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Research Papers: Forced Convection

# Effect of Return Bend and Entrance on Heat Transfer in Thermally Developing Laminar Flow in Round Pipes of Some Heat Transfer Fluids With High Prandtl Numbers

[+] Author and Article Information
Predrag S. Hrnjak

Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, IL 61801pega@illinois.edu

S. H. Hong

Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, IL 61801

J. Heat Transfer 132(6), 061701 (Mar 19, 2010) (12 pages) doi:10.1115/1.4000704 History: Received July 02, 2008; Revised October 20, 2009; Published March 19, 2010; Online March 19, 2010

## Abstract

The paper presents experimental results and analysis of heat transfer in a thermally developing region of round pipes for three fluids typically used as low temperature coolants, in the range of $0–−40°C$. The experiments were performed at low Re (200–1000) and high Pr (80–140) numbers that are typically found in secondary refrigeration loop conditions. The effect of horizontal U-bend is also presented. It is shown that the positive effect of thermal development (high Nu number) lasts long because of the technically significant length of the thermally developing region. Secondary flows developed in and after the U-bend are so significant that they have almost an identical effect as the thermal development at the pipe entrance. That is a reason for the extremely good performance of the heat exchangers with secondary refrigerants in laminar flow regimes. Experimental data are presented with developed empirical correlations, which show good relationships to several existing correlations.

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## Figures

Figure 1

Elements of heat transfer characteristics in a laminar developing flow

Figure 2

Experimental facility (thermocouple configuration discussed later)

Figure 3

Schematic of the test section

Figure 4

Joint of two sections

Figure 5

Hard plastic rings. The top ring (a) separates the test sections and the bottom ring (b) is the end cap for each end of the coaxial heat exchanger tubes (numbers are in inches).

Figure 6

Positions of the thermocouples for wall temperature measurements

Figure 7

Schematic of a test section

Figure 8

Comparison of refrigerant temperature predictions to potassium formate data

Figure 20

Published correlations for thermally and simultaneously developing flows

Figure 17

Nusselt number after the U-bend with published correlations

Figure 18

Heat transfer in the coaxial heat exchanger experimental results preceding the U-bend—comparison of several experimental results: from Ref. 2 (solid circles), from Ref. 7, and from this work (open symbols)

Figure 19

Heat transfer in the coaxial heat exchanger experimental results following the U-bend—comparison of several experimental results: from Ref. 2 (solid circles), from Ref. 7, and from this work (open symbols)

Figure 9

Comparison of predicted refrigerant heat transfer coefficients to measured values with potassium formate (Vr=0.62 m/s)

Figure 10

Heat transfer preceding and following the U-bend for propylene glycol

Figure 11

Heat transfer preceding and following the U-bend for potassium acetate

Figure 12

Heat transfer preceding and following the U-bend for potassium formate

Figure 13

Local Nusselt number versus x* preceding the U-bend. Figure 1 gives the curve-fit as well as a 99% confidence interval and R2 for the data-fit curve for all three fluids together. Its standard deviation is 3.92.

Figure 14

Nusselt number versus x* in a straight section following the U-bend

Figure 15

Ratio of the Nusselt number preceding and following the U-bend for each of the three fluids, individually and together

Figure 16

Nusselt number before the U-bend with published correlations

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