Analytical solutions of heat transfer for laminar flow in rectangular channels

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

Journal of Heat Transfer ◽

10.1115/1.1857950 ◽

2005 ◽

Vol 127 (3) ◽

pp. 352-356 ◽

Cited By ~ 20

Author(s):

Michael W. Egner ◽

Louis C. Burmeister

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Laminar Flow ◽

Cross Section ◽

Rectangular Cross Section ◽

Three Dimensional ◽

Radius Of Curvature ◽

Dean Number ◽

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 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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Heat Transfer and Pressure Drop Correlation for Helicoidal Pipes of Rectangular Cross Section

Volume 9: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B and C ◽

10.1115/imece2009-12677 ◽

2009 ◽

Author(s):

Christopher Katinas ◽

Ahmad Fakheri

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Aspect Ratio ◽

Friction Factor ◽

Cross Section ◽

Numerical Solutions ◽

Rectangular Cross Section ◽

Dean Number ◽

Curvature Effects ◽

The Impact

In this study, flow and heat transfer for laminar flow in curved channels of rectangular cross section is examined. The focus of the numerical solutions is on rectangular cross sections with an aspect ratio less than one, since little information is available for heat transfer in curved rectangular pipes whose width is greater than height. The study examines the impact of the aspect ratio and Dean number on both friction factor and Nusselt number. The results show that although both friction factor and Nusselt number increase as a result of curvature effects, the heat transfer enhancements significantly outweigh the friction factor penalty. Numerical solutions in this study consider the more realistic case of hydrodynamically developed and thermally developing flow.

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Flow in a pipe of rectangular cross-section

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1928.0175 ◽

1928 ◽

Vol 120 (786) ◽

pp. 691-700 ◽

Cited By ~ 102

Keyword(s):

Laminar Flow ◽

Turbulent Flow ◽

Cross Section ◽

Rectangular Cross Section ◽

Stream Line ◽

Parallel Plates ◽

Rectangular Section ◽

Circular Section ◽

Line Flow ◽

Minimum Ratio

The object of the research was to investigate the flow of water in a pipe of rectangular cross-section. Much work has been done on similar problems with pipes of circular section, and pipes of rectangular section have been investigated by Fromm and Davies and White. Fromm avoided with pipes in which the ratio of the sides was never less than 6 to 1; his report deals only with turbulent flow. In the case of Davies and White's research, the minimum ratio of the sides was 40 to 1, so that the laminar flow could be calculated from the formula for flow between infinitely wide parallel plates. The present writer used a pipe of section 1·178 cms. by 0·404 cms, (ratio of sides = 2·92); this presents a fresh problem were stream line flow is concerned, and shows interesting results in the region of the critical velocity.

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