Problem of a Ball Cooling Down with a Heat-Transfer Coefficient Depending on the Temperature Head at the Ball Surface

In view of the centrosymmetric character of the process, solving the problem must give the current (at a moment of time τ ) temperature distribution T = T ( r , τ ) along the radial coordinate r of the ball. When considering the ball cooling ( T > θ ), it is convenient to introduce the excess temperature t © T — θ (ball temperature relative to the temperature θ of the environment) and to seek t = t ( r , τ ) . Mathematically, the problem is formulated as [1‐3]