Numerical Investigation of Hydromagnetic Effect on the Natural Convection Heat Transfer from Circular Cylinder in an Enclosed Enclosure

Abstract

The natural convection heat transfer from horizontal circular cylinder placed in a square enclosure is investigated numerically. The study deals with the effect of magnetic field on the flow and heat transfer characteristics. The investigation employs different Hartman numbers (0, 50, 100, 200), different Rayleigh numbers (10³, 10⁴, and 10⁵) with constant enclosure width to cylinder diameter ratios W/D = 2.5. The study included the solving of the governing equations in the form of the vorticity-stream function to be fitted with coordinate system. The algebraic grid generation is used to generate initial transformation. The elliptic grid generation is used to fit with physical domain between the heated horizontal cylinder and the enclosure into a computational domain. The resulting equations are solved using finite difference method that based on the finite volume. The research studied the influence of the variation the Hartman number on the local and average Nusselt numbers, flow patterns and temperature distributions with different Rayleigh numbers. The effect of Hartman numbers on the flow patterns and temperature distributions will be displayed using streamlines and isotherms. The results show that the conduction heat transfer is the dominant mode for low Rayleigh numbers. The convection heat transfer is the dominant mode of the heat transfer for high Rayleigh number in absence of the magnetic effect. The convection heat transfer convert to conduction mode at high Rayleigh numbers due to the effect of the magnetic field in the fluid. Also, the results show that the behavior of the local Nusselt numbers for Ha = 0 are unique and differ from those of other higher Hartman numbers for all Rayleigh numbers.