Second law analysis of magnetized Casson nanofluid flow in squeezing geometry with porous medium and thermophysical influence

Figures & data

Figure 1. Model physical abstract.

Figure 2. Convergence/residual error analysis.

Table 1. Comparison results of Skin friction ($-u^{″}\left(0\right)$) and heat transfer ($-H^{\prime }\left(0\right)$) coefficients for different values of Z when ${\xi }_1={\xi }_2={\xi }_3=0$, Pr = 1, Nb = Nt = 0, $Ec=E{c}_r=0$, $V_0=B{i}_1=1$ $F_1=F_2=F_3=0$ and $\text{β}=\mathrm{\infty }$.

Values			Present result (CCA)		Sobomowo et al. [68] (DTM)		Hayat et al. [69] (HAM)
Da	Ha	Z	$-u^{″}\left(0\right)$	$-H^{\prime }\left(0\right)$	$-u^{″}\left(0\right)$	$-H^{\prime }\left(0\right)$	$-u^{″}\left(0\right)$	$-H^{\prime }\left(0\right)$
$\to \mathrm{\infty }$	1	$-0.2$	12.055564	0.593082	12.05556	0.59308	12.05556	0.59308
		$-0.1$	11.744107	0.592925	11.74411	0.59293	11.74411	0.59293
		0.1	11.117313	0.592609	11.11731	0.59261	11.11731	0.59261
		0.2	10.801983	0.592452	10.801983	0.59245	10.80198	0.59245
1	1	$-0.2$	12.284382	0.592950	12.28438	0.59295	–	–
		$-0.1$	11.967907	0.592793	11.96791	0.59248	–	–
		0.1	11.331126	0.592479	11.33113	0.59248	–	–
		0.2	11.010827	0.592321	11.01083	0.59232	–	–

Table 2. Comparison results of the velocity ($u\left(\eta \right)$) and temperature ($H\left(\eta \right)$) and concentration $\left(G\right(\eta \left)\right)$ profiles for different values of variable $\left(\eta \right)$ when Z = 1.0, ${\xi }_1={\xi }_2={\xi }_3=0$, Ec = 0 $E{c}_r=0.1$, Sc = 1, Pr = 2, Nb = Nt = 0, $\delta =0.1$, $V_0=-0.1$, $\alpha =B{i}_1=B{i}_2=0.2$ $K_D=0.1$, Ha = 1, $Da=5.0$, Pr = 7.2, Nt = Nb = 0.1 and $\text{β}=0.5$.

Variable	Present result (CCA)			Present result (RKFM)
η	$u\left(\eta \right)$	$H\left(\eta \right)$	$G\left(\eta \right)$	$u\left(\eta \right)$	$H\left(\eta \right)$	$G\left(\eta \right)$
0.0	1.0515491957	1.0885349934	$-1.0526618075$	1.0515491961	1.08853499441	$-1.0526618085$
0.2	0.3818078613	$-1.5633431615$	1.51330246046	0.38180786151	$-1.5633431597$	1.5133024582
0.4	$-0.27458238784$	$-4.9503135601$	4.8354888555	$-0.2745823878$	$-4.95031355840$	4.8354888528
0.6	$-0.9423624746$	$-7.6490917951$	7.4388822589	$-0.9423624747$	$-7.64909179143$	7.43888225384
0.8	$-1.6471751043$	$-8.8684776183$	8.534980325	$-1.6471751047$	$-8.8684776132$	8.5349803187
1.0	$-2.4177931369$	$-9.210199661$	8.818448224	$-2.417793137$	$-9.2101996633$	8.818448227

Figure 3. Influence of darcy number (Da) on (a) axial velocity, (b) radial velocity, (c) temperature, (d) nanoparticle concentration.

Figure 4. Influence of thermophoresis number (Nt) on (a) temperature, (b) nanoparticle concentration.

Figure 5. Influence of Brownian motion number (Nb) on (a) temperature, (b) nanoparticle concentration.

Figure 6. Influence of (a) viscosity, (b) thermal conductivity, (c) Brownian motion, (d) Casson number: on entropy generation rate.

Figure 7. Influence of (a) Prandtl number, (b) Eckert number, (c) squeezing rate, and (d) thermophoresis number: on entropy generation rate.

Figure 8. Influence of (a) darcy number, (b) magnetic number on entropy generation rate.

Figure 9. Influence of (a) viscosity, (b) thermal conductivity, (c) squeezing rate, (d) Casson number: on irreversibility distribution ratio.

Figure 10. Influence of (a) Prandtl number, (b) Eckert number, (c) Darcy number, (d) magnetic number: on irreversibility distribution ratio.

Sobamowo MG, Yinusa AA, Aladenusi ST. Impacts of magnetic field and thermal radiation on squeezing flow and heat transfer of third grade nanofluid between two disks embedded in a porous medium. Heliyon. 2020;6(5):e03621.

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Hayat T, Nazar H, Imtiaz M, et al. Axisymmetric squeezing flow of third grade fluid in presence of convective conditions. Chin J Phys. 2017;55(3):738–754.

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