https://orcid.org/0000-0002-3678-1641
Abstract
Recently, Jain [ASME J. Heat Mass Transfer, 220 (2024)] provided spreading-resistance formulas for an isothermal source on compound, orthotropic, semi-infinite, two-dimensional (axisymmetric) flux channels (tubes). The boundary condition (BC) in the source plane was a discontinuous convection (Robin) one. Along the source, a sufficiently large heat transfer coefficient was imposed to approximate an isothermal condition; elsewhere, it was set to zero, imposing an adiabatic BC. An eigenfunction expansion resolved the problem. Distinctly, we impose, precisely, a mixed isothermal-adiabatic BC in the source plane and use conformal maps to resolve the spreading resistance for the limiting case of a compound, isotropic flux channel. Our complimentary approach requires more time to compute the spreading resistance. However, it converges uniformly rather than pointwise, converges to the exact spreading resistance rather than one with an error, eliminates the Gibbs phenomenon at the edges of the source and fully resolves the square-root singularities in heat flux as the discontinuity in the BC is approached.
Issue Section:
Conduction
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