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Year 2007, Volume 38 / Issue 6

DOI: 10.1615/HeatTransRes.v38.i6

Pages: 88

DOI: 10.1615/HeatTransRes.v38.i6.80

Article price - $35.00

On the Paradox about the Propagation of Thermal Energy Speed in a Semi-Infinite Body Heated by a Forced Convective Flow

Antonio Campo
Department of Mechanical Engineering, The University of Vermont, Burlington, VT 05405, USA

Salah Chikh
Faculté de Génie Mécanique et de Génie des Procédés Université des Sciences et de la Technologie Houari Boumedienne, B. P. 32 EL Alia, Bab Ezzouar 16111, Algeria

An algebraic evaluation proclaims that the surface heat flux in a semi-infinite body with uniform initial temperature T₀ and prescribed uniform temperature T_S at the exposed surface ascends to infinity when time approaches zero. This unreasonable behavior responds to a well-known pathology of the phenomenological Fourier's law that translates into an infinite speed of thermal energy propagation in semi-infinite bodies, which is extensive to finite bodies. From thermal physics, it is expected that when the uniform temperature T_S at the exposed surface in a semi-infinite body (a Dirichlet boundary condition) is replaced by a generalized convective boundary condition (a Robin boundary condition), the surface heat flux should climb up to infinity also when time approaches zero. Two answers exist. The prevalent abnormal situation happens when the phenomenological Fourier's law is applied at the exposed surface, i.e., from the solid side. On the contrary, the abnormal situation does not occur when the empirical Newton's "equation of cooling" is applied at the exposed surface, i.e., from the fluid side.

pages 565-572

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