ANALYTICAL SOLUTION FOR THE TRANSIENT TEMPERATURE DISTRIBUTION IN A MOVING ROD OR PLATE OF FINITE-LENGTH WITH SURFACE HEAT-TRANSFER

An analytical solution for the transient temperature distribution in a wide flat plate and in a cylindrical rod of finite length moving at a constant speed and subjected to convective heat transfer at the surfa ce is obtained. The analytical solution is obtained as an infinite ser ies. However, inclusion of the first 25 terms of the series was found to be sufficient to obtain a converged solution in most caws. The anal ytical solutions are compared with previously obtained numerical solut ions for this moving boundary problem. Excellent agreement between the analytical and numerical results is obtained, indicating the importan ce of the analytical solution for the validation of numerical schemes. The variation of the temperature field within the material with time is investigated. Even though this is one of the first attempts to solv e, analytically, the problem of a finite-length moving material subjec ted to surface heat transfer, the analytical solutions are found to be of limited use at moderate or large times. However, at very small tim es, following the start of the process, numerical solutions are often quiet inaccurate. Then the analytical results are particularly useful. The versatility and ease of application of the numerical method are d iscussed.