Parametric study of unsteady forced convection with pressure gradient

By an extension of differential method, this paper has successfully examined the unsteady forced convection heat transfer from a flow over a flat plate. Transient state is inherent to a sudden change on the heat flux density at the surface of a plate. The general case where the pressure along the direction of flow is not constant is presented. The differential momentum and heat transfer equations are solved numerically. The results are given for different values of pressure gradient parameter m, in the cases of attached boundary layer, and for several values of Prandtl number corresponding to usual fluids (0.71 ⩽ Pr ⩽ 100). The dependences of transient behaviours with Pr number and parameter m are evidenced from the evolutions in time of temperature profile, Stanton number, and duration of unsteady process. Solutions given from the beginning of transient state to the ultimate steady state are discussed. Moreover, analytical solutions, as function of Pr and m, are deduced for Stanton number and duration of unsteady regime.