Figure from:Effect of viscous dissipation on natural convection flow between vertical parallel plates with time-periodic boundary conditions

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Fig. (5). (a) Variation of temperature distribution with 7 for Fig. (4). Variation of temperature distribution with 7 varying n n=0.5 varying yand R fixing Gr =0.01 and ¢=0.01. (5b). — Figure 5 (5). (a) Variation of temperature distribution with 7 for Fig. (4). Variation of temperature distribution with 7 varying n n=0.5 varying yand R fixing Gr =0.01 and ¢=0.01. (5b).

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Fig. (1). Physical Model and coordinate system. Consider the steady, laminar, two-dimensional natural convection boundary layer flow over a semi-infinite vertical flat embedded in a saturated porous medium as shown in Fig. (1). The fluid is considered to be gray, absorbing- emitting radiation but non-scattering medium, and the Rosse- land approximation is used to describe the radiative heat flux in the energy equation. The x -coordinate is taken along the plate and y-coordinate is measured normal to the plate, while the origin of the reference system is taken at the lead- ing edge of the plate. The porous medium is assumed to be transparent and in thermal equilibrium with the fluid. The wall and ambient media temperature, respectively, are T and 7;,, where 7, >T7!, (heated plate). The fluid flow is moderate and the permeability of the medium is assumed to be low so that the Forchheimer flow model is applicable and the boundary-drag effect is neglected. The flow is steady, laminar and two dimensional. With the usual boundary layer and linear Boussinesq approximations, the governing equa- tions, namely the equation of continuity, the non-Darcy flow

The radiative heat flux term q. is written using Rosse- [29], the modified permeability of the flow K’ of the non- Newtonian power law fluid is defined as land approximation (Raptis [17], Murthy et al. [19]) as

Table 1. Comparison of the Heat Transfer Coefficient tO) for Newtonian Fluid when R a Non-dimensional velocity in the non-Darcy medium is plotted for fixed value of Gr’, y and R for various values of power law index n and viscous dissipation parameter € in Fig. (2). It is interesting to note that the value of the slip ve- locity f’ increases with the power law index n. And at the same time, an increase in the value of the dissipation pa- rameter increases the velocity distribution inside the bound- ary layer. In Figs. (3a and 3b). the non-dimensional velocity profiles are plotted in the non-Darcy medium for n=0.5 (pseudoplastic fluid) and n=1.5 (dilatant fluid), respec- tively with fixed value of Gr’ and € for various values of y and R. It is observed that for all n (n<1,n=land n>1) the velocity increases inside the boundary layer as the viscosity parameter increases and, therefore, decreases the boundary layer thickness, which results in decrease in temperature as

Fig. (2). Variation of velocity distribution with varying n and

which results in an increase in the heat transfer coefficien with increasing the power law index n as indicated in the Figs. (6-9). Figs. (5a and 5b), respectively, show the varia. tion of the non-dimensional temperature profile @ across the boundary layer for n = 0.5 and n = 1.5 various values of vis cosity parameter y and R for fixed values of other parame- ters. It is seen that increasing the viscosity parameter y tend: to decreases the thermal boundary layer thickness result: increment in heat transfer coefficient as shown in the Figs. (¢ and 9). Again with an increase in the coefficient of therma radiation R, a rise in temperature distribution in the boundary layer is seen for all values of n.