Abstract
This paper discusses the integration of unsteady onedimensional nonlinear problems of the heat conduction or diffusion type. In all cases the diffusivity coefficient is dependent upon the state variable, and hence the problem is nonlinear. A simpler system is produced by reducing the original PDE I-BVP to a nonlinear ODE BVP, which is subsequently solved in closed-form. This solution is applicable to several classes of problems, including mass, momentum and energy transport phenomena. A fluid flow example in a hydrocarbon reservoir is presented as a special case, and interpreted in terms of well interference testing.
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