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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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Figures

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Fig. 1

Physical model and the coordinate system

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Fig. 2

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

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Fig. 3

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

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Fig. 4

Variation of Nux with X*

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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

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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

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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}

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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

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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

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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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