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An exact analysis of low peclet number thermal entry region heat transfer in transversely nonuniform velocity fields
Author(s) -
Hsu ChiaJung
Publication year - 1971
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690170343
Subject(s) - thermal conduction , eigenfunction , nusselt number , péclet number , heat transfer , mechanics , heat flux , eigenvalues and eigenvectors , adiabatic process , physics , laminar flow , boundary value problem , partial differential equation , mathematical analysis , mathematics , thermodynamics , reynolds number , turbulence , quantum mechanics
A theoretical method is described for obtaining the exact solution to the problem of thermal entry region heat transfer which takes into account both transverse non‐uniformity in the velocity field and axial conduction. To allow for the effect of upstream conduction, the fluid temperature was taken to be uniform at × = – ∞, and the first 20 eigenvalues and the corresponding eigenfunctions were determined separately for the heated and adiabatic regions. Both the temperatures and temperature gradients were then matched at × = 0 by constructing a pair of orthonormal functions from the nonorthogonal eigenfunctions. Nusselt numbers calculated for pipe flow subject to the boundary condition of uniform wall heat flux show virtually perfect agreement with those reported recently by Hennecke, who solved the governing partial differential equation numerically. To illustrate its general applicability, the present method was further employed to analyze the corresponding problem in parallel‐plate channel flow, for which no solution has hitherto been reported.