Symmetrical impulsive thermo-fluid dynamic field along a thick plate

Abstract

The thermo-fluid dynamic field arising on a thick and thermal conductive semi-infinite flat plate is studied when, on one of its sides, a viscous fluid is impulsively accelerated. The case of adiabatic conditions on the unwetted side of the plate is presented. This condition is also representative of symmetrical flow (with respect to the plate axis) around a thick plate with both sides wetted by the fluid. The adopted model, which has been developed in the case of Prandtl number equal to one, is based on an integral formulation of the governing equations. It has been already applied to the case of isothermal condition on the plate side; however main differences characterize the present more complex problem since the governing equations lead to a second-order hyperbolic equation in the space-time variables instead of a first-order one. The solution has been obtained by the Laplace's transformation technique. The effects of the main physical parameters on the temperature behavior at the solid–fluid interface are shown and discussed. The solution accuracy has been verified by comparing the results to those of the limiting case of plate of infinite length.