Abstract
A method for obtaining approximate solutions of transient three-dimensional heat-conduction problems has been investigated here analytically and experimentally. The method is based on the well-known principle of analogy between flow of heat and electricity and comprises a continuous resistance medium of resistivity ρe but discrete capacitances, which are introduced into the resistance medium through spherical electrodes. It has been shown that the internal behavior of the system is influenced only by the pitch diameter ratio λ of the spheres. Fundamental solutions for the infinite medium have been obtained and the analysis has shown that the system behaves like one having a resistivity ρe* which can be calculated from the actual resistivity of the liquid and the steady-state Green’s function of the fluid-sphere system. Experiments for the determination of the steady-state and transient Green’s functions are described. The accuracy of the method has also been investigated, and an illustrative example is given.
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