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Research Papers: Forced Convection

Unsteady Laminar Forced-Convective Tube Flow Under Dynamic Time-Dependent Heat Flux

[+] Author and Article Information
M. Fakoor-Pakdaman

Laboratory for Alternative Energy
Convection (LAEC),
School of Mechatronic Systems Engineering,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: mfakoorp@sfu.ca

Mehdi Andisheh-Tadbir

Laboratory for Alternative Energy
Convection (LAEC),
School of Mechatronic Systems Engineering,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: mandishe@sfu.ca

Majid Bahrami

Laboratory for Alternative Energy
Convection (LAEC),
School of Mechatronic Systems Engineering,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: mbahrami@sfu.ca

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 3, 2013; final manuscript received November 20, 2013; published online February 12, 2014. Assoc. Editor: D. K. Tafti.

J. Heat Transfer 136(4), 041706 (Feb 12, 2014) (10 pages) Paper No: HT-13-1277; doi: 10.1115/1.4026119 History: Received June 03, 2013; Revised November 20, 2013

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow (SF) condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel's integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict (i) fluid temperature distribution inside the tube, (ii) fluid bulk temperature and (iii) the Nusselt number. A new definition, cyclic fully developed Nusselt number, is introduced and it is shown that in the thermally fully developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ansys fluent to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

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References

Agyenim, F., Hewitt, N., Eames, P., and Smyth, M., 2010, “A Review of Materials, Heat Transfer and Phase Change Problem Formulation for Latent Heat Thermal Energy Storage Systems (LHTESS),” Renewable Sustainable Energy Rev., 14(2), pp. 615–628. [CrossRef]
Hale, M., 2000, “Survey of Thermal Storage for Parabolic Trough Power Plants,” NREL Report, No. NREL/SR-550-27925, pp. 1–28.
Garrison, J. B., and Webber, M. E., 2012, “Optimization of an Integrated Energy Storage for a Dispatchable Wind Powered Energy System,” ASME 2012 6th International Conference on Energy Sustainability, pp. 1–11.
Sawin, J. L., and Martinot, E., 2011, “Renewables Bounced Back in 2010,” Finds REN21 Global Report," Renewable Energy World, September. Available at: http://www.renewableenergyworld.com/rea/news/article/2011/09/renewables-bounced-back-in-2010-finds-ren21-global-report
Cabeza, L. F., Mehling, H., Hiebler, S., and Ziegler, F., 2002, “Heat Transfer Enhancement in Water When Used as PCM in Thermal Energy Storage,” Appl. Therm. Eng., 22(10), pp. 1141–1151. [CrossRef]
Energy, R., and Kurklo, A., 1998, “Energy Storage Applications in Greenhouses by Means of Phase Change Materials (PCMs): A Review,” Renew Energy, 13(1), pp. 89–103. [CrossRef]
Garrison, J. B., 2012, “Optimization of an Integrated Energy Storage Scheme for a Dispatchable Solar and Wind Powered Energy System," Proceedings of the ASME 6th International Conference on Energy Sustainability, July 23–26, San Diego, CA.,” pp. 1–11.
Bennion, K., 2007, “Plug-in Hybrid Electric Vehicle Impacts on Power Electronics and Electric Machines,” National Renewable Energy Laboratory Report No. NREL/MP-540-36085.
Bennion, K., and Thornton, M., 2010, “Integrated Vehicle Thermal Management for Advanced Vehicle Propulsion Technologies, SAE 2010 World Congress, Detroit, MI, April 13–15, Report No. NREL/CP-540-47416.
Boglietti, A., Member, S., Cavagnino, A., Staton, D., Shanel, M., Mueller, M., and Mejuto, C., 2009, “Evolution and Modern Approaches for Thermal Analysis of Electrical Machines,” IEEE Trans. Ind. Elect., 56(3), pp. 871–882. [CrossRef]
Canders, W.-R., Tareilus, G., Koch, I., and May, H., 2010, “New Design and Control Aspects for Electric Vehicle Drives,” Proceedings of 14th International Power Electronics and Motion Control Conference EPE-PEMC 2010.
Hamada, K., 2008, “Present Status and Future Prospects for Electronics in Electric Vehicles/Hybrid Electric Vehicles and Expectations for Wide Bandgap Semiconductor Devices,” Phys. Status Solidi (B), 245(7), pp. 1223–1231. [CrossRef]
Sparrow, E. M., and Siegel, R., 1958, “Thermal Entrance Region of a Circular Tube Under Transient Heating Conditions,” Third U. S. National Congress of Applied Mechanics, pp. 817–826.
Siegel, R., and Sparrow, E. M., 1959, “Transient Heat Transfer for Laminar Forced Convection in the Thermal Entrance Region of Flat Ducts,” Heat Transfer, 81, pp. 29–36.
Siegel, R., 1959, “Transient Heat Transfer for Laminar Slug Flow in Ducts,” Appl. Mech., 81(1), pp. 140–144.
Siegel, R., 1960, “Heat Transfer for Laminar Flow in Ducts With Arbitrary Time Variations in Wall Tempearture,” Trans. ASME, 27(2), pp. 241–249. [CrossRef]
Siegel, R., and Perlmutter, M., 1963, “Laminar Heat Transfer in a Channel With Unsteady Flow and Wall Heating Varying With Position and Time,” Trans. ASME, 85, pp. 358–365. [CrossRef]
Perlmutter, M., and Siegel, R., 1961, “Two-Dimensional Unsteady Incompressible Laminar Duct Flow With a Step Change in Wall Temperature,” Trans. ASME, 83, pp. 432–440. [CrossRef]
Siegel, R., 1963, “Forced Convection in a Channel With Wall Heat Capacity and With Wall Heating Variable With Axial Position and Time,” Int. J. Heat Mass Transfer, 6, pp. 607–620. [CrossRef]
Von, K. T., and Biot, M. A., 1940, Mathematical Methods in Engineering, McGraw-Hill, New York.
Incropera, F. P., Dewitt, D. P., Bergman, T. L., and Lavine, A. S., 2007, Introduction to Heat Transfer, John Wiley & Sons, New York.

Figures

Grahic Jump Location
Fig. 1

Schematic of the two-region tube and the coordinate system

Grahic Jump Location
Fig. 2

The methodology adopted to find the transient thermal response of the tube flow under arbitrary time-dependent heat flux

Grahic Jump Location
Fig. 3

Variations of the dimensionless tube- wall temperature, Eqs. (13) and (14), versus the Fo number for a cyclic heat flux, q"=q"`r[1+sin(8πFo)]

Grahic Jump Location
Fig. 4

Variations of the dimensionless fluid temperature, Eqs. (11) and (12), at an arbitrarily-chosen axial position of X = 0.4 and angular frequency of 8π at different radial positions across the tube against the Fo number for cyclic and step heat fluxes

Grahic Jump Location
Fig. 5

Variations of the dimensionless tube-wall temperature, Eqs. (13) and (14), at an arbitrarily chosen axial position of X = 0.4 against (a): the Fourier number for different angular frequencies of the heat flux, (b) the angular frequency at different Fourier numbers, and (c) the angular frequency and the Fourier number

Grahic Jump Location
Fig. 6

Variations of the local Nusselt number, Eqs. (21) and (22), at an arbitrarily chosen axial position of X = 0.4 against (a): The Fourier number for different angular frequencies and comparison with the “quasi-steady” model (b): the angular frequency for different Fourier numbers, and (c): the Fourier number and the angular frequency

Grahic Jump Location
Fig. 7

Variations of the applied heat flux, q" = q"`r[1 + sin(8πFo)], and the corresponding Nusselt number for a few axial positions along the tube, Eqs. (21) and (22)

Grahic Jump Location
Fig. 8

Variations of the average Nusselt number, Eq. (24), with the angular frequency and comparison with the quasi-steady model

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