Finite element analysis of mixed convection flow in a trapezoidal cavity with non-uniform temperature

Abstract

A two dimensional flow analysis in a cavity shaped isosceles trapezium is carried out. Non-parallel sides of a trapezium are adiabatic. A varying sinusoidal temperature is applied to the lower wall while the upper wall is at constant temperature. Upper wall of the cavity moves with a velocity η0 in the positive x-direction. Also, B0 is constant magnetic field of strength aligned in the same x-direction and Newtonian fluid is considered. The values of magnetic field parameter used are Ha=0,50, the Richardson number is Ri=0.1,1,10, Re=100 is Reynolds number used for the analysis, the amplitude of sinusoidal temperature is m=0.25,0.5,1. The impacts of different leading parameters are analyzed by plotting streamlines for flow fields and isotherm contours for temperature of the flow dynamics. The graphs that signify the variation of average Nusselt number and local Nusselt number are sketched for both lower and upper walls of the cavity. Result indicated that with constant temperature the top wall of the boundary layer thickness decreases as Richardson number Ri increases and for bottom wall with variable temperature. The Nusselt number gets higher with an increment in the amplitude of the oscillation of temperature function. Furthermore, the study revealed that the average Nusselt number gets reduced as the intensity of magnetic field is enhanced. The variation in transit of heat at the bottom wall is similar but the maximum value of heat transfer at the bottom wall shows a variation from 3.8 to 20 when Ha=0 and from 3 to 18 when Ha=50. The accuracy of the present numerical algorithms is also established.