Natural convection of nanoliquid from elliptic cylinder in wavy enclosure under the effect of uniform magnetic field: numerical investigation

In the current article, a three-dimensional numerical simulation is conducted to scrutinize the steady laminar natural convective flow and transfer of heat between a cold wavy porous enclosure and a hot elliptic cylinder. Alumina nanoparticles are dispersed in the water to enhance the heat exchange process. The nanofluid flow is taken as laminar and incompressible, while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The influences of different governing parameters such as nanoparticles volume fraction (ϕ), angle of rotation (α), Darcy number (Da), Hartmann number (Ha), and Rayleigh number (Ra) on the fluid flow, temperature (T) filed and average Nusselt number are presented. The results exhibit that the heat transfer is enhanced when either of Ra, Da and ϕ is raised. The permeability increment achieved a 12.73% enhancement in the heat transfer rate. Also, when Ha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Ha}$$\end{document} is altered from 0 to 100, a reduction in values of the Nusselt number is given up to 22.22%. Furthermore, the optimal inclination angle for the convective process is α = 45°.