The forced convection flow of a uniform stream over a flat surface with a convective surface boundary condition

The forced convection heat transfer resulting from the flow of a uniform stream over a flat surface on which there is a convective boundary condition is considered. In previous papers [5], [6], [7] and [8] it was assumed that the convective heat transfer parameter hf associated with the hot surface depended on x, where x measures distance along the surface, so that problem could be reduced to similarity form. Here it is assumed that this heat transfer parameter hf is a constant, with the result that the temperature profiles and overall heat transfer characteristics evolve as the solution develops from the leading edge. The heat transfer near the leading edge (small x), which we find to be dominated by the surface heat flux, the solution at large distances along the surface (large x), which dominated by the surface temperature, are discussed. A numerical solution to the full problem is then obtained for a range of values of the Prandtl number to join these two solution regimes.

Research Highlights► Extension of previous work on variable heat transfer coefficients to a constant coefficient. ► Non-similarity solutions. ► Numerical solution of a forced convection boundary-layer flow. ► Series solutions valid near the leading edge and far downstream. ► Asymptotic solutions for small and large Prandtl numbers.