Most of the existing studies and derived correlations relate to a uniform and constant heat flux or temperature imposed on a solid surface on which a parallel flow is developed. More recent works deal with unsteady forced convection over a flat plate when the boundary conditions change in the time. The present study presents a mathematical model of the unsteady convective heat transfer when the heat flux density is variable in time. Based on the energy equation formulation, this allows the analysis of the heat transfer characteristics associated with a constant laminar parallel flow over a negligible thickness plate. Transients are induced by two heat flux step changes imposed on the plate surface. The modelling approach is based on two methods: the integral method where a fourth order Karman-Pohlhausen polynomials are used for velocity and temperature profiles within the boundary layers, and the differential method with similarity solution. The purpose of this work is to provide new insights into unsteady convection modelling. In addition, we meant to draw attention to some discordance between the temporal evolution of the dimensionless parameters and the physical ones.