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Cooling of a plate with general boundary conditions. (English) Zbl 0955.35036

Summary: We consider the steady state temperature distribution in a homogeneous rectangular infinite plate the lower part of which is cooled by a fluid flowing at a constant velocity while the upper part satisfies general mixed boundary conditions. The Wiener-Hopf method has been used to obtain the solution in infinite series form and some special cases have been discussed.

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
80A20 Heat and mass transfer, heat flow (MSC2010)
35C10 Series solutions to PDEs
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