Unsteady 3D heat transport in hybrid nanofluid containing brick shaped ceria and zinc-oxide nanocomposites with heat source/sink

Figures & data

Figure 1. Graphical abstract of the present modeling.

Table 1. Thermophysical properties of ceria and zinc oxide with water as host liquid [9–11].

Thermophysical properties	Host liquid	Nanoparticles
	$H_{2}O$	$Ce{O}_2 ({\psi }_1)$	$\mathit{ZnO}$ $({\psi }_2)$
Density $\left(\rho \right):kg/m^3$	997.1	7600	5600
Thermal conductivity $\left(k\right):W/mK$	0.613	4.54	13
Specific heat $\left(C_p\right):J/\mathit{kgK}$	4179	390.0	495.2
Electrical conductivity: $\left(\sigma \right):\mathrm{S}/m$	0.05	10	0.01
Prandtl number: $Pr$	6.20	–	–

Table 2. Convergence of the Keller-Box simulation under the control of parameters $\alpha =S=M=0.5,\gamma =0.2,r=s=1.0,{\psi }_1=0.03,{\psi }_2=0.02.$

$n_p$	$-f″(0)$	$-g″(0)$	$-\theta \prime (0)$	$\frac{1}{\varphi (0)}$
500	1.114045	0.500372	3.341994	3.808766
1000	1.114045	0.500368	3.341426	3.808118
1500	1.114045	0.500367	3.341321	3.807998
2000	1.114045	0.500367	3.341284	3.807956
2500	1.114045	0.500367	3.341267	3.807937
3000	1.114045	0.500367	3.341257	3.807926
3500	1.114045	0.500367	3.341252	3.80792
4000	1.114045	0.500367	3.341248	3.807916
4500	1.114045	0.500367	3.341246	3.807913
5000	1.114045	0.500367	3.341244	3.807911
5500	1.114045	0.500367	3.341243	3.807909
6000	1.114045	0.500367	3.341242	3.807908
6500	1.114045	0.500367	3.341242	3.807908

Figure 2. (a, b). Heat estimations with the influence of $\gamma$ for VST state (pattern a) and for VHF state (pattern b).

Figure 3. (a, b). Heat estimations with the influence of $r$ for VST state (pattern a) and for VHF state (pattern b).

Figure 4. (a, b). Heat estimations with the influence of $s$ for VST state (pattern a) and for VHF state (pattern b).

Figure 5. (a-c). Nusselt number estimations with the pairs (a): ${\psi }_1$ (ceria) versus $\gamma ,$ (b): ${\psi }_2$ (zinc-oxide) versus ${\psi }_1$ (ceria) for heat sink situation, and ${\psi }_1$ (ceria) versus ${\psi }_2$ (zinc-oxide) for heat source situation.

Figure 6. (a-c). Skin-friction coefficients for ceria nanocomposites with the pairs (a): ${\psi }_1$ versus $S,$ (b): ${\psi }_1$ versus $\alpha ,$ and (c): ${\psi }_1$ versus $M.$

Figure 7. Comparison between rate of heat transfer by ceria $(1\mathit{\text{ wt\%}}, 3\mathit{\text{ wt\%}},5\mathit{\text{ wt\%}},7\mathit{\text{ wt\%}})$ and rate of heat transfer by zinc-oxide $(1\mathit{\text{ wt\%}}, 3\mathit{\text{ wt\%}},5\mathit{\text{ wt\%}},7\mathit{\text{ wt\%}})$ against the wide range of unsteady stretching parameter $S.$

Table 3. Calculation of Nusselt number for solid volume fractions ${\psi }_1$ (ceria) and ${\psi }_2$ (zinc-oxide) with $\alpha =S=M=0.5,\gamma =0.2,r=s=1.0.$

Volume percentages of nanocomposites		Nusselt number
		VST state		VHF state
		KBM	HAM	KBM	HAM
0.03	0.02	3.807908	3.807906	3.807908	3.807906
0.06	0.02	3.930894	3.930891	3.930894	3.930891
0.09	0.02	4.035562	4.035561	4.035562	4.035561
0.03	0.04	3.920627	3.920625	3.920627	3.920625
0.03	0.06	4.031697	4.031694	4.031697	4.031694
0.03	0.08	4.133501	4.133501	4.133501	4.133501