Research Papers: Natural and Mixed Convection

Transient Couple Stress Fluid Past a Vertical Cylinder With Bejan’s Heat and Mass Flow Visualization for Steady-State

[+] Author and Article Information
H. P. Rani

Department of Mathematics,
National Institute of Technology,
Warangal 506004, India
e-mail: hprani@nitw.ac.in

G. Janardhan Reddy

School of Physical Sciences,
Department of Mathematics,
Central University of Karnataka,
Gulbarga 585311, India
e-mail: janardhanreddy.nitw@gmail.com

Chang Nyung Kim

Department of Mechanical Engineering,
College of Advanced Technology
(Industrial Liaison Research Institute),
Kyung Hee University,
Gyeonggi-do 446-701, South Korea
e-mail: cnkim@khu.ac.kr

Y. Rameshwar

Department of Mathematics,
College of Engineering,
Osmania University,
Hyderabad 500 007, India
e-mail: yrhwrr1@yahoo.co.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 24, 2013; final manuscript received October 25, 2014; published online December 17, 2014. Assoc. Editor: Danesh / D. K. Tafti.

J. Heat Transfer 137(3), 032501 (Mar 01, 2015) (12 pages) Paper No: HT-13-1437; doi: 10.1115/1.4029085 History: Received August 24, 2013; Revised October 25, 2014; Online December 17, 2014

In the present study, the transient, free convective, boundary layer flow of a couple stress fluid flowing over a vertical cylinder is investigated, and the heat and mass functions for the final steady-state of the present flow are developed. The solution of the time dependent nonlinear and coupled governing equations is obtained with the aid of an unconditionally stable Crank–Nicolson type of numerical scheme. Numerical results for the time histories of the skin-friction coefficient, Nusselt number, and Sherwood number as well as the steady-state velocity, temperature, and concentration are presented graphically and discussed. Also, it is observed that time required for the flow variables to reach the steady-state increases with the increasing values of Schmidt and Prandtl numbers, while the opposite trend is observed with respect to the buoyancy ratio parameter. To analyze the flow variables in the steady-state, the heatlines and masslines are used in addition to streamlines, isotherms, and isoconcentration lines. When the heat and mass functions are properly made dimensionless, its dimensionless values are related to the local and overall Nusselt and Sherwood numbers. Boundary layer flow visualization indicates that the heatlines and masslines are dense in the vicinity of the hot wall, especially near the leading edge.

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Fig. 1

Schematic of the investigated problem

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Fig. 2

Grid independent test

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Fig. 3

Comparison of the temperature and concentration profiles

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Fig. 4

The simulated (a) transient velocity (U) at the point (1, 3.09) and (b) steady-state velocity (U) profile at X = 1.0

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Fig. 5

The simulated (a) transient temperature (T) at the point (1, 1.34) and (b) steady-state temperature (T) profile at X = 1.0

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Fig. 12

Steady-state masslines (M*) for (a) Sc = 0.6, Pr = 0.7, Bu = 2.0; (b) Sc = 0.94, Pr = 0.7, Bu = 2.0; (c) Sc = 0.94, Pr = 7.0, Bu = 2.0; and (d) Sc = 0.94, Pr = 0.7, Bu = 0.8

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Fig. 9

The simulated average Nusselt number (Nu¯)

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Fig. 10

The simulated average Sherwood number (Sh¯)

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Fig. 11

Steady-state streamlines (ψ*) (left) and heatlines (H*) (right) for (a) Sc = 0.6, Pr = 0.7, Bu = 2.0; (b) Sc = 0.94, Pr = 0.7, Bu = 2.0; (c) Sc = 0.94, Pr = 7.0, Bu = 2.0; and (d) Sc = 0.94, Pr = 0.7, Bu = 0.8

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Fig. 6

The simulated (a) transient concentration (C) at the point (1, 1.34) and (b) steady-state concentration (C) profile at X = 1.0

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Fig. 7

The simulated average skin-friction coefficient (Cf¯)

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Fig. 8

Comparison of the local Nusselt (NuX) and Sherwood number (ShX)

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Fig. 13

Steady-state velocity (U), temperature (T), and concentration (C) contours with Sc = 0.6, Pr = 0.7, and Bu = 2.0 for (a) couple stress fluid and (b) Newtonian fluid




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