Forced convection from a rectangular heat source in uniform shear flow: The conjugate Peclet number in the thin plate limit

An analytical Green's function method is used to formulate the solution to conjugate heat transfer from rectangular heat sources on thin conducting boards in boundary layer flow. The boundary layer flow is modeled by a uniform shear flow approximation. The Green's functions, which are solutions to the temperature field that arises from a point heat source on the surface, provide a relationship between the local heat flux and surface temperature on the plate, effectively serving the same role as the heat transfer coefficient. The conjugate solution is found by coupling the pointwise Green's function to a finite element discretization of the thin plate. An extensive parametric study was performed on the effects of Peclet number, board conductivity and thickness, and heat source geometry. A robust correlation for conjugate heat transfer is presented for the limit where the substrate plate can be considered to be thin. The correlation simultaneously accounts for the effects of convective heat transfer and conduction heat transfer into the plate through the use of a conjugate Peclet number defined for the thin plate limit.