Analytic solution of a free and forced convection with suction and injection over a non-isothermal wedge (Q934250)

The authors apply the governing principle of dissipative processes to the problem of boundary-layer free and forced convection flows and heat transfer over a permeable non-isothermal wedge with suction and injection, using the thermodynamics of irreversible processes. The velocity and temperature functions inside the boundary layers are approximated by simple third-order polynomials, and a variational principle is formulated. In addition, Euler-Lagrange equations of the variational principle are obtained as coupled polynomial equations in terms of momentum and thermal boundary-layer thickness. The governing parameters in this problem are the local Reynolds number \(Re\), Prandtl number \(Pr\), Grashoff number \(Gr\), buoyancy parameter \(K\), the wall temperature exponent \(n\), wedge parameter \(\beta\) and the dimensionless suction/injection parameter \(S\). Values of skin friction and heat transfer obtained in this paper for \(Pr=0.7, \beta = 0\) (flat plate) and impermeable plate are compared with the results from the literature, and it is shown that the agreement is good enough. Further, the variation of skin friction coefficient and heat transfer along the wedge is shown in eight figures for several values of governing parameters. It is shown that when \(K < 0\), that is when \(T^0 - T^\infty < 0\) (cooled plate), and the free and forced convection are in the opposite directions, the flow separation occurs. Thus, the authors have shown that when \(\beta = 0.5, H = 0, n = 0\) (isothermal wedge) and \(Re = 100\), the boundary-layer flow separates for \(Pr = 0.7, 1.0\) and \(3.0\) at \(K = - 0.0952, - 0.1007\) and \(- 0.1322\), respectively. It reveals that the separation is delayed with the increasing Prandtl number \(Pr\). It is has been also shown that the flow separation is delayed with the increase in wall temperature exponent. Finally, the authors state that the great advantage involved in their method is that the results are obtained with remarkable accuracy and the cost of calculation is considerably less than that of numerical procedure. Hence, this variational technique is a unique approximate method based on sound physical reasoning as a powerful tool for solving heat transfer and boundary-layer problems.