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Low peclet number heat transfer in the thermal entrance region of parallel‐plate channels with unequal wall temperatures
Author(s) -
Wu Rayshing,
Cheng K. C.,
Ou JennWuu
Publication year - 1976
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450540529
Subject(s) - péclet number , mechanics , heat transfer , thermal conduction , thermal , boundary layer , thermal diffusivity , eigenfunction , thermodynamics , hagen–poiseuille equation , physics , materials science , flow (mathematics) , eigenvalues and eigenvectors , quantum mechanics
Abstract The problem of low‐Peclet‐number thermal entry heat transfer for plane Poiseuille flow in parallel‐plate channels with uniform but unequal wall temperatures is approached by the eigenfunction expansion method utilizing the Gram‐Schmidt orthonormalization procedure. The formulation considers axial heat conduction and allows upstream heat penetration through the thermal entrance. Numerical results are obtained for the case with entrance condition parameter θ 0 = 1 and Peclet number Pe = 1, 5, 10 and 50. The effect of Peclet number on temperature distributions in both upstream and downstream regions is studied. At Pe = 50, the concept of thermal boundary layer is applicable and the present series solution does not yield physically reasonable temperature distribution locally near the upper plate at the thermal entrance. The difficulty may be attributed to the nature of thermal boundary conditions at the thermal entrance and the transition from elliptic problem to parabolic problem with the increase of Peclet number.