# Rate of heat transfer and heat conductors

by alexbib
Tags: conductors, heat, rate, transfer
 Emeritus Sci Advisor PF Gold P: 11,155 It's not a straightforward calculation : If the water is contained in a vessel or cavity, what is the temperature of the walls of the vessel/cavity. Is this temperature going to change, ie : is the vessel infinitely thick compared to the volume of water ?) You need to set up a 2D heat flow equation inside the water, and you need to add heat loss due to evaporation (though this is probably small). Assume some temperature distribution T(r,z) for a cylindrical pool. Then : $$Q_r = -KA(r) {\frac {\partial{T}} {\partial{r}}}, and$$ $$A(r) = 2\pi rh$$ Similarly for the z-direction. Try a separable solution. Put in the boundary conditions and solve.