Integral transform solution of transient forced convection in external flow

The Generalized Integral Transform Technique (GITT), under its partial transformation mode, is employed in the hybrid numerical–analytical solution of transient laminar forced convection over flat plates, subjected to arbitrary time variations of wall heat flux applied from above. From the available Blasius velocity distributions and employing a coordinate transformation to account only for the thermally affected region along the main flow direction, the transient temperature distribution is expanded in terms of eigenfunctions obtained from the diffusion operator in the transversal direction. The resulting coupled system of partial differential equations for the transformed potentials is numerically solved in terms of the dimensionless time variable and longitudinal coordinate, by making use of the method of lines implemented in the Mathematica routine NDSolve. Numerical solutions for the wall temperature and heat transfer coefficient are then readily computed, yielding the time evolution and the longitudinal distribution of these parameters, for any specified wall heat flux time function.