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

Kalinga Institute of Industrial Technology (KIIT) University, School of Mechanical Engineering (KIIT) University Bhubaneswar, Odisha, 751024, India

P.K. Das

ASME Membership, Indian Institute of Technology Kharagpur, Department of Mechanical Engineering, (IIT) Kharagpur, West Bengal, 721302, India

1Corresponding author.

ASME doi:10.1115/1.4039352 History: Received November 16, 2016; Revised January 26, 2018


Hydro-dynamically 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, change 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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