An Analytic Benchmark for H1 Heat Transfer With Slip in an Equilateral Triangular Duct

Abstract

Abstract. We derive a fully analytic benchmark for thermally fully developed H1 heat transfer with slip in an equilateral triangular duct. The result complements the semi-analytic benchmark data reported by Wang (2013) (“Benchmark Solutions for Slip Flow and H1 Heat Transfer in Rectangular and Equilateral Triangular Ducts,” ASME J. Heat Mass Transfer-Trans. ASME 135(2), p. 021703). For the classical no temperature-jump limit γ=0, the temperature field is obtained via an eigenfunction expansion built from threefold symmetric Dirichlet modes. The associated energy integral is evaluated in closed form, leading to an explicit Nusselt-number formula. Representative values are tabulated and provide a convenient reference for numerical verification.