Sage Journals: Discover world-class research

Abstract

In this study, an analytical investigation for analyzing the effects of viscous dissipation on the limiting Nusselt number for a hydro-dynamically fully developed laminar shear-driven flow through an asymmetrically heated annulus of two infinitely long concentric cylinders has been made, where the inner cylindrical rod is moving in an axial direction at a constant speed. On the basis of some common assumptions, an analytical framework has been devised to explore the effects of viscous dissipation on the heat transfer characteristics for the flow of Newtonian fluid, and, consequently, closed-form expressions for the limiting Nusselt numbers are evaluated. In the analysis, focus has been given on the viscous dissipative effect due to the shear produced by the movable inner cylindrical rod apart from the viscous dissipation due to internal fluid friction for the flow of a Newtonian fluid. The interactive effects of the Brinkman number and degree of asymmetry on the limiting Nusselt number are analytically investigated. It is observed from this study that the limiting Nusselt number becomes independent of Brinkman number when both the walls of the annulus are kept at an equal temperature. Moreover, the temperature profile in the conduction limit obtained with the consideration of viscous dissipation effect provides a boundary condition required for solving energy equation including the axial conduction in the fluid.

Keywords

Viscous dissipation limiting Nusselt number Newtonian fluid Brinkman number shear-driven flow asymmetrically heated annulus axial conduction

Get full access to this article

View all access options for this article.

References

Gad-el-Hak

. The fluid mechanics of micro-devices - the Freeman scholar lecture. J Fluids Eng 1999; 121: 5–33.

Brinkman

. Heat effects in capillary flow I. Appl Sci Res 1951; A2: 120–124.

Cheng

. Viscous dissipation effects on convective instability and heat transfer in plane Poiseuille flow heated from below. Appl Sci Res 1976; 32: 327–346.

Pinho

Oliveira

. Analysis of forced convection in pipes and channels with the simplified Phan-Thien-Tanner fluid. Int J Heat Mass Transfer 2000; 43: 2273–2287.

Lahjomri

Zniber

Oubarra

. Heat transfer by laminar Hartmann’s flow in the thermal entrance-region with uniform wall heat-flux: the Graetz problem extended. Energy Convers Manage 2003; 44: 11–34.

Nield

Kuznetzov

Xiong

. Thermally developing forced convection in a porous medium: parallel-plate channel with walls at a uniform temperature with axial conduction and viscous-dissipation effects. Int J Heat Mass Transfer 2003; 46: 643–651.

White

Muller

. Viscous heating and the stability of Newtonian and Viscoelastic Taylor-Couette flows. Phys Rev Lett 2000; 84: 5130–5133.

Aydin

. Effects of viscous dissipation on the heat transfer in a forced pipe. Part 1. Both hydrodynamically and thermally developed flow. Energy Convers Manage 2005; 46: 757–769.

Aydin

. Effects of viscous dissipation on the heat transfer in a forced pipe flow. Part 2. Thermally developing flow. Energy Convers Manage 2005; 46: 3091–3102.

10.

Aydin

Avci

. Viscous-dissipation effects on the heat transfer in a Poiseuille flow. Appl Energy 2006; 83: 495–512.

11.

Sheela-Francisca

Tso

. Viscous dissipation effects on parallel plates with constant heat flux boundary condition. Int Commun Heat Mass Transfer 2009; 36: 249–254.

12.

Hudson

Bankoff

. Heat transfer to steady coquette flow with pressure gradient. J Chem Eng Sci 1965; 20: 415–423.

13.

Sestak

Rieger

. Laminar heat transfer to a steady Couette flow between parallel plates. Int J Heat Mass Transfer 1969; 12: 71–80.

14.

Bruin

. Temperature distribution in Couette flow with and without additional pressure. Int J Heat Mass Transfer 1972; 15: 341–349.

15.

El-Ariny

Aziz

. Heat transfer in plane Couette flow. Trans ASME J Heat Transfer 1976; 198: 427–431.

16.

Lin

. Heat transfer to plane non-Newtonian Couette flow. Int J Heat Mass Transfer 1979; 22: 1117–1123.

17.

Davaa

Shigechi

Momoki

. Effects of viscous dissipation on fully-developed heat transfer of non-Newtonian fluids in plane laminar Poiseuille-Couette flow. Int Commun Heat Mass Transfer 2004; 31(5): 663–672.

18.

Tso

Sheela-Francisca

Hung

. Viscous dissipation effects of power-law fluid flow within parallel plates with constant heat fluxes. J Non-Newtonian Fluid Mech 2011; 165: 625–630.

19.

Lahjomri

Oubarra

Alemany

. Heat transfer by laminar Hartmann flow in the thermal entrance-region with a step change in wall temperature: the Graetz problem extended. Int J Heat Mass Transfer 2002; 45: 1127–1148.

20.

Barletta

. Laminar mixed convection with viscous dissipation in a vertical channel. Int J Heat Mass Transfer 1998; 41: 3501–3513.

Viscous dissipation effects on the limiting value of Nusselt numbers for a shear-driven flow through an asymmetrically heated annulus

Abstract

Keywords

Get full access to this article

References