Variational approach to free convection boundary-layer flow with suction and injection

The Gyarmati variational principle — a significant development in the field of the thermodynamics of irreversible processes — is employed to study suction and injection effects in flow and heat transfer in a free convection boundary layer over a cone. The velocity and temperature distributions inside respective boundary layers are considered as simple polynomial functions, and with the use of the perturbation procedure the variational principle is formulated. The Euler-Lagrange equations are reduced to coupled polynomial equations in terms of boundary-layer thicknesses. The skin-friction (shear-stress) and heat-transfer (Nusselt number) values with constant wall temperature are computed for various values of the suction and injection parameters and the cone-angle parameter. The comparison of the present solution with an available numerical solution shows good agreement. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 6, pp. 109–115, November–December, 2007.