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TECHNICAL BRIEFS

# Effectiveness of a Spiral-Plate Heat Exchanger With Equal Capacitance Rates

[+] Author and Article Information
Louis C. Burmeister

Department of Mechanical Engineering, University of Kansas, Lawrence, KS 66045mrub@ku.edu

J. Heat Transfer 128(3), 295-301 (Aug 08, 2005) (7 pages) doi:10.1115/1.2150839 History: Received February 10, 2005; Revised August 08, 2005

## Abstract

A formula is derived for the dependence of heat exchanger effectiveness on the number of transfer units for a spiral-plate heat exchanger with equal capacitance rates. The difference-differential equations that describe the temperature distributions of the two counter-flowing fluids, neglecting the effects of thermal radiation, are solved symbolically to close approximation. Provision is made for the offset inlet and exit of the hot and cold fluids at the outer periphery and for large heat transfer coefficients in the entrance regions. The peak effectiveness and the number of transfer units at which it occurs are linear functions of the maximum angle of the Archimedean spiral that describes the ducts; entrance region effects reduce both.

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## Figures

Figure 1

Geometry of the spiral-plate heat exchanger in overview

Figure 2

Effectiveness ε versus number of transfer units NTU From Eq. 16 for zi=2, φ=π∕2, Ro=1=Ri and several values of zm

Figure 3

Comparison of predicted effectiveness versus number of transfer units for zi=2.5, φ=π, Ro=1=Ri, and zm=11.25

Figure 4

Inverse maximum effectiveness deficit versus maximum dimensionless angle: (a) (24) for zi=2.5, ϕ=π, Ro=1=Ri; (b) (16) for zi=2, ϕ=π, Ro=1=Ri; (c) Eq. 16 for zi=2, ϕ=π, Ro=1=Ri; (d) Eq. 16 for zi=3, ϕ=π, Ro=1=Ri; (e) Eq. 16 for zi=2, ϕ=0, Ro=1=Ri; (f) Eq. 16 for zi=2, ϕ=0, Ro=2=Ri; (g) Eq. 16 for zi=2, ϕ=π, Ro=2=Ri

Figure 5

Maximal number of transfer units NTUm at which the maximum effectiveness εm occurs versus maximum dimensionless angle zm: (a) Strenger et al. (24) for zi=2.5, ϕ=π, Ro=1=Ri; (b) Bes and Roetzel (16) for zi=2, ϕ=0, Ro=1=Ri; (c) Eq. 16 for zi=2, ϕ=π, Ro=1=Ri; (d) Eq. 16 for zi=3, ϕ=π, Ro=1=Ri; (e) Eq. 16 for zi=2, ϕ=0, Ro=1=Ri; (f) Eq. 16 for zi=2, ϕ=π, Ro=2=Ri; (g) Eq. 16 for zi=2, ϕ=0, Ro=2=Ri

Figure 6

The effect of parameters on effectiveness ε versus number of transfer units NTU from Eq. 16 for zm=10: (a) zi=2, ϕ=π, Ro=1=Ri; (b) zi=4, ϕ=π, Ro=1=Ri; (c) zi=2, ϕ=0, Ro=1=Ri; (d) zi=2, ϕ=π, Ro=2=Ri; (e) zi=2, ϕ=0, Ro=2=Ri

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