MHD forced convection of nanofluid flow in an open-cell metal foam heatsink under LTNE conditions

Abstract

In this paper, nanofluid forced convective heat transfer through an open-cell metal foam heatsink under a uniform heat flux, numerically has been investigated. A uniform magnetic field has been applied to the nanofluid flow. For the momentum equation, Darcy–Brinkman model and, for the energy equation, two-equation model under the condition of fully developed from the thermal and hydrodynamical standpoints have been used. In recent study, by utilizing a numerical method, an attempt was made to avoid a complete and complex CFD approach. To validate the results, the dimensionless parameters such as non-dimensional velocity and temperature, pressure gradient and Nusselt number have been compared with previous researches and a good agreement appeared. Eventually, the effects of different dimensionless parameters such as porosity, Hartman number, nanofluid volume fraction, Reynolds number, thermal conductivity ratio and pore density on the hydrodynamical and thermal characteristics of heatsink have been investigated. The outcomes show that the rise of pore density and Hartman number and the decline of the porosity will enhance the thermal performance; however, it also will reinforce the resistance to the flow through the porous media. Focusing on results illustrates that Nusselt number variation for increasing porosity from 0.85 to 0.95 at the minimum and maximum of the pore density are $$\left( {\Delta {\text{Nu}}_{{\left(\upvarepsilon \right)}} } \right)_{{\upomega = 10}} = - 331.7$$ and $$\left( {\Delta {\text{Nu}}_{{\left(\upvarepsilon \right)}} } \right)_{\omega = 60} = - 367.8$$ , and these values for friction factor are equal to $$\left( {\Delta f_{{\left(\upvarepsilon \right)}} } \right)_{{\upomega = 10}} = - 22.3$$ and $$\left( {\Delta f_{{\left(\upvarepsilon \right)}} } \right)_{{\upomega = 60}} = - 793$$ , respectively. On the other hand, increasing Hartman number from 0 to 100 would change the Nusselt number and friction factor as $$\left( {\Delta {\text{Nu}}_{{\left( {\text{Ha}} \right)}} } \right)_{{\upomega = 10}} = 9.4$$ , $$\left( {\Delta {\text{Nu}}_{{\left( {\text{Ha}} \right)}} } \right)_{{\upomega = 60}} = 0.2$$ , $$\left( {\Delta f_{{\left( {\text{Ha}} \right)}} } \right)_{{\upomega = 10}} = 213$$ , and $$\left( {\Delta f_{{\left( {\text{Ha}} \right)}} } \right)_{{\upomega = 60}} = 211$$ , respectively. The amount of Hartman and Reynolds numbers effects on the heat transfer rate depends on the pore density. In other words, when the pore density becomes saturated, the effects of these parameters decrease. In addition, the use of nanofluid will improve the heatsink thermal performance.