The combined effects of anisotropic porous medium and stably stratified fluid on free convective flow through an annulus

Figures & data

Figure 1 The physical geometry of the problem.

Table 1. Comparing the numerical values for Riemann sum approximation method with the exact solutions obtained for steady states velocity and temperature profiles when $Da=0.01,\theta ={30}^0,K^{\ast }=0.2,$ $\gamma =1.5,$ $S=0.04$ and $Pr=7.1$.

		Velocity			Temperature
$t$	$R$	Riemann Sum Approximation Method for transient state	Exact solution for steady state	Difference (%)	Riemann Sum Approximation Method for transient state	Exact solution for steady state	Difference (%)
7	1.2	0.0066	0.0066	0	0.7368	0.7368	0
	1.4	0.0059	0.0059	0	0.5144	0.5144	0
	1.6	0.0039	0.0039	0	0.3218	0.3218	0
	1.8	0.0019	0.0019	0	0.1519	0.1519	0
8	1.2	0.0066	0.0066	0	0.7368	0.7368	0
	1.4	0.0059	0.0059	0	0.5144	0.5144	0
	1.6	0.0039	0.0039	0	0.3218	0.3218	0
	1.8	0.0019	0.0019	0	0.1519	0.1519	0
9	1.2	0.0066	0.0066	0	0.7368	0.7368	0
	1.4	0.0059	0.0059	0	0.5144	0.5144	0
	1.6	0.0039	0.0039	0	0.3218	0.3218	0
	1.8	0.0019	0.0019	0	0.1519	0.1519	0

Figure 2. Temperature profile with different values of $t$ for $Pr=7.1,$ $\theta ={30}^0,$ $S=0.04,Da=0.1,$ $\gamma =2.0$, $\lambda =2.0$ and $k^{\ast }=0.2$.

Figure 3. Temperature profile with different values of $Pr$ for $t=0.4,$ $\theta ={30}^0,$ $S=0.04,Da=0.1,$ $\gamma =2.0$, $\lambda =2.0$ and $k^{\ast }=0.2$.

Figure 4. Temperature profile with different values of $S$ for $Pr=7.1,$ $\theta ={30}^0,$ $t=4.0,Da=0.1,$ $\gamma =2.0$, $\lambda =2.0$ and $k^{\ast }=0.2$.

Figure 5. Temperature profile with different values of $\theta$ and $k^{\ast }$ for $Pr=7.1,$ $S=0.04,Da=0.1,$ $\gamma =0.5$, $\lambda =2.0,R=1.5$ and $t=0.4$.

Figure 6. Velocity profile with different values of $t$ for $Pr=7.1,$ $\theta ={30}^0,$ $S=0.04,Da=0.1,$ $\gamma =0.5$, $\lambda =2.0$ and $k^{\ast }=0.2$.

Figure 7. Velocity profile with different values of $Pr$ for $Da=0.1,$ $\theta ={30}^0,$ $S=0.04,t=0.4,$ $\gamma =0.5$, $\lambda =2.0$ and $k^{\ast }=0.2$.

Figure 8. Velocity profile with different values of $S$ for $Pr=7.1,$ $k^{\ast }=0.2,$ $\theta ={30}^0,Da=0.1,$ $\gamma =0.5$, $\lambda =2.0$ and t$=4.0$.

Figure 9. Velocity profile with different values of $\theta$ for $k^{\ast }$ for $Pr=7.1,$ $S=0.04,Da=0.1,$ $\gamma =0.5$, $\lambda =2.0,R=1.5$ and t$=0.4$.

Figure 10. Velocity profile with different values of $Da$ for $Pr=7.1,$ $\theta ={30}^0,$ $S=0.04,t=0.4,$ $\gamma =0.5$, $\lambda =2.0$ and $k^{\ast }=0.2$.