Bejan’s Heat Flow Visualization for Unsteady Micropolar Fluid Past a Vertical Slender Hollow Cylinder with Large Grashof Number

Abstract

The heat function concept has been developed for the heatline visualization to study the conjugate heat transfer effects at large Grashof number. The time-dependent natural convective micropolar fluid flow past a vertical slender hollow cylinder with the inner wall kept at a uniform temperature is the physical model. The mathematical model of this problem is given by highly time reliant non-linear coupled equations and is resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and heat transport coefficients as well as the steady-state velocity, microrotation and temperature are plotted for different values of non-dimensional parameters arising in the system across the boundary layer. As the vortex viscosity parameter increases, the time taken for the flow-field variables to attain the time-independent state decreases, while the reverse trend is noticed for the conjugate heat transfer parameter. The dimensionless heat function values are closely associated with the overall rate of heat transfer. The Bejan’s heat flow visualization implies that the heat function contours are compact in the neighborhood of leading edge of the hot cylindrical wall. It is observed that as the vortex viscosity parameter values get amplified, the deviations of heatlines from the heated wall is more. It is seen that the deviations of flow variables from the heated wall for a micropolar fluid are significant compared to the Newtonian fluid.