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Research Papers: Forced Convection

Semi-Analytical Solution of the Heat Transfer Including Viscous Dissipation in the Steady Flow of a Sisko Fluid in Cylindrical Tubes

[+] Author and Article Information
Sumanta Chaudhuri

School of Mechanical Engineering (KIIT),
Kalinga Institute of Industrial Technology (KIIT),
Bhubaneswar 751024, Odisha, India
e-mail: sc4692@gmail.com

Prasanta Kumar Das

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

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 16, 2016; final manuscript received January 26, 2018; published online March 23, 2018. Assoc. Editor: Amitabh Narain.

J. Heat Transfer 140(7), 071701 (Mar 23, 2018) (9 pages) Paper No: HT-16-1747; doi: 10.1115/1.4039352 History: Received November 16, 2016; Revised January 26, 2018

Hydrodynamically and thermally fully developed flow of a Sisko fluid through a cylindrical tube has been investigated considering the effect of viscous dissipation. The effect of the convective term in the energy equation has been taken into account, which was neglected in the earlier studies for Sisko fluid flow. This convective term can significantly affect the temperature distribution if the radius of the tube is relatively large. The equations governing the flow and heat transfer are solved by the least square method (LSM) for both heating and cooling of the fluid. The results of the LSM solution are compared with that of the closed form analytical solution of the Newtonian fluid flow case and are found to match exactly. The results indicate that Nusselt number decreases with the increase in Brinkman number and increases with the increase in the Sisko fluid parameter for the heating of the fluid. In case of cooling, Nusselt number increases with the increase in the Brinkman number asymptotically to a very large value, changes its sign, and then decreases with the increase in Brinkman number. With the increase in the non-Newtonian index, Nusselt number is observed to increase.

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Figures

Grahic Jump Location
Fig. 1

Hydrodynamically and thermally fully developed flow through a section of tube

Grahic Jump Location
Fig. 7

Variation of Nu with Br for different values of n and N1 = −8, b = 0.9

Grahic Jump Location
Fig. 2

Nondimensional temperature and Nusselt number in Newtonian fluid flow for different Br, comparison between exact solution and analysis through LSM: (a) nondimensional temperature and (b) Nusselt number

Grahic Jump Location
Fig. 3

Nondimensional temperature for different values of the parameters: (a) for different b (constant Br = 5 and N1 = −2) and (b) for different Br (constant b = 0.4 and N1 = −2)

Grahic Jump Location
Fig. 4

Location of the maximum temperature with Brinkman number for different values of b for n = 2

Grahic Jump Location
Fig. 5

Nondimensional temperatures in case of heating for different parameters: (a) for different N1, Br = 5, b = 0.4 and (b) for different n, Br = 2, b = 0.5, and N1 = −8

Grahic Jump Location
Fig. 6

Variation of Nu with different parameters: (a) variation with b (for a constant Br) and (b) variation with Br (for constant b)

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