# Solid in Liquid Heat Transfer

If there is a solid immersed in a large (but finite) pool of water, where the solid has temperature $T_s$ and the water has temperature $T_w$, with $T_w>T_s$, how can I calculate $T_s(t)$ and $T_w(t)$? (Suppose that the masses and the material properties of the solid are known.)

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The solution $T_s(x,y,z,t)$ will give you the evolution of temperature at every point of the solid.
The boundary condition is $\nabla T = aT + b$ with $a$, $b$ constants because you will suppose that energy is exchanged by natural convection and conduction (the latter might be neglected depending on the properties of the bodies and the initial conditions) .