In a 2D plane heat flux q'' is incident on an insulation layer (which has a thickness L and a thermal conductivity k). The bottom surface of this insulation layer is exposed to water cooling with a velocity v and thermal conductivity k_w. The bottom surface of the water cooling channel is perfectly insulated. The goal here is to determine the temperature of the bottom surface of the water cooling.
My steps are as follows: q'' = k * ΔT / L => ΔT = q'' * L / k. For water cooling, the Reynolds Number (Re) is calculated as Re = ρ * v * l / μ. The Nusselt Number (Nu) is Nu = 0.023 * (Re^0.8) * (Pr^0.3) = h * L / k_w. From this point, I can find the convective heat transfer coefficient (h). Instead of using the water channel's inlet and outlet temperatures, is it possible to calculate the insulated bottom surface temperature (Tb) by determining the mean water temperature? What should be the remaining steps to find Tb? You may consider other parameters if required.