Table 1 Mathematical formulations of the thermophysical properties of \({C}_{2}{H}_{6}{O}_{2}-A{l}_{2}{O}_{3}\) and \(Cu-{Al}_{2}{O}_{3}/{C}_{2}{H}_{6}{O}_{2}\)39.

From: Transport properties of two-dimensional dissipative flow of hybrid nanofluid with Joule heating and thermal radiation

Properties

Nanofluid (\({Al}_{2}{O}_{3}-{H}_{2}O\))

Hybrid nanofluid (\(Cu-{Al}_{2}{O}_{3}/{H}_{2}O\))

Viscosity

\({\mu }_{nf}=\frac{{\mu }_{f}}{{\left(1-\varphi \right)}^{2.5}}.\)

\({\mu }_{hnf}=\frac{{\mu }_{f}}{{{\left(1-{\phi }_{1}\right)}^{2.5}\left(1-{\phi }_{2}\right)}^{2.5}}\),

Electrical conductivity

\(\frac{{\sigma }_{nf}}{{\sigma }_{f}}=1+\frac{3\left(\sigma -1\right)\phi }{\left(\sigma +2\right)-\left(\sigma -1\right)\phi }\),

\(\frac{{\sigma }_{hnf}}{{\sigma }_{bf}}=\frac{{\sigma }_{{s}_{2}}+2{\sigma }_{bf}-2{\phi }_{2}\left({\sigma }_{bf}-{\sigma }_{{s}_{2}}\right)}{{\sigma }_{{s}_{2}}+2{\sigma }_{bf}+{\phi }_{2}\left({\sigma }_{bf}-{\sigma }_{{s}_{2}}\right)}\),

where,

\(\frac{{\sigma }_{bf}}{{\sigma }_{f}}=\frac{{\sigma }_{{s}_{1}}+2{\sigma }_{f}-2{\phi }_{1}\left({\sigma }_{f}-{\sigma }_{{s}_{1}}\right)}{{\sigma }_{{s}_{1}}+2{\sigma }_{f}+{\phi }_{1}\left({\sigma }_{f}-{\sigma }_{{s}_{1}}\right)}\),

Heat capacity

\({\left(\rho {C}_{p}\right)}_{nf}=\varphi {\left(\rho {C}_{p}\right)}_{s}+\left(1-\varphi \right){\left(\rho {C}_{p}\right)}_{f}.\)

\({\left(\rho {C}_{p}\right)}_{hnf}={\left(\rho {C}_{p}\right)}_{f}\left(1-{\phi }_{2}\right)\left\{1-{\phi }_{1}+{\phi }_{1}{\left(\rho {C}_{p}\right)}_{{s}_{1}}\right\}+{\phi }_{2}{\left(\rho {C}_{p}\right)}_{{s}_{2}}\)

Density

\({\rho }_{nf}=\varphi {\rho }_{s}+\left(1-\varphi \right){\rho }_{f}\)

\({\rho }_{hnf}={\rho }_{f}\left(1-{\phi }_{2}\right)\left\{1-{\phi }_{1}+{\phi }_{1}{\rho }_{{s}_{1}}\right\}+{\phi }_{2}{\rho }_{{s}_{2}}\),

Thermal conductivity

\(\frac{{k}_{nf}}{{k}_{f}}=\frac{\left(\frac{{k}_{s}}{{k}_{f}}+2\right)-2\varphi \left(1-\frac{{k}_{s}}{{k}_{f}}\right)}{\left(\frac{{k}_{s}}{{k}_{f}}+2\right)+\varphi \left(1-\frac{{k}_{s}}{{k}_{f}}\right)}.\)

\(\frac{{k}_{hnf}}{{k}_{bf}}=\frac{{k}_{{s}_{2}}+\left(n-1\right){k}_{bf}-\left(n-1\right){\phi }_{2}\left({k}_{bf}-{k}_{{s}_{2}}\right)}{{k}_{{s}_{2}}+\left(n-1\right){k}_{bf}+{\phi }_{2}\left({k}_{bf}-{k}_{{s}_{2}}\right)}\),

Where,

\(\frac{{k}_{bf}}{{k}_{f}}=\frac{{k}_{{s}_{1}}+\left(n-1\right){k}_{f}-\left(n-1\right){\phi }_{1}\left({k}_{f}-{k}_{{s}_{1}}\right)}{{k}_{{s}_{1}}+\left(n-1\right){k}_{f}+{\phi }_{1}\left({k}_{f}-{k}_{{s}_{1}}\right)}\),

Back to article page