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RESEARCH PAPERS

# Transient Natural Convection Heat Transfer Correlations for Tube Bundles Immersed in a Thermal Storage

[+] Author and Article Information
Yan Su

Department of Mechanical Engineering,  University of Minnesota, 111 Church Street S.E., Minneapolis, MN 55455

Jane H. Davidson1

Department of Mechanical Engineering,  University of Minnesota, 111 Church Street S.E., Minneapolis, MN 55455jhd@me.umn.edu

1

Corresponding author.

J. Sol. Energy Eng 129(2), 210-214 (Dec 08, 2005) (5 pages) doi:10.1115/1.2710492 History: Received June 20, 2005; Revised December 08, 2005

## Abstract

A scale analysis of the transient discharge of a fully mixed thermal storage vessel with an immersed single-tube heat exchanger is extended to provide a generalized expression for the transient natural convection Nusselt number for heat exchangers comprising many tubes. The transient Nusselt number is expressed in terms of the Rayleigh number at the initiation of the discharge (or charge) process and easily measured geometric parameters. Nusselt numbers measured for a 240-tube heat exchanger immersed in a fully mixed $126L$ storage vessel are well correlated in the proposed form. The applicability of the approach to thermally stratified storage fluids is evaluated for both a single-tube and the 240-tube bundle. For heat exchangers of practical size for solar systems, for example the 240-tube bundle, buoyancy driven flow within the storage is sufficient to mix an initially stratified fluid. In this case, Nusselt numbers during the discharge process are predicted accurately by the proposed transient formulation. However, if the storage fluid remains stratified during discharge, as is the case for an initially stratified vessel with a single-tube heat exchanger, the transient formulation is not recommended.

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## Figures

Figure 1

Conceptual sketch of an immersed tube bundle in a thermal energy storage tank. The heat exchanger is shown here in two positions: (a) at top of the tank for discharge during which energy is removed from the tank; and (b) at the bottom for charging of the tank.

Figure 2

Comparison of measured and predicted values of Nusselt number and dimensionless tank temperature for a fully mixed storage vessel with a single-tube immersed heat exchanger. Legend: (—) predicted NuD*¯ from Eq. 16; (◇) measured NuD*¯(1); (---) predicted Θ¯ from Eq. 12; and (엯) measured Θ¯(1).

Figure 3

Comparison of measured and predicted values of Nusselt number and dimensionless tank temperature for an initially stratified storage vessel with a single-tube immersed heat exchanger. Legend: (—) predicted NuD*¯ from Eq. 16; (◇) measured NuD*¯(1); (---) predicted Θ¯ from Eq. 12; and (엯) measured Θ¯(1).

Figure 5

Comparison of measured and predicted values of Nusselt number and dimensionless tank temperature for an initially stratified storage vessel with a 240-tube immersed heat exchanger. Legend: (—) predicted NuD*¯ from Eq. 17; (◇) measured NuD*¯(1); (---) predicted Θ¯ from Eq. 12; and (엯) measured Θ¯(3).

Figure 4

Comparison of measured and predicted values of Nusselt number and dimensionless tank temperature for a fully mixed storage vessel with a 240-tube immersed heat exchanger. Legend: (—) predicted NuD*¯ from Eq. 17; (◇) measured NuD*¯(3); (---) predicted Θ¯ from Eq. 12; and (엯) measured Θ¯(3).

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