Table 4. Equations for estimating... | Emerald Publishing

Table 4.

Equations for estimating nanofluid properties

Nanofluid properties	Applied model
Thermal expansion coefficient	${(ρ β)}_{n f} = ϕ {(ρ β)}_{p} + (1 - ϕ) {(ρ β)}_{f}$
Density	$ρ_{n f} = (1 - ϕ) ρ_{f} + ϕ ρ_{p}$
Heat capacitance	${(ρ C_{p})}_{n f} = (1 - ϕ) {(ρ C_{p})}_{f} + ϕ {(ρ C_{p})}_{p}$
Thermal diffusivity	$α_{n f} = \frac{k_{n f}}{{(ρ C_{p})}_{n f}}$
Thermal conductivity	$\frac{k_{n f}}{k_{f}} = \frac{k_{p} + (n - 1) k_{f} - (n - 1) ϕ (k_{f} - k_{p})}{k_{p} + (n - 1) k_{f} + ϕ (k_{f} - k_{p})}$ ⁠, for nonspherical nanoparticles
	$\frac{k_{n f}}{k_{f}} = \frac{k_{p} + 2 k_{f} - 2 ϕ (k_{f} - k_{p})}{k_{p} + 2 k_{f} + ϕ (k_{f} - k_{p})}$ ⁠, for spherical nanoparticles
Dynamic viscosity	$μ_{n f} = μ_{f} (1 + A_{1} ϕ + A_{2} ϕ^{2})$ ⁠, for nonspherical nanoparticles
	$μ_{n f} = \frac{μ_{f}}{{(1 - ϕ)}^{2.5}}$ ⁠, for nanoparticles with spherical shape
Shape of the nanoparticle	χ	n = 3/χ	A₁	A₂
Blade	0.36	8.6	14.6	123.3
Cylinder	0.62	4.9	13.5	904.4
Platelet	0.52	5.7	37.1	612.6
Brick	0.81	3.7	1.9	471.4

Nanofluid properties	Applied model
Thermal expansion coefficient	${(ρ β)}_{n f} = ϕ {(ρ β)}_{p} + (1 - ϕ) {(ρ β)}_{f}$
Density	$ρ_{n f} = (1 - ϕ) ρ_{f} + ϕ ρ_{p}$
Heat capacitance	${(ρ C_{p})}_{n f} = (1 - ϕ) {(ρ C_{p})}_{f} + ϕ {(ρ C_{p})}_{p}$
Thermal diffusivity	$α_{n f} = \frac{k_{n f}}{{(ρ C_{p})}_{n f}}$
Thermal conductivity	$\frac{k_{n f}}{k_{f}} = \frac{k_{p} + (n - 1) k_{f} - (n - 1) ϕ (k_{f} - k_{p})}{k_{p} + (n - 1) k_{f} + ϕ (k_{f} - k_{p})}$ , for nonspherical nanoparticles
	$\frac{k_{n f}}{k_{f}} = \frac{k_{p} + 2 k_{f} - 2 ϕ (k_{f} - k_{p})}{k_{p} + 2 k_{f} + ϕ (k_{f} - k_{p})}$ , for spherical nanoparticles
Dynamic viscosity	$μ_{n f} = μ_{f} (1 + A_{1} ϕ + A_{2} ϕ^{2})$ , for nonspherical nanoparticles
	$μ_{n f} = \frac{μ_{f}}{{(1 - ϕ)}^{2.5}}$ , for nanoparticles with spherical shape
Shape of the nanoparticle	χ	n = 3/χ	A₁	A₂
Blade	0.36	8.6	14.6	123.3
Cylinder	0.62	4.9	13.5	904.4
Platelet	0.52	5.7	37.1	612.6
Brick	0.81	3.7	1.9	471.4

Sources: Yan et al. (2020); Dogonchi et al. (2021); Kumar et al. (2023)