Laplace solution for heat transfer model of dam leakage

The mechanism of the action between the leakage and temperature field in the dam was analyzed.Based on the heat transfer and the combination of the conservation of energy equation,heat transfer model in the dam was presented.Dimensionless equations of the transfer model obtained in the Laplace spaces at the boundary and initial condition were expressed in terms of ordinary Bessel function.The analytical solutions in real spaces were made by the contour integration method.A practrical example was given,and the numerical computation was completed by the Mathematica software package as well.