Mathematical Modeling of Free Convection Flow and Boundary Layer Control

摘要

Gyarmati's variational principle developed on the thermodynamic theory of irreversible processes is formulated for the problem of heat transfer in free convection boundary layer flow with suction and injection over a non-isothermal flat plate. The velocity and temperature functions inside their respective boundary layer are approximated by simple polynomial functions and the variational principle is formulated. The hydrodynamical and thermal boundary layer thicknesses are derived as the Euler-Lagrange equations of the variational principle. The skin friction and heat transfer values were computed for different values of suction and injection parameter, Prandtl number and wall temperature exponent. The obtained analytical solution for different values of Prandtl number, suction and injection parameter and wall temperature exponent is compared with the known solution and the comparison shows in good agreement.