Analytical Solution of a Two-Dimensional Transient Parabolic Boundary Value Problem subjected to Space and Time Dependent Conditions
An analytical solution of the two-dimensional parabolic boundary value problem is developed in the present paper. This analytical solution is versatile in nature and can be used to solve groundwater flow as well as heat flow equations in two-dimensions subjected to space and time-dependent conditions. The complexity of the flow system increases when the initial and boundary conditions become variable in space and time and that is generally the real field case. Many 2-D groundwater flow problems remain unsolved analytically for which either numerical solution or Laplace transformation approached is used. Many a times, Laplace or Fourier transformation solution ceases due to complicacy in achieving the inverse transformation. In such potential difficulties, the proposed analytical solution can be an important tool. The application of the analytical solution has been illustrated with the aid of an example.
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