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Laminar forced convection in the thermal entrance region of curved pipes with uniform wall temperature
Author(s) -
Akiyama Mitsunobu,
Cheng K. C.
Publication year - 1974
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.5450520217
Subject(s) - prandtl number , nusselt number , laminar flow , mechanics , turbulent prandtl number , heat transfer , magnetic prandtl number , thermal , forced convection , film temperature , physics , thermodynamics , materials science , reynolds number , turbulence
Abstract The thermal entrance region heat transfer problem for fully developed laminar flow in curved pipes with uniform wall temperature is approached by an alternating direction implicit method for the parabolic energy equation for a flow regime with Dean number ranging from 0 to an order of 100. This work represents an extension of the classical Graetz problem in straight tubes to curved pipes. The graphical results for temperature developments in the form of temperature profiles through the horizontal and vertical planes, isothermals and local Nusselt number variations in the thermal entrance region are presented in such a way as to illustrate clearly the interaction between the secondary flow and the developing temperature field for Prandtl numbers of 0.1, 0.7, 10 and 500. For a given Dean number, the effect of Prandtl number is to shorten the thermal entrance length (I/Gz) and the temperature field develops rather rapidly with large Prandtl number. The effect of Dean number is similar to that of Prandtl number with Dean number effect becoming much more appreciable at high Prantdl numbers than at low Prandtl number.