Table 8. Thermo-physical properties of... | Emerald Publishing

Table 8.

Thermo-physical properties of tetra-hybrid nanofluid (Paul and Das, 2024; Guedri et al., 2026)

Property	Formula
Density	$ρ_{t e t h n f} = (1 - ϕ_{4}) ((1 - ϕ_{3}) ((1 - ϕ_{2}) ((1 - ϕ_{1}) ρ_{f} + ϕ_{1} ρ_{s 1}) + ϕ_{2} ρ_{s 2}) + ϕ_{3} ρ_{s 3}) + ϕ_{4} ρ_{s 4}$
Dynamic viscosity	$μ_{t e t h n f} = \frac{μ_{f}}{{(1 - ϕ_{1})}^{2.5} {(1 - ϕ_{2})}^{2.5} {(1 - ϕ_{3})}^{2.5} {(1 - ϕ_{4})}^{2.5}}$
Thermal conductivity	$\frac{k_{t e t h n f}}{k_{f}} = {\begin{cases} \frac{k_{s 4} + 2 k_{t h n f} - 2 ϕ_{4} (k_{t h n f} - k_{s 4})}{k_{s 4} + 2 k_{t h n f} + ϕ_{4} (k_{t h n f} - k_{s 4})} \times \frac{k_{s 3} + 2 k_{h n f} - 2 ϕ_{3} (k_{h n f} - k_{s 3})}{k_{s 3} + 2 k_{h n f} + ϕ_{3} (k_{h n f} - k_{s 3})} \times \\ \frac{k_{s 2} + 2 k_{n f} - 2 ϕ_{2} (k_{n f} - k_{s 3})}{k_{s 2} + 2 k_{n f} + ϕ_{2} (k_{n f} - k_{s 3})} \times \frac{k_{s 1} + 2 k_{f} - 2 ϕ_{1} (k_{f} - k_{s 1})}{k_{s 1} + 2 k_{f} + ϕ_{1} (k_{f} - k_{s 1})} \end{cases}$
Heat capacity	${(ρ C p)}_{t e t h n f} = (1 - ϕ_{4}) ((1 - ϕ_{3}) (\begin{array}{l} (1 - ϕ_{2}) (\begin{array}{l} (1 - ϕ_{1}) {(ρ C p)}_{f} \\ + ϕ_{1} {(ρ C p)}_{s 1} \end{array}) \\ + ϕ_{2} {(ρ C p)}_{s 2} \end{array}) + ϕ_{3} {(ρ C p)}_{s 3}) + ϕ_{4} {(ρ C p)}_{s 4}$
Thermal expansion	${(ρ β)}_{t e t h n f} = (1 - ϕ_{4}) ((1 - ϕ_{3}) (\begin{array}{l} (1 - ϕ_{2}) (\begin{array}{l} (1 - ϕ_{1}) {(ρ β)}_{f} \\ + ϕ_{1} {(ρ β)}_{s 1} \end{array}) \\ + ϕ_{2} {(ρ β)}_{s 2} \end{array}) + ϕ_{3} {(ρ β)}_{s 3}) + ϕ_{4} {(ρ β)}_{s 4}$
Electrical conductivity	$\frac{σ_{t e t h n f}}{σ_{f}} = {\begin{cases} \frac{σ_{s 4} + 2 σ_{t h n f} - 2 ϕ_{4} (σ_{t h n f} - σ_{s 4})}{σ_{s 4} + 2 σ_{t h n f} + ϕ_{4} (σ_{t h n f} - σ_{s 4})} \times \frac{σ_{s 3} + 2 σ_{h n f} - 2 ϕ_{3} (σ_{h n f} - σ_{s 3})}{σ_{s 3} + 2 σ_{h n f} + ϕ_{3} (σ_{h n f} - σ_{s 3})} \times \\ \frac{σ_{s 2} + 2 σ_{n f} - 2 ϕ_{2} (σ_{n f} - σ_{s 3})}{σ_{s 2} + 2 σ_{n f} + ϕ_{2} (σ_{n f} - σ_{s 3})} \times \frac{σ_{s 1} + 2 σ_{f} - 2 ϕ_{1} (σ_{f} - σ_{s 1})}{σ_{s 1} + 2 σ_{f} + ϕ_{1} (σ_{f} - σ_{s 1})} \end{cases}$