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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.v38.i6.80
pages 565-572

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
USTHB, Faculty of Mechanical and Process Engineering, LTPMP, Alger 16111, Algeria

ABSTRACT

An algebraic evaluation proclaims that the surface heat flux in a semi-infinite body with uniform initial temperature T0 and prescribed uniform temperature TS 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 TS 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.


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