Analytical solution for unsteady heat transfer in a pipe

Under consideration is transient, convective heat transfer to a fluid flow within a pipe due to a sudden change in the temperature of the ambient medium outside the pipe. A solution is developed by the Laplace transformation, for the fastest portion of the transient, which gives the pipe wall temperature, surface heat flux, and fluid bulk mean temperature. These analytical results are compared with available finite difference results and with quasi-steady solutions. A criterion is developed that indicates when the zero-thermal capacity wall solution can be used with adequate accuracy