RT Journal Article
ID 57d6f1cf1fc0557f
A1 Campo, Antonio
A1 Chikh, Salah
T1 On the Paradox about the Propagation of Thermal Energy Speed in a Semi-Infinite Body Heated by a Forced Convective Flow
JF Heat Transfer Research
JO HTR
YR 2007
FD 2007-10-17
VO 38
IS 6
SP 565
OP 572
AB 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.
PB Begell House
LK https://www.dl.begellhouse.com/journals/46784ef93dddff27,1fb87f7a0d02e7a7,57d6f1cf1fc0557f.html