General solutions of the diffusion equations coupled at boundary conditions

Abstract

New finite integral transform and the corresponding inversion formula are introduced for the solution of the diffusion equations in a finite region of arbitrary geometry and initial conditions with general coupling boundary conditions. The resulting eigenvalue problem does not fall within the range of the conventional Sturm-Liouville system and therefore a new integral condition was devised which serves as an orthogonality relation. The solutions obtained permit the studying of many new problems, such as heat transfer coefficients in concurrent flow double pipe heat exchangers, simultaneous heat and mass transfer in internal gas flows in a duct whose walls are coated with a sublimable material and elsewhere. In addition the Luikov system of equations of a simultaneous mass and heat transfer in a finite capillary porous body of arbitrary geometry are rearranged to the pure diffusion equations coupled only at boundary conditions and consequently to a special case of the problem studied here.