wall temperature or heat flux distribution embedded in non-Newtonian power-law fluid-saturated porous media.…”

Combined convection in power-law fluids along a nonisothermal vertical plate in a porous medium

“…Chert and Chen [9] and Mehta and Rao [10] presented similarity solutions for free convection of non-Newtonian fluids over vertical surfaces in porous media. Nakayama and Koyama [11] studied the natural convection over a nonisothermal body of arbitrary geometry placed in a porous medium.…”