The Diffusion Problem for a Solid in Contact with a Stirred Liquid;

A cylindrical solid of length $a$ in a direction $x$ and of arbitrary cross-section normal to $x$ is in contact on its plane face $x=a$ with a well-stirred liquid. The face $x=0\mathrm{}$ of the solid and the lateral surface are impervious to heat. The liquid extends from $x=a$ to $x=a+b$. At $x=a+b$ the liquid is in contact with a source of heat at the constant temperature $\theta$, the transfer of heat from this source being proportional to the difference in temperature between the outside source and the liquid. If the initial temperatures of solid and liquid are given, the problem of the temperature distribution at any subsequent time can be obtained by means of a modification of the wellknown Fourier analysis.