Immersed boundary method for MHD unsteady natural convection around a hot elliptical cylinder in a cold rhombus enclosure filled with a nanofluid

摘要

In this study, the numerical investigation of the natural convection heat transfer around a hot elliptical cylinder inside acold rhombus enclosure filled with a nanofluid in the presence of a uniform magnetic field is conducted. An immersedboundary method as a computational tool has been extended and applied to solve the problem. The influence ofvarious parameters such as cylinder diameters (a, b), Hartmann number (Ha = 0, 50 and 100), nanofluid volume fraction( Φ = 0, 2.5%and5% ), and Rayleigh number (Ra = 1~03, 10~4,10~5,10~6,and 10~7)has been studied. Streamlines and isothermscontours as well as average Nusselt number have been specified for different modes. An equation for the average Nusseltnumber as a function of mentioned parameters is presented in this paper. The results show that at lower Ra numbersof Ra = 10~3 and 10~4,the magnetic field effect is negligible. However, at higher Rayleigh numbers, the average Nusseltnumber (Nuave) decreases with the increasing Ha number. The maximum decrease in Nuaveat Ra = 10~5, 10~6 and 10~7arecalculated −8.15%, −23.4% and −27.3%, respectively. An asymmetry-unsteady flow is observed at Ra = 10~7 for Ha = 0.However, at higher Ha numbers a steady-symmetrical flow is formed.