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.
Issue Section:
Natural and Mixed Convection
References
1.
Sparrow
, E. M.
, and Gregg
, J. L.
, 1956
, “Laminar Free Convection Heat Transfer From the Outer Surface of a Vertical Circular Cylinder
,” ASME J. Heat Transfer
, 78
(8
), pp. 1823
–1829
.2.
Minkowycz
, W. J.
, and Sparrow
, E. M.
, 1974
, “Local Nonsimilar Solutions for Natural Convection on a Vertical Cylinder
,” ASME J. Heat Transfer
, 96
(2
), pp. 178
–183
.10.1115/1.34501613.
Fujii
, T.
, and Uehara
, H.
, 1970
, “Laminar Natural Convective Heat Transfer From the Outer Surface of a Vertical Cylinder
,” Int. J. Heat Mass Transfer
, 13
(3
), pp. 607
–615
.10.1016/0017-9310(70)90125-04.
Lee
, H. R.
, Chen
, T. S.
, and Armaly
, B. F.
, 1988
, “Natural Convection Along Slender Vertical Cylinders With Variable Surface Temperature
,” ASME J. Heat Transfer
, 110
(1
), pp. 103
–108
.10.1115/1.32504395.
Bottemanne
, F. A.
, 1972
, “Experimental Results of Pure and Simultaneous Heat and Mass Transfer by Free Convection About a Vertical Cylinder for Pr = 0.71 and Sc = 0.63
,” Appl. Sci. Res.
, 25
(1
), pp. 372
–382
.10.1007/BF003823106.
Chen
, T. S.
, and Yuh
, C. F.
, 1980
, “Combined Heat and Mass Transfer in Natural Convection Along a Vertical Cylinder
,” Int. J. Heat Mass Transfer
, 23
(4
), pp. 451
–461
.10.1016/0017-9310(80)90087-37.
Gebhart
, B.
, and Pera
, L.
, 1971
, “The Nature of Vertical Natural Convection Flows Resulting From the Combined Buoyancy Effects of Thermal and Mass Diffusion
,” Int. J. Heat Mass Transfer
, 14
(12
), pp. 2025
–2050
.10.1016/0017-9310(71)90026-38.
Dring
, R. P.
, and Gebhart
, B.
, 1966
, “Transient Natural Convection From Thin Vertical Cylinders
,” ASME J. Heat Transfer
, 88
(2
), pp. 246
–247
.10.1115/1.36915229.
Evan
, L. B.
, Reid
, R. C.
, and Drake
, E. M.
, 1968
, “Transient Natural Convection in a Vertical Cylinder
,” AIChE J.
, 14
(2
), pp. 251
–261
.10.1002/aic.69014021010.
Rani
, H. P.
, and Kim
, C. N.
, 2009
, “A Numerical Study of the Dufour and Soret Effects on Unsteady Natural Convection Flow Past an Isothermal Vertical Cylinder
,” Korean J. Chem. Eng.
, 26
(4
), pp. 946
–954
.10.1007/s11814-009-0158-y11.
Eringen
, A. C.
, 1966
, “Theory of Micropolar Fluids
,” J. Math. Mech.
, 16
(1
), pp. 1
–18
.10.1512/iumj.1967.16.1600112.
13.
Chu
, H. M.
, Li
, W. L.
, and Hu
, S. Y.
, 2006
, “Effects of Couple Stresses on Pure Squeeze EHL Motion of Circular Contacts
,” J. Mech.
22
(1
), pp. 77
–84
.10.1017/S172771910000080014.
Lin
, J.
, 1998
, “Squeeze Film Characteristics of Finite Journal Bearings: Couple Stress Fluid Model
,” Tribol. Int.
, 31
(4
), pp. 201
–207
.10.1016/S0301-679X(98)00022-X15.
Naduvinamani
, N. B.
, and Patil
, S. B.
, 2009
, “Numerical Solution of Finite Modified Reynolds Equation for Couple Stress Squeeze Film Lubrication of Porous Journal Bearings
,” Comput. Struct.
, 87
(21
), pp. 1287
–1295
.10.1016/j.compstruc.2009.08.00416.
Chang-Jian
, C.
, Yau
, H.
, and Chen
, J.
, 2010
, “Nonlinear Dynamic Analysis of a Hybrid Squeeze-Film Damper-Mounted Rigid Rotor Lubricated With Couple Stress Fluid and Active Control
,” Appl. Math. Modell.
, 34
(9
), pp. 2493
–2507
.10.1016/j.apm.2009.11.01417.
Srivastava
, V. P.
, 2003
, “Flow of a Couple Stress Fluid Representing Blood Through Stenotic Vessels With a Peripheral Layer
,” Indian J. Pure Appl. Math.
, 34
(12
), pp. 1727
–1740
.18.
Srivastava
, L. M.
, 1986
, “Peristaltic Transport of a Couple Stress Fluid
,” Rheol. Acta
, 25
(6
), pp. 638
–641
.10.1007/BF0135817219.
Umavathi
, J. C.
, and Malashetty
, M. S.
, 1999
, “Oberbeck Convection Flow of a Couple Stress Fluid Through a Vertical Porous Stratum
,” Int. J. Non-Linear Mech.
, 34
(6
), pp. 1037
–1045
.10.1016/S0020-7462(98)00074-220.
Habtu
, A.
, and Radhakrishnamacharya
, G.
, 2010
, “Dispersion of a Solute in Peristaltic Motion of a Couple Stress Fluid Through a Porous Medium With Slip Condition
,” Int. J. Chem. Biol. Eng.
, 3
(4
), pp. 205
–210
.21.
Tasawar
, H.
, Muhammad
, A.
, Ambreen
, S.
, and Hendi
, Awatif A.
, 2012
, “Unsteady Three Dimensional Flow of Couple Stress Fluid Over a Stretching Surface With Chemical Reaction
,” Nonlinear Anal.
, 17
(1
), pp. 47
–59
.22.
Kimura
, S.
, and Bejan
, A.
, 1983
, “The Heatline Visualization of Convective Heat Transfer
,” ASME J. Heat Transfer
, 105
(4
), pp. 916
–919
.10.1115/1.324568423.
Bejan
, A.
, 1984
, Convection Heat Transfer
, 1st ed., Wiley
, New York
, pp. 22
, 23, 450, and 452.24.
Trevisan
, O. V.
, and Bejan
, A.
, 1987
, “Combined Heat and Mass Transfer by Natural Convection in a Vertical Enclosure
,” ASME J. Heat Transfer
, 109
(1
), pp. 104
–112
.10.1115/1.324802725.
Costa
, V. A. F.
, 2000
, “Heatline and Massline Visualization of Laminar Natural Convection Boundary Layers Near a Vertical Wall
,” Int. J. Heat Mass Transfer
, 43
(20
), pp. 3765
–3774
.10.1016/S0017-9310(00)00028-426.
Costa
, V. A. F.
, 2006
, “Bejan’s Heatlines and Masslines for Convection Visualization and Analysis
,” ASME Appl. Mech. Rev.
, 59
(3
), pp. 126
–145
.10.1115/1.217768427.
Aggarwal
, S. K.
, and Manhapra
, A.
, 1989
, “Use of Heatlines for Unsteady Buoyancy-Driven Flow in a Cylindrical Enclosure
,” ASME J. Heat Transfer
, 111
(2
), pp. 576
–578
.10.1115/1.325071928.
Aggarwal
, S. K.
, and Manhapra
, A.
, 1989
, “Transient Natural Convection in a Cylindrical Enclosure Nonuniformly Heated at the Top Wall
,” Numer. Heat Transfer, Part A
, 15
(3
), pp. 341
–356
.10.1080/1040778890894469229.
Mukhopadhyay
, A.
, Qin
, X.
, Aggarwal
, S. K.
, and Puri
, I. K.
, 2002
, “On Extension of Heatline and Massline Concepts to Reacting Flows Through Use of Conserved Scalars
,” ASME J. Heat Transfer
, 124
(4
), pp. 791
–799
.10.1115/1.147313930.
Basak
, T.
, Singh
, A. K.
, Richard
, R.
, and Roy
, S.
, 2013
, “Finite Element Simulation With Heatlines and Entropy Generation Minimization During Natural Convection Within Porous Tilted Square Cavities
,” Ind. Eng. Chem. Res.
, 52
(23
), pp. 8046
–8061
.10.1021/ie400575531.
Singh
, C.
, 1982
, “Lubrication Theory for Couple Stress Fluids and Its Applications to Short Bearing
,” Wear
, 88
(3
), pp. 281
–290
.10.1016/0043-1648(82)90256-332.
Stokes
, V. K.
, 1984
, Theories of Fluids With Microstructure
, Springer-Verlag
, New York
.33.
Ganesan
, P.
, and Rani
, H. P.
, 1998
, “Transient Natural Convection Along Vertical Cylinder With Heat and Mass Transfer
,” Heat Mass Transfer
, 33
(5–6
), pp. 449
–455
.10.1007/s002310050214Copyright © 2015 by ASME
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