Modeling of anisotropic flow and thermodynamic properties of magnetic nanofluids induced by external magnetic field with varied imposing directions

Magnetic field can enhance both thermal conductivity and Lorentz force resistance of the magnetic nanofluids (MNFs), in which the former is favored while the latter often leads to pressure drop of the flow. It is assumed that there would exist a balance between the magnetic field induced thermal conductivity and Lorentz force if one can appropriately adjust the angle of the imposing magnetic field with respect to the direction of the flow. In the present study, the effects of direction of magnetic field (⁠$α)$ on anisotropic thermodynamic properties of magnetic nanofluids in channel were studied. The effects of direction of magnetic field on thermal conductivity, Nusselt number, global total entropy generation, and other parameters, such as velocity, temperature, and concentration, have been discussed in detail. A greater $α$ can lead to a larger thermal conductivity normal to the walls of channel and a more uniform temperature field. However, the velocity of magnetic nanofluid tends to decrease. There is a threshold for magnetic intensity (B). When magnetic intensity becomes large than the threshold, its effect on thermal conductivity will tends to be constant. The effect of increase of $α$ is found to be similar to that of increasing Hartmann number (⁠$Ha$⁠) and both can lead to augment of Lorentz resistance force along flow direction. With the increases of $α$ and $Ha$⁠, both heat transfer efficiency (Nu) and global total entropy generation (⁠$ST$⁠) increase. Here, $ST$ indicates the extent of loss of useful work due to the irreversibility of the process. A comprehensive utility index, $Iu$⁠, is defined for evaluation of the performance of a practical heat transfer system employing MNFs. For the case where the purpose of heat transfer is to cool an equipment such as electrical device, guaranteeing heat transfer efficiency (Nu) is more important than decreasing useful energy loss (⁠$ST$⁠); thus, we propose a large $α$ relative to the flow direction. For industrial processes, where energy loss (⁠$ST$⁠) have to be particularly considered, a small $α$ is recommended.