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# Extended Results for Fully Developed Laminar Forced Convection Heat Transfer in Trapezoidal Channels of Plate-Fin Exchangers

[+] Author and Article Information
O. A. Huzayyin, M. A. Jog

Thermal-Fluids & Thermal Processing Laboratory, College of Engineering and Applied Science, University of Cincinnati, Cincinnati, OH 45221-0072

R. M. Manglik1

Thermal-Fluids & Thermal Processing Laboratory, College of Engineering and Applied Science, University of Cincinnati, Cincinnati, OH 45221-0072raj.manglik@uc.edu

In essence, $ϕ=63.4 deg$ was chosen in the present analysis so as to characterize the trapezoidal geometry that corresponds to the isosceles triangle with cross section aspect ratio of $γ=1.0$.

1

Corresponding author.

J. Thermal Sci. Eng. Appl 2(4), 044501 (Jan 19, 2011) (6 pages) doi:10.1115/1.4003281 History: Received October 29, 2010; Revised December 17, 2010; Published January 19, 2011; Online January 19, 2011

## Abstract

Fully developed laminar flow heat transfer in a plate-fin heat exchanger with interfin core channels of trapezoidal cross section and by extension, its limiting rectangular and triangular cross section geometries, is considered. With heating or cooling at the partition plates of the core given by the constant wall temperature, or $T$, and uniform heat flux, or $H1$, conditions, the fin effectiveness is modeled to be zero. This condition is representative of poor contact between the fin and partition plate, encountered in mass-produced compact cores and/or low conductivity fin materials. Computational solutions, obtained by second-order accurate control-volume schemes, highlight the effects of geometry and thermal condition on the Nusselt number ($NuT$ and $NuH1$), and the results complement and extend the literature on compact-channel internal forced convection. Also, as a design and optimization tool for the practicing engineer, polynomial functions of the flow cross section aspect ratio are presented to predict both the friction factor and the Nusselt number for the different trapezoidal and triangular fin core geometries considered.

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## Figures

Figure 1

A compact plate-fin heat exchanger: (a) a typical core configuration showing fins and partition plates and (b) commonly used geometrical variations of plate-fin channel cross section (rectangular, trapezoidal, and triangular)

Figure 2

Compact plate-fin core: (a) interfin channels of trapezoidal cross section and limiting models for fin-surface thermal boundary conditions, (b) coordinate system and geometrical details, and (c) schematic of transformed computational domain

Figure 3

Results from typical grid refinement in the computational domain and the relative accuracy of numerical solutions

Figure 4

Variation of Fanning friction factor with aspect ratio for fully developed laminar flow in interfin channels of trapezoidal, rectangular, and triangular cross sections

Figure 6

Variation of Nusselt number with aspect ratio for fully developed laminar flow in interfin channels of trapezoidal, rectangular, and triangular cross sections with the H1 condition at the partition plates and fin η=1 (open symbols and solid lines) and 0 (filled symbols and dashed lines)

Figure 5

Variation of Nusselt number with aspect ratio for fully developed laminar flow in interfin channels of trapezoidal, rectangular, and triangular cross sections with the T condition at the partition plates and fin η=1 (open symbols and solid lines) and 0 (filled symbols and dashed lines)

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