The effect of non-uniform gravity on mixed convection along a vertical surface

摘要

This paper considers the effect of non-uniform gravity on mixed convection along a vertical plate with an inverse-linear temperature distribution. The gravity varies with the distance from the leading edge of the isothermal plate. Two cases are taken into account: a) finite hot plate of length x_0, rotating at angular speed ω in a radial plane about the line x = 0 (where x is the coordinate along the plate); b) infinite cold plate, rotating at angular speed w in a radial plane with its leading edge beginning at a distance x_0 from the axis of rotation. A pseudo-similarity transformation in the new variables (ζ, η) is introduced in order to obtain a parabolic system of differential equations in non-similar form, which is solved by means of the Keller-box method. Using a non-uniform grid, concentrated towards the wall to enhance the resolution and accuracy, with the first step of T taken as 0.01, we used throughout the calculations a value η_(max) = 10 and a number of 241 points in the η-direction. The grid along the ζ axis was concentrated towards ζ = 0 and the number of points on this direction was 121. The level of precision imposed to the Keller-box scheme was le-10. The skin-friction coefficient and Nusselt number are obtained for various values of the Prandtl number and mixed convection parameter λ. Both aiding and opposite effects are considered.