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Research Papers

Effect of Entry Temperature on Forced Convection Heat Transfer With Viscous Dissipation in Thermally Developing Region of Concentric Annuli

[+] Author and Article Information
M. M. J. Kumar

School of Mechanical and Building Sciences,
Vellore Institute of Technology University,
Vellore, Tamilnadu 632014, India
e-mail: mohan.jagadeeshkumar@vit.ac.in

V. V. Satyamurty

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India
e-mail: vvsmurty@mech.iitkgp.ernet.in

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 16, 2014; final manuscript received January 28, 2015; published online August 11, 2015. Assoc. Editor: P.K. Das.

J. Heat Transfer 137(12), 121001 (Aug 11, 2015) (8 pages) Paper No: HT-14-1195; doi: 10.1115/1.4030908 History: Received April 16, 2014

Steady laminar forced convection heat transfer in the thermal entrance region of concentric annuli has been studied considering viscous dissipation characterized by the Brinkman number. The inner and outer pipes have been kept at constant and equal temperature. Two cases of entry temperatures have been considered, case 1: an entry temperature that varies with the radial coordinate, obtained by an adiabatically prepared fluid, i.e., attained by the fluid due to viscous dissipation in an adiabatic concentric annular duct and case 2: the conventional uniform entry temperature. The numerical results presented include the nondimensional temperature profiles, Nusselt numbers, and heat transferred from (or to) the inner and outer pipes. It has been shown from the numerical solutions that it is necessary to employ the dissipative entry temperature in place of conventional uniform entry temperature for higher Brinkman numbers. The results for circular pipes follow when the radius ratio takes the limiting value of zero.

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References

Graetz, L. , 1883, “Uber die Wrmeleitungsfähigkeit von Flüssigkeiten,” Annu. Phys. Chem., 18, pp. 79–94.
Graetz, L. , 1885, “Uber die Wärmeleitungsfähigkeit von Flüssigkeiten,” Annu. Phys. Chem., 25, pp. 337–357. [CrossRef]
Nusselt, W. , 1910, “Die Abhängigkeit der Wäreübergangszahl von der Rohrlänge,” VDIZ, 54, pp. 1154–1158.
Shah, R. K. , and London, A. L. , 1978, Laminar Flow Forced Convection in Ducts, Advances in Heat Transfer, Academic, New York.
Kakac, S. , Shah, R. K. , and Aung, W. , 1987, Handbook of Single-Phase Convective Heat Transfer, Wiley, New York.
Urbanovich, L. I. , 1968, “Temperature Distribution and Heat Transfer in a Laminar Incompressible Annular-Channel Flow With Energy Dissipation,” J. Eng. Phys. (USSR), 14(4), pp. 402–403. [CrossRef]
Urbanovich, L. I. , 1968, “The Transfer of Heat in the Laminar Flow of an Incompressible Liquid in an Annular Channel With Non Symmetric Boundary Conditions of the II-nd Kind Relative to the Axis of the Flow,” J. Eng. Phys. (USSR), 15(2), pp. 753–754. [CrossRef]
Avci, M. , and Aydin, O. , 2006, “Laminar Forced Convection With Viscous Dissipation in a Concentric Annular Duct,” C. R. Mec., 334(3), pp. 164–169. [CrossRef]
Coelho, P. M. , and Pinho, F. T. , 2006, “Fully-Developed Heat Transfer in Annuli With Viscous Dissipation,” Int. J. Heat Mass Transfer, 49(19–20), pp. 3349–3359. [CrossRef]
Jambal, O. , Shigechi, T. , Davaa, G. , and Momoki, S. , 2005, “Effects of Viscous Dissipation and Fluid Axial Heat Conduction on Heat Transfer for Non-Newtonian Fluids in Ducts With Uniform Wall Temperature Part II. Annular Ducts,” Int. Commun. Heat Mass Transfer, 32(9), pp. 1174–1183. [CrossRef]
Barletta, A. , and Magyari, E. , 2006, “Thermal Entrance Heat Transfer of an Adiabatically Prepared Fluid With Viscous Dissipation in a Tube With Isothermal Wall,” ASME J. Heat Transfer, 128(11), pp. 1185–1193. [CrossRef]
Barletta, A. , and Magyari, E. , 2007, “Forced Convection With Viscous Dissipation in the Thermal Entrance Region of a Circular Duct With Prescribed Wall Heat Flux,” Int. J. Heat Mass Transfer, 50(1–2), pp. 26–35. [CrossRef]
Aydin, O. , and Avci, M. , 2010, “On the Constant Wall Temperature Boundary Condition in Internal Convection Heat Transfer Studies Including Viscous Dissipation,” Int. Commun. Heat Mass Transfer, 37(5), pp. 535–539. [CrossRef]
Satyamurty, V. V. , 1984, “Successive Accelerated Replacement Scheme Applied to Study of Natural Convection Heat Transfer in Porous Cryogenic Insulations,” ASME Paper No. 84-WA/HT-37.
Marpu, D. R. , and Satyamurty, V. V. , 1989, “Influence of Variable Fluid Density on Free Convection in Rectangular Porous Media,” ASME J. Energy Resour. Technol., 111(4), pp. 214–220. [CrossRef]
Satyamurty, V. V. , and Marpu, D. R. , 1988, “Relative Effects of Variable Fluid Properties and Non-Darcy Flow on Convection in Porous Media,” ASME-HTD, 96, pp. 613–621.
Satyamurty, V. V. , and Bhargavi, D. , 2010, “Forced Convection in Thermally Developing Region of a Channel Partially Filled With a Porous Material and Optimal Porous Fraction,” Int. J. Therm. Sci., 49(2), pp. 319–332. [CrossRef]
Repaka, R. , and Satyamurty, V. V. , 2010, “Local and Average Heat Transfer in the Thermally Developing Region of an Asymmetrically Heated Channel,” Int. J. Heat Mass Transfer, 53(9–10), pp. 1654–1665. [CrossRef]
Liu, C. Y. , Gooi, B. C. , Wong, Y. W. , and Yeo, J. H. , 1994, “The Effect of Inlet Velocity Distribution on the Temperature Field of a Rotating Circular Pipe,” Int. Commun. Heat Mass Transfer, 21(6), pp. 829–837. [CrossRef]
Kays, W. M. , Crawford, M. E. , and Weigand, B. , 2005, Convective Heat and Mass Transfer, McGraw Hill International Edition, New York.
Antia, H. M. , 1991, Numerical Methods for Scientists and Engineers, Tata McGraw-Hill, New Delhi.
Dellinger, T. C. , 1971, “Computations on Non-Equilibrium Merged Shock Layer by Successive Accelerated Replacement Scheme,” AIAA J., 9(2), pp. 262–269. [CrossRef]
Kumar, M. M. J. , and Satyamurty, V. V. , 2011, “Limiting Nusselt Numbers for Laminar Forced Convection in Asymmetrically Heated Annuli With Viscous Dissipation,” Int. Commun. Heat Mass Transfer, 38(7), pp. 923–927. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

Physical model and coordinate system of adiabatic annulus: (a) dimensional and (b) nondimensional

Grahic Jump Location
Fig. 1

Physical model and the coordinate system

Grahic Jump Location
Fig. 6

Variation of θ2 with R for different X*:R*= 0.5: (a) Br2 = Br1/ζ = −0.0667 and (b) Br2 = Br1/ζ = 0.1333

Grahic Jump Location
Fig. 3

Variation of θde(R) with R: (a) concentric annulus and (b) circular pipe

Grahic Jump Location
Fig. 4

Variation of Nux with X*

Grahic Jump Location
Fig. 5

Variation of θ1 with R for different X*:R*= 0.5: (a) Br1 = −0.1, (b) Br1 = 0.1, and (c) Br1 = 0.0

Grahic Jump Location
Fig. 7

Variation of θ1* and θ2* with X*:R*= 0.5: (a) Br1 = −0.1 and Br2 = −0.1/ζ {with ζ = 1.125 and 1.5} and (b) Br1 = 0.1 and Br2 = 0.1/ζ {with ζ = 0.9 and 0.75}

Grahic Jump Location
Fig. 8

Variation of Nuix1,2 and Nuox1,2 with X* for R*= 0.5 and Br1 = Br2 = −0.1 and Br3 = −Br2/ζ {with ζ = 1.125 and 0.5}: (a) inner pipe and (b) outer pipe

Grahic Jump Location
Fig. 9

Variation of Nuix1,2 and Nuox1,2 with X* for R*= 0.5 and Br1 = Br2 = 0.1 and Br3 = Br2/ζ {with ζ = 0.9 and 0.75}: (a) at the inner pipe and (b) at the outer pipe

Grahic Jump Location
Fig. 10

Variation of Q¯txw with X* for R*= 0.5: (a) Br1 = −0.1 and Br2 = −0.1/ζ{with ζ = 1.125 and 1.5} and (b) Br1 = 0.1 and Br2 = 0.1/ζ{with ζ = 0.9 and 0.75}

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