Laminar flow heat transfer for simultaneously developing velocity and temperature profiles in ducts of rectangular cross section

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined by making use of the FLUENT computational fluid dynamics program. The peripherally averaged Nusselt number is presented as a function of distance from the inlet and of the Dean number. Fully developed values of the Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in postentry regions. These results are applicable to spiral-plate heat exchangers.

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Analytical solutions of heat transfer for laminar flow in rectangular channels

Archives of Thermodynamics ◽

10.2478/aoter-2014-0031 ◽

2014 ◽

Vol 35 (4) ◽

pp. 29-42 ◽

Cited By ~ 5

Author(s):

Witold Rybiński ◽

Jarosław Mikielewicz

Keyword(s):

Nusselt Number ◽

Laminar Flow ◽

Friction Factor ◽

Cross Section ◽

Constant Temperature ◽

Analytical Solutions ◽

Rectangular Cross Section ◽

Temperature Profiles ◽

Mathematical Form ◽

Parallel Plates

Abstract The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type). The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.

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Laminar Flow and Heat Transfer in Spiral Ducts of Rectangular Cross Section

Volume 2, Parts A and B ◽

10.1115/ht-fed2004-56053 ◽

2004 ◽

Author(s):

Michael W. Egner ◽

Louis C. Burmeister

Keyword(s):

Heat Transfer ◽

Laminar Flow ◽

Cross Section ◽

Rectangular Cross Section ◽

Three Dimensional ◽

Radius Of Curvature ◽

Dean Number ◽

Flow And Heat Transfer ◽

Aspect Ratios ◽

Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined with the aide of the FLUENT computational fluid dynamics program. Peripherally-averaged coefficients of friction and Nusselt numbers are presented as a function of distance from the inlet and of the Dean number. Fully-developed values of friction coefficient and Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in post-entry regions. These results are applicable to spiral-plate heat exchangers.

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