Table 2.

The thermophysical characteristics of CNTs are given.

Properties	SWCNT’s and MWCNT’s
Dynamic viscosity	$A_1=$$\frac{{\mu }_{\mathit{NF}}}{{\mu }_F}=\frac{1}{{(1-\phi )}^{2.5}}$
Heat capacity	$A_4=\frac{{(\rho c)}_{\mathit{NF}}}{{(\rho c)}_F}=(1-\phi )+\phi \frac{{(\rho c)}_{\mathit{CNT}}}{{(\rho c)}_F}$
Density	$A_2=\frac{{\rho }_{\mathit{NF}}}{{\rho }_F}=(1-\phi )+\phi \frac{{\rho }_{\mathit{CNT}}}{{\rho }_F}$
Thermal conductivity	$\begin{array}{c}{A}_3=\frac{k_{\mathit{NF}}}{k_F},\frac{k_{\mathit{NF}}}{k_{\mathit{bF}}}=\left(\frac{1-{\phi }_2+2{\phi }_2\frac{k_{\mathit{MWCNT}}}{k_{\mathit{MWCNT}}-k_F}ln\left(\frac{k_{\mathit{MWCNT}}+k_F}{2k_F}\right)}{1-{\phi }_2+2{\phi }_2\frac{k_f}{k_{\mathit{MWCNT}}-k_F}ln\left(\frac{k_{\mathit{MWCNT}}+k_F}{2k_F}\right)}\right)\\ \frac{k_{\mathit{bF}}}{k_f}=\left(\frac{1-{\phi }_1+2{\phi }_1\frac{k_{\mathit{SWCNT}}}{k_{\mathit{SWCNT}}-k_F}ln\left(\frac{k_{\mathit{SWCNT}}+k_F}{2k_F}\right)}{1-{\phi }_1+2{\phi }_1\frac{k_f}{k_{\mathit{SWCNT}}-k_F}ln\left(\frac{k_{\mathit{SWCNT}}+k_F}{2k_F}\right)}\right)\\ \end{array}$
For hybrid nanofluid
Density	${\rho }_{\mathit{HNF}}={\phi }_2{\rho }_{s_2}+\left\{{\phi }_1\right){\rho }_{s_1}+(1-{\phi }_1){\rho }_F\left((1-{\phi }_2)\right\},$
Heat capacity	$\begin{array}{c}{(\rho c_p)}_{\mathit{HNF}}={\phi }_2{(\rho c_p)}_{s_2}+\left\{{\phi }_1\right){(\rho c_p)}_{s_1}+[(1-{\phi }_2){(\rho c_p)}_F\left((1-{\phi }_1)]\right\}\\ \\ \end{array}$
Variable viscosity	${\mu }_{\mathit{HNF}}=\frac{{\mu }_F}{{(1-{\phi }_1)}^{2.5}{(1-{\phi }_2)}^{2.5}},$
Thermal conductivity	$\begin{array}{c}\frac{k_{\mathit{HNF}}}{k_{\mathit{bF}}}=\frac{(n-1)k_{\mathit{bF}}+k_{s_2}-(k_{\mathit{bF}}-k_{s_2})(n-1){\phi }_2}{(n-1)k_{\mathit{bF}}+k_{s_2}+(k_{\mathit{bF}}-k_{s_2}){\phi }_2}\\ \frac{k_{\mathit{bF}}}{k_F}=\frac{(n-1)k_F+k_{s_1}-(k_F-k_{s_1})(n-1){\phi }_1}{(n-1)k_F+k_{s_1}+(k_F-k_{s_1}){\phi }_1},\\ \end{array}$