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The Joule-Thomson effect on the thermoelectric conductors. (English) Zbl 1162.35358

Summary: The transmission of an electric current in a conductor is a process in which some electrical energy is converted into heat (thermal energy). We deal with a nonlinear boundary value elliptic problem which describes the electrical heating of a solid conductor and the Joule-Thomson effect is taken into account. The existence of a weak solution is proved under both space and temperature dependence of the electrical and thermal conductivities. When the coefficients are only dependent on their temperature argument, some regularity results are stated.

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J60 Nonlinear elliptic equations
78A99 General topics in optics and electromagnetic theory
80A20 Heat and mass transfer, heat flow (MSC2010)
35D05 Existence of generalized solutions of PDE (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B65 Smoothness and regularity of solutions to PDEs
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