Simultaneous use of non-uniform magnetic field and porous medium for the intensification of convection heat transfer of a magnetic nanofluid inside a tube

This paper investigates the influence of a magnetic field on the ferrofluid forced convection characteristics in a semi-porous tube by applying the finite volume method and the Darcy–Brinkman–Forchheimer model. Two-phase simulation is performed by taking into account the effects of Brownian motion, thermophoresis, and magnetophoresis of nanoparticles. Two cases are considered for this: case 1 with a porous medium at the center of the tube and case 2 with a porous layer in the vicinity of the wall. Some influential parameters, including magnetic and Darcy numbers, thickness, and thermal conductivity of porous medium, are studied in the pressure drop and heat transfer enhancement in both cases. Results indicate that in case 1, the applied magnetic field (with Mn=1×106\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Mn = 1 \times 10^{6}$$\end{document}) can only lead to an increase of about 78% while a porous medium (with Da=10-4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Da = 10^{ - 4}$$\end{document}) causes a 78% improvement alone. The effect of both techniques simultaneously will, however, result in an approximately 120% enhancement in the heat transfer rate.