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Research Papers: Forced Convection

Conjugate Nusselt Numbers for Simultaneously Developing Flow Through Rectangular Ducts

[+] Author and Article Information
Georgios Karamanis

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
e-mail: Georgios.Karamanis@tufts.edu

Marc Hodes

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
email: Marc.Hodes@tufts.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 25, 2018; final manuscript received April 12, 2019; published online June 17, 2019. Assoc. Editor: Sara Rainieri.

J. Heat Transfer 141(8), 081701 (Jun 17, 2019) (9 pages) Paper No: HT-18-1474; doi: 10.1115/1.4043623 History: Received July 25, 2018; Revised April 12, 2019

We consider conjugate forced-convection heat transfer in a rectangular duct. Heat is exchanged through the isothermal base of the duct, i.e., the area comprised of the wetted portion of its base and the roots of its two side walls, which are extended surfaces within which conduction is three-dimensional. The opposite side of the duct is covered by an adiabatic shroud, and the external faces of the side walls are adiabatic. The flow is steady, laminar, and simultaneously developing, and the fluid and extended surfaces have constant thermophysical properties. Prescribed are the width of the wetted portion of the base, the length of the duct, and the thickness of the extended surfaces, all three of them nondimensionalized by the hydraulic diameter of the duct, and, additionally, the Reynolds number of the flow, the Prandtl number of the fluid, and the fluid-to-extended surface thermal conductivity ratio. Our conjugate Nusselt number results provide the local one along the extended surfaces, the local transversely averaged one over the isothermal base of the duct, the average of the latter in the streamwise direction as a function of distance from the inlet of the domain, and the average one over the whole area of the isothermal base. The results show that for prescribed thermal conductivity ratio and Reynolds and Prandtl numbers, there exists an optimal combination of the dimensionless width of the wetted portion of the base, duct length, and extended surface thickness that maximize the heat transfer per unit area from the isothermal base.

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References

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Figures

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Fig. 1

Rectangular duct under consideration

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Fig. 2

Computational domain

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Fig. 3

T̃e versus ỹ for s̃=0.525, L̃=26.25, ReDh=882.92,Ke=11.1×10−5, and Pr = 0.71, at different streamwise locations and selected values of t̃

Grahic Jump Location
Fig. 4

q̃″e versus ỹ for s̃=0.525, L̃=26.25, ReDh=882.92, Ke=11.1×10−5, and Pr = 0.71, at different streamwise locations and selected values of t̃

Grahic Jump Location
Fig. 5

Nue versus ỹ for s̃=0.525, L̃=26.25, ReDh=882.92,Ke=11.1×10−5, and Pr = 0.71, at different streamwise locations and selected values of t̃

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Fig. 6

NuB and Nu¯B versus z̃ for s̃=0.525, L̃=26.25, ReDh=882.92, Ke=11.1×10−5, and Pr = 0.71 for selected values of t̃

Grahic Jump Location
Fig. 7

Nu¯B,L̃ versus ReDh for s̃=0.525, L̃=26.25, Ke=11.1×10−5 and Pr = 0.71 for selected values of t̃

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