Exact analytical solution for 2-D transient heat conduction in a rectangle with partial heating on one edge

An exact solution is presented for two-dimensional transient heat conduction in a rectangular plate heated at y = 0 from x = 0 to x = L1 and insulated over the other edges. This problem does not have a steady-state solution, but does have a quasi-steady solution. Because of this, Green's functions are used to determine the exact solution. The solution consists of four parts, each of which is determined separately and totalled at the end to achieve the complete solution. A number of algebraic identities are used to reduce some steady- and quasi-steady state series in the solution. Intrinsic verification principles are used to verify the solution. The solution can be used as a building block for a number of related problems.