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

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 [Formula: see text] in the positive x-direction. Also, [Formula: see text] 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 [Formula: see text] , the Richardson number is [Formula: see text] , [Formula: see text] is Reynolds number used for the analysis, the amplitude of sinusoidal temperature is [Formula: see text]. 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 [Formula: see text] and from 3 to 18 when [Formula: see text]. The accuracy of the present numerical algorithms is also established.