Table 2 The effective characteristics of hybrid nanofluids associated with Fe3O4 and MWCNTs are given below, Khan et al.24.

From: A comparative study of finite difference approach and bvp4c techniques for water base hybrid nanofluid containing multiple walls carbon nanotubes and magnetic oxide

Property

Hybrid nanofluid

Effective viscosity

\(\mu_{h\,n\,f} = \mu_{f} \left( {1 - \phi_{hnf} } \right)^{ - 2.5}\)

Density

\(\rho_{hnf} = \rho_{{Fe_{3} O_{4} }} \phi_{{Fe_{3} O_{4} }} + \rho_{MWCNTs} \,\phi_{MWCNTs} + \rho_{f} \left( {1 - \phi_{hnf} } \right)\)

Buoyancy coefficient

\(\left( {\rho \beta } \right)_{h\,\,n\,f} = \phi_{{_{MWCNTs} }} \left( {\rho \beta } \right)_{{_{MWCNTs} }} + \phi_{{_{{Fe_{3} O_{4} }} }} \left( {\rho \beta } \right)_{{_{{Fe_{3} O_{4} }} }} + \left( {1 - \phi } \right)\left( {\rho \beta } \right)_{f}\)

Heat capacitance

\(\left( {\rho C_{p} } \right)_{hnf} = \left( {\rho C_{p} } \right)_{{Fe_{3} O_{4} }} \phi_{{Fe_{3} O_{4} }} + \left( {\rho C_{p} } \right)_{{_{MWCNTs} }} \phi_{{_{MWCNTs} }} + \left( {\rho C_{p} } \right)_{f} \left( {1 - \phi_{hnf} } \right)\)

Effective thermal conductivity

\(\begin{aligned}\frac{{{k_{h\,nf}}}}{{{k_f}}} &= \left(\begin{array}{l} \frac{\left( {{\phi _{_{F{e_{3\,}}{O_4}}}}{k_{_{F{e_3}{O_4}}}} + {\phi _{MWCNTs}}{k_{MWCNTs}}} \right)}{\phi _{hnf}} + 2{k_f}\\ + 2\left( {{\phi _{_{F{e_{3\,}}{O_4}}}}{k_{_{F{e_3}{O_4}}}} + {\phi _{MWCNTs}}{k_{MWCNTs}}} \right) - \left( {2{\phi _{hnf}}{k_f}} \right)\end{array}\right)\\ &\quad \times \left( \begin{array}{l} \frac{{\left( {{\phi _{_{F{e_{3\,}}{O_4}}}}{k_{_{F{e_3}{O_4}}}} + {\phi _{MWCNTs}}{k_{MWCNTs}}} \right)}}{{{\phi _{hnf}}}} + 2{k_{\,f}}\\ - \left( {{\phi _{_{F{e_{3\,}}{O_4}}}}{k_{_{F{e_3}{O_4}}}} + {\phi _{MWCNTs}}{k_{MWCNTs}}} \right) + \left( {{\phi _{hnf}}{k_f}} \right) \end{array} \right)\end{aligned}\)

Thermal diffusivity

\(\alpha_{h\,n\,f} = \frac{{k_{h\,n\,f} }}{{\left( {\rho C_{p} } \right)_{h\,n\,f} }}\)

Mass diffusivity

\(D_{h\,n\,f} = D_{f} \left( {1 - \phi_{hnf} } \right)\,Where\,\,\,\,\phi_{hnf} = \phi_{{Fe_{3} O_{4} }} + \phi_{MWCNTs}\)

Electrical conductivity

\(\frac{{\sigma_{hnf} }}{{\sigma_{f} }} = 1 + \frac{{3\left[ {\left( {\frac{{\phi_{{Fe_{3} O_{4} }} \sigma_{{Fe_{3} O_{4} }} + \phi_{{_{MWCNTs} }} \sigma_{{_{MWCNTs} }} }}{{\phi_{hnf} }}} \right) - \phi_{hnf} } \right]}}{{\left[ {\frac{{\phi_{MWCNTs} \sigma_{MWCNTs} + \phi_{{Fe_{3} O_{4} }} \sigma_{{Fe_{3} O_{4} }} }}{{\sigma_{f} \phi_{hnf} }} - \left( {\frac{{\phi_{{Fe_{3} O_{4} }} \sigma_{{Fe_{3} O_{4} }} + \phi_{{_{MWCNTs} }} \sigma_{{_{MWCNTs} }} }}{{\sigma_{f} }}} \right) - \phi_{hnf} } \right]}}\)

Back to article page