Radiative Free Convective Non-Newtonian Fluid Flow past a Wedge Embedded in a Porous Medium

Abstract

An isothermal boundary layer analysis is presented for the convection flow of a second-order non-Newtonian fluid past a two-dimensional wedge embedded in a non-Darcian porous medium in the presence of significant thermal radiation, surface transpiration and Eckert viscous heating. Nonsimilar numerical solutions are generated for the shear stresses and local heat transfer rates at the surface of the wedge using the Keller difference technique extended to a higher matrix order. It is found that the heat transfer magnitude is enhanced by an increase in the radiative flux parameter (Boltzmann -Rosseland number, Bo), but depressed considerably with an increase in the viscoelasticity of the second-order fluid parameter, K. The surface shear stresses are markedly decreased with rise in the viscoelasticity parameter K. Conversely, surface lateral mass flux (transpiration) is seen to lower the shear stresses at the surface and to greatly boost the heat transfer there. The effects of Eckert heating are also presented graphically and discussed. Grashof number = ratio of buoyancy to viscous hydrodynamic forces,Reynolds number = ratio of inertial to viscous hydrodynamic force, U 0 L/ν; Pr Prandtl number = ratio of momentum and thermal diffusivities, ν/α m ; m wedge-law parameter i. e. power-law index; L reference length.Greek Symbols ε porosity of the porous medium; [5]. Other research into biomechanics of blood and plasma fluids has also emerged in the past several decades, as reported, for example, by Kang and Eringen [6]. Such fluids exhibit a flow behaviour which cannot be characterized by Newtonian relationships and therefore, they are referred to as non-Newtonian fluids. Most of the studies performed utilize the simpler constitutive formulations for non-Newtonian fluids, for example, Bingham plastics [7], visco-inelastic (power-law fluids) [8,9], etc. These fluids models allow for the generation of differential equations of the boundary-layer type (parabolic) which are numerically easier to solve.In recent years, with the advances in computing power, and simultaneous developments in more robust numerical solvers, engineering scientists have attempted more complex and realistic numerical simulations using the more advanced constitutive models for non-Newtonian fluids, as reviewed by Schowalter [10]. A large body of the literature has therefore emerged in the study of viscoelastic Such studies have dwelled on only two of the three fundamental modes of heat transfer, namely, conduction and convection. The presence of significant thermal radiation heat transfer in various geophysical and technological systems has, however, necessitated the need to extend such studies to incorporate thermal radiation heat transfer. Examples of geophysical processes invoking the three modes of heat transfer of viscoelastic materials include volcanic flows, hydrothermal systems, and other deep-earth processes [19]. In solar engineering structures, designed by civil engineers, thermal radiation effects (due to solar energy) occur in unison wi...

Theoretical Analysis of Radiative Effects on Transient Free Convection Heat Transfer past a Hot Vertical Surface in Porous Media

“…Takhar et al [26] used shooting quadrature to analyze the mixed convection flow with thermal radiation effects in Darcy-Forchheiimer porous media. More recently Chamkha et al [27] studied Rosseland radiation-conduction number effects on boundary layer wedge convection of a viscoelastic fluid in non-Darcian porous material. All of the above studies however were for steady flows.…”

Network Numerical Simulation of Impulsively-Started Transient Radiation-Convection Heat and Mass Transfer in a Saturated Darcy-Forchheimer Porous Medium

“…A mesh system with 20 × 200 nodes is proven to suggest mesh-independent results. An advantage of the NSM is that the derivatives involved in equations (21) to (23) are directly evaluated, while other methods for example using five-point approximation formula. The integrals (24) to (26) are evaluated using Newton-Cotes closed integration formula.…”

“…16. Finally using expressions (21) to (23) we have computed in Figs. 18 to 20, the variation of transient local skin friction, local Nusselt number and local Sherwood number with streamwise distance for the selected effects of N , Da and Fs parameter, at fixed time, t = 1.…”

“…Takhar et al [20] employed a Runge-Kutta-Merson shooting quadrature and the Rosseland diffusion algebraic radiation model to analyze the mixed radiation-convection flow in a non-Darcy porous medium, showing that temperature gradients are boosted with radiative flux. More recently Chamkha et al studied [21] the influence of thermal radiation on steady natural convection in a viscoelastic-fluid saturated non-Darcian porous medium using the Keller Box numerical scheme. Temperatures were seen to be substantially boosted with an increase in radiative parameter.…”

Dissipation, MHD and Radiation Effects on an Unsteady Convective Heat and Mass Transfer in a Darcy-Forcheimer Porous Medium

“…In all cases, radiation significantly affects flow. Chamkha, Takhar & Beg (2004) studied the influence of thermal radiation on steady natural convection in a non-newtonian fluid past a wedge embedded in a porous medium using keller Box numerical scheme and reported among other things that the temperature increases with an increase in the radiation parameter. Recently, Anwar Beg et al (2008) studied the network numerical simulation of impulsively-started transient radiation convection heat and mass transfer in a non-Darcy porous medium neglecting the effects of dissipation and magnetic field.…”