Influence of activation energy on triple diffusive entropy optimized time-dependent quadratic mixed convective magnetized flow

Figures & data

Figure 1. Flow model.

Table 1. A comparison of the current time-independent findings with [30] and [31] at $Pr=0.73$.

	Current findings		Singh et al. [30]		Kumari et al. [31]
Wedge angle parameter	$F_{\eta }\left(\xi ,0\right)$	$G_{\eta }\left(\xi ,0\right)$	$F_{\eta }\left(\xi ,0\right)$	$G_{\eta }\left(\xi ,0\right)$	$F_{\eta }\left(\xi ,0\right)$	$G_{\eta }\left(\xi ,0\right)$
0	0.46975	0.42061	0.46975	0.42046	0.46975	0.42079
0.0141	0.50475	0.42620	0.50481	0.42606	0.50472	0.42635
0.0435	0.56898	0.43567	0.56895	0.43559	0.56904	0.43597
0.0909	0.65495	0.44750	0.65490	0.44742	0.65501	0.44770
0.1429	0.73200	0.45718	0.73196	0.45705	0.73202	0.45728
0.2000	0.80212	0.46525	0.80208	0.46511	0.80214	0.46534
0.3333	0.92766	0.47822	0.92767	0.47815	0.92766	0.47840

Figure 2. Impact of pressure gradient parameter $m$ and time $\tau$ on $F\left(\xi ,\eta ,\tau \right)$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$ when $\alpha =0.5$, $\xi =0.5$, $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $n_1=n_2=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$, $Re=5$.

Figure 3. Impact of pressure gradient parameter $m$ and unsteadiness parameter $\alpha$ on $R{e}_x^{1/2}{C}_{fx}$ when $\xi =0.5$, $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $n_1=n_2=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$.

Figure 4. Impact of pressure gradient parameter $m$ and unsteadiness parameter $\alpha$ on $R{e}_x^{-1/2}S{h}_{1x},R{e}_x^{-1/2}S{h}_{2x}$ when $\xi =0.5$, $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $n_1=n_2=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$.

Figure 5. Effect of magnetic parameter $M$, axial distance $\xi$ and time $\tau$ on $F\left(\xi ,\eta ,\tau \right)$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$ when $\alpha =0.5$, $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $Ec=0.1$, $m=0.2$, $n_1=n_2=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$, $Re=5$.

Figure 6. Effect of magnetic parameter $M$, axial distance $\xi$ and unsteadiness parameter $\alpha$ on $R{e}_x^{1/2}{C}_{fx}$ when $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $Ec=0.1$, $m=0.2$, $n_1=n_2=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$.

Figure 7. Effect of quadratic combined convection parameter ${\text{β}}_t$ and time $\tau$ on $\left(H,S\right)\left(\xi ,\eta ,\tau \right)$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$ when $\alpha =0.5$, $\xi =0.5$, $Ri=10$, ${\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $m=0.2$, $n_1=n_2=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$, $Re=5$.

Figure 8. Effect of quadratic combined convection parameter ${\text{β}}_t$ and unsteadiness parameter $\alpha$ on $R{e}_x^{-1/2}S{h}_{1x},R{e}_x^{-1/2}S{h}_{2x}$ when $\xi =0.5$, $Ri=10$, ${\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $m=0.2$, $n_1=n_2=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$.

Figure 9. Influence of $K{c}_1$, activation energy $E_1$, and time $\tau$ on $H\left(\xi ,\eta ,\tau \right)$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$ when $\alpha =0.5$, $\xi =0.5$, $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $m=0.2$, $n_1=n_2=0.2$, $K{c}_2=E_2=\delta =0.1$, $Re=5$.

Figure 10. Influence of $K{c}_2$, activation energy $E_2$, and time $\tau$ on $S\left(\xi ,\eta ,\tau \right)$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$ when $\alpha =0.5$, $\xi =0.5$, $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $m=0.2$, $n_1=n_2=0.2$, $K{c}_1=E_1=\delta =0.1$, $Re=5$.

Figure 11. Influence of $K{c}_1$, activation energy $E_1$, and unsteadiness parameter $\alpha$ on $R{e}_x^{-1/2}S{h}_{1x}$ when $\xi =0.5$, $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $m=0.2$, $n_1=n_2=0.2$, $K{c}_2=E_2=\delta =0.1$.

Figure 12. Influence of $K{c}_2$, activation energy $E_2$, and unsteadiness parameter $\alpha$ on $R{e}_x^{-1/2}S{h}_{2x}$ when $\xi =0.5$, $Ri=10$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $m=0.2$, $n_1=n_2=0.2$, $K{c}_2=E_2=\delta =0.1$.

Figure 13. Effect of $Ri$, ${\text{β}}_t$ and $\alpha$ on $R{e}_x^{1/2}{C}_{fx}$ when $Ri=10$, $\xi =0.5$, ${\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $m=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$,$n_1=n_2=0.2$.

Figure 14. Effect of $Ri$, ${\text{β}}_t$ and $\alpha$ on $R{e}_x^{-1/2}N{u}_x$ when $Ri=10$, $\xi =0.5$, ${\text{β}}_{c_1}={\text{β}}_{c_2}=0.1$, $N{c}_1=N{c}_2=0.1$, $M=Ec=0.1$, $m=0.2$, $K{c}_1=K{c}_2=E_1=E_2=\delta =0.1$, $n_1=n_2=0.2$.

Figure 15. Impact of $Br$ on $S_G$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$, $\alpha =0.5$, when $Ri=10$, $\xi =0.5$, $S{c}_1=160$, $S{c}_2=340$, $Re=5$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_1}=N{c}_1=N{c}_2=0.1$, $M_1=M_2=M_3=0.5$, and ${\mathrm{\Omega }}_T={\mathrm{\Omega }}_{c_1}={\mathrm{\Omega }}_{c_2}=0.5$.

Figure 16. Impact of $Br$ on $Be$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$, $\alpha =0.5$, when $Ri=10$, $\xi =0.5$, $S{c}_1=160$, $S{c}_2=340$, $Re=5$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_1}=N{c}_1=N{c}_2=0.1$, $M_1=M_2=M_3=0.5$, and ${\mathrm{\Omega }}_T={\mathrm{\Omega }}_{c_1}={\mathrm{\Omega }}_{c_2}=0.5$.

Figure 17. Impact of $Re$ on $S_G$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$, $\alpha =0.5$, when $Ri=10$, $\xi =0.5$, $S{c}_1=160$, $S{c}_2=340$, $Br=0.1$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_1}=N{c}_1=N{c}_2=0.1$, $M_1=M_2=M_3=0.5$, and ${\mathrm{\Omega }}_T={\mathrm{\Omega }}_{c_1}={\mathrm{\Omega }}_{c_2}=0.5$.

Figure 18. Impact of ${\mathrm{\Omega }}_T$ on $S_G$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$, $\alpha =0.5$, when $Ri=10$, $\xi =0.5$, $S{c}_1=160$, $S{c}_2=340$, $Br=0.1$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_1}=N{c}_1=N{c}_2=0.1$, $M_1=M_2=M_3=0.5$, ${\mathrm{\Omega }}_{c_1}={\mathrm{\Omega }}_{c_2}=0.5$, and $Re=5$.

Figure 19. Impact of ${\mathrm{\Omega }}_T$ on $Be$ for $\varphi \left(\tau \right)=1+\alpha {\tau }^2$, $\alpha =0.5$, when $Ri=10$, $\xi =0.5$, $S{c}_1=160$, $S{c}_2=340$, $Br=0.1$, ${\text{β}}_t={\text{β}}_{c_1}={\text{β}}_{c_1}=N{c}_1=N{c}_2=0.1$, $M_1=M_2=M_3=0.5$, ${\mathrm{\Omega }}_{c_1}={\mathrm{\Omega }}_{c_2}=0.5$, and $Re=5$.

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