I am an engineer trying to design a simple 1D program for evaluating the temperatures of a multi-layer heatsink that includes convection and radiation heat transfer from the external surface.
For a known heat input to the bottom layer, I want to calculate the bottom surface temperature of the first layer given the material properties, and the radiation and convection properties of the external surface.
In heat transfer textbooks I've found the flat plate model with constant heat flux model to be applicable. In this model, the temperature of the external surface is allowed to vary but heat rejection from it is a constant rate in the flow direction. In an example it is shown that the maximum plate temperature occurs at the trailing edge, and can be found from Newton's law of cooling by Ts(L) = Tf + Qdot"/h(L), where Ts(L) is the trailing edge surface temperature, Tf is the incoming free stream temperature [K], Qdot" is heat input rate per unit area [W/m^2], and h(L) is the convection coefficient at the trailing edge [W/(m^2*K)], calculated from the Nusselt number fluid conductivity and plate thickness.
I would like to couple this model with one that includes radiation from the external surface. For this I will solve for the temperature of the external surface at each point and then iteratively calculate the combined heat transfer until it matches the heat input.
My question is how accurate is the surface temperature calculation using the iso-flux condition with thermal boundary layer theory? According the model, the leading edge of the plate should be at the incoming free stream temperature, and have infinite heat transfer rate. This isn't reasonable because it seems a plate strongly heated in a low convection stream would have a leading edge temp greater than the free stream. What then is the accuracy of the model vs the distance from the edge?
Does anyone have any insight into the accuracy of the model or what I can use, or what references I can review to improve accuracy for this calculation?