The present paper investigates analytically the two-dimensional heat transfer and entropy generation characteristics of axisymmetric, incompressible viscous fluid flow in a horizontal circular pipe. The flow is subjected to an externally applied uniform suction across the wall in the normal direction and a constant magnetic field. Constant wall temperature is considered as the thermal boundary condition. The reduced Navier–Stokes equations in a cylindrical coordinate system are solved to obtain the velocity and temperature distributions. The velocity distributions are expressed in terms of stream function and the solution is obtained using the homotopy analysis method (HAM). Validation with earlier nonmagnetic solutions in the literature is incorporated. The effects of various parameters on axial and radial velocities, temperature, axial and radial entropy generation numbers, and axial and radial Bejan numbers are presented graphically and interpreted at length. Streamlines, isotherms, pressure, entropy generation number, and Bejan number contours are also visualized. Increasing magnetic body force parameter shifts the peak of the velocity curve near to the axis, whereas it accelerates the radial flow. The study is relevant to thermodynamic optimization of magnetic blood flows and electromagnetic industrial flows featuring heat transfer.

References

References
1.
Berman
,
A. S.
,
1953
, “
Laminar Flow in Channels With Porous Walls
,”
J. App. Phys.
,
24
(
9
), pp.
1232
1235
.
2.
Bansal
,
J. L.
,
1967
, “
Laminar Flow Through a Uniform Circular Pipe With Small Suction
,”
Proc. Natl. Acad. Sci.
,
32A
(4), pp.
368
378
.https://insa.nic.in/writereaddata/UpLoadedFiles/PINSA/Vol32A_1966_4_Art06.pdf
3.
Terril
,
R. M.
,
1982
, “
An Exact Solution for Flow in a Porous Pipe
,”
J. Appl. Math. Phys.
,
33
(4), pp.
547
542
.
4.
Terril
,
R. M.
,
1983
, “
Laminar Flow Through a Porous Tube
,”
ASME J. Fluids Eng.
,
105
, pp.
303
306
.
5.
Tsangaris
,
S.
,
Kondaxakis
,
D.
, and
Vlachakis
,
N. W.
,
2007
, “
Exact Solution for Flow in a Porous Pipe With Unsteady Wall Suction/Injection
,”
Commun. Nonlinear Sci. Numer. Simul.
,
12
(
7
), pp.
1181
1189
.
6.
Cox
,
B. J.
, and
Hill
,
J. M.
,
2011
, “
Flow Through a Circular Tube With Permeable Navier Slip Boundary
,”
Nanoscale Res. Lett.
,
6
(
1
), pp.
389
397
.
7.
Ramana Murthy
,
J. V.
,
Nagaraju
,
G.
, and
Muthu
,
P.
,
2012
, “
Micropolar Fluid Flow Generated by a Circular Cylinder Subject to Longitudinal and Torsional Oscillations With Suction/Injection
,”
Tamkang J. Math.
,
43
(3), pp.
339
356
.
8.
Boutros
,
Y. Z.
,
Abd-el-Malek
,
M. B.
,
Badran
,
N. A.
, and
Hassan
,
H. S.
,
2006
, “
Lie-Group Method for Unsteady Flows in a Semi-Infinite Expanding or Contracting Pipe With Injection or Suction Through a Porous Wall
,”
J. Comput. Appl. Math.
,
197
(
2
), pp.
465
494
.
9.
Terril
,
R. M.
, and
Shrestha
,
G. M.
, “
Laminar Flow Through Channels With Porous Walls and With an Applied Transverse Magnetic Field
,”
Appl. Sci. Res.
,
11
(
1–2
), pp.
134
144
.
10.
Attia
,
H. A.
,
2003
, “
Unsteady Flow of a Dusty Conducting Non-Newtonian Fluid Through a Pipe
,”
Can. J. Phys.
,
81
(
5
), pp.
789
795
.
11.
Attia
,
H. A.
, and
Ahmed
,
M. E. S.
,
2005
, “
Circular Pipe MHD Flow of a Dusty Bingham Fluid
,”
Tamkang J. Sci. Eng.
,
8
(4), pp.
257
265
.http://www2.tku.edu.tw/~tkjse/8-4/8-4-1.pdf
12.
Moustafa
,
E.
,
2006
, “
MHD of a Fractional Viscoelastic Fluid in a Circular Tube
,”
Mech. Res. Commun.
,
33
(2), pp.
261
268
.
13.
Ramana Murthy
,
J. V.
,
Bahali
,
N. K.
, and
Srinivasacharya
,
D.
,
2010
, “
Unsteady Flow of a Micropolar Fluid Through a Circular Pipe Under a Transverse Magnetic Field With Suction/Injection
,”
Selguk J. Appl. Math.
,
11
(2), pp.
13
25
.
14.
Ramana Murthy
,
J. V.
,
Sai
,
K. S.
, and
Bahali
,
N. K.
,
2011
, “
Steady Flow of Micropolar Fluid in a Rectangular Channel Under Transverse Magnetic Field With Suction
,”
AIP Adv.
,
1
(
3
), p.
032123
.
15.
Ou
,
J. W.
, and
Cheng
,
K. C.
,
1973
, “
Viscous Dissipation Effects on Thermal Entrance Heat Transfer in Pipe Flows With Uniform Wall Heat Flux
,”
Appl. Sci. Res.
,
28
(
1
), pp.
289
301
.
16.
El Dabe
,
N. T.
,
Moatimid
,
G. M.
, and
Ali
,
H. S. M.
,
2002
, “
Rivlin-Ericksen Fluid in Tube of Varying Cross Section With Mass and Heat Transfer
,”
Z. Naturforsch. A
,
57
(A), pp.
863
873
.
17.
Jha
,
B. K.
, and
Ajibade
,
A. O.
,
2012
, “
Effect of Viscous Dissipation on Natural Convection Flow Between Vertical Parallel Plates With Time-Periodic Boundary Conditions
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
, pp.
1576
1587
.
18.
Srinivas
,
S.
,
Vijayalakshmi
,
A.
,
Reddy
,
A. S.
, and
Mohan
,
T. R. R.
,
2016
, “
MHD Flow of a Nanofluid in an Expanding or Contracting Porous Pipe With Chemical Reaction and Heat Source/Sink
,”
Propul. Power Res.
,
5
(
2
), pp.
134
148
.
19.
Sahin
,
A. Z.
, and
Ben-Mansour
,
R.
,
2003
, “
Entropy Generation in Laminar Fluid Flow Through a Circular Pipe
,”
Entropy
,
5
(
5
), pp.
404
416
.
20.
Ben-Mansour
,
R.
, and
Sahin
,
A. Z.
,
2005
, “
Entropy Generation in Developing Laminar Fluid Flow Through a Circular Pipe With Variable Properties
,”
Heat Mass Transfer
,
42
(
1
), pp.
1
11
.
21.
Haddad
,
O. M.
,
Alkam
,
M. K.
, and
Khasawneh
,
M. T.
,
2004
, “
Entropy Generation Due to Laminar Forced Convection in the Entrance Region of a Concentric Annulus
,”
Energy
,
29
(
1
), pp.
35
55
.
22.
Ozalp
,
A. A.
,
2009
, “
Entropy Analysis of Laminar-Forced Convection in a Pipe With Wall Roughness
,”
Int. J. Exergy
,
6
(
2
), pp.
249
275
.
23.
Sarkar
,
S.
,
Ganguly
,
S.
, and
Dalal
,
A.
,
2014
, “
Analysis of Entropy Generation During Mixed Convective Heat Transfer of Nanofluids Past a Rotating Circular Cylinder
,”
ASME J. Heat Transfer
,
136
(6), p. 062501.
24.
Nagaraju
,
G.
,
Srinivas
,
J.
,
Ramana Murthy
,
J. V.
, and
Rashad
,
A. M.
,
2017
, “
Entropy Generation Analysis of the MHD Flow of Couple Stress Fluid Between Two Concentric Rotating Cylinders With Porous Lining
,”
Heat Transfer Asian Res.
,
46
(
4
), pp.
316
330
.
25.
Alizadeh
,
R.
,
Rahimi
,
A. B.
,
Arjmandzadeh
,
R.
,
Najafi
,
M.
, and
Alizadeh
,
A.
,
2016
, “
Unaxisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid With Variable Viscosity on a Cylinder in Constant Heat Flux
,”
Alexandria Eng. J.
,
55
(
2
), pp.
1271
1283
.
26.
Ramana Murthy
,
J. V.
, and
Srinivas
,
J.
,
2013
, “
Second Law Analysis for Poiseuille Flow of Immiscible Micropolar Fluids in a Channel
,”
Int. J. Heat Mass Transfer
,
65
, pp.
254
264
.
27.
Adesanya
,
S. O.
,
Kareem
,
S. O.
,
Falade
,
J. A.
, and
Arekete
,
S. A.
,
2015
, “
Entropy Generation Analysis for a Reactive Couple Stress Fluid Flow Through a Channel Saturated With Porous Material
,”
Energy
,
93
, pp.
1239
1245
.
28.
Srinivasacharya
,
D.
, and
Hima Bindu
,
K.
,
2015
, “
Entropy Generation in a Micropolar Fluid Flow Through an Inclined Channel With Slip and Convective Boundary Conditions
,”
Energy
,
91
, pp.
72
83
.
29.
Srinivas
,
J.
,
Nagaraju
,
G.
, and
Bég
,
O. A.
,
2016
, “
Mathematical Modeling of Entropy Generation in Magnetized Micropolar Flow Between co-Rotating Cylinders With Internal Heat Generation
,”
Alexandria Eng. J.
,
55
(3), pp.
1969
1982
.
30.
Aksoy
,
Y.
,
2016
, “
Effects of Couple Stresses on the Heat Transfer and Entropy Generation Rates for a Flow Between Parallel Plates With Constant Heat Flux
,”
Int. J. Therm. Sci.
,
107
, pp.
1
12
.
31.
Nezhad
,
A. H.
, and
Shahri
,
M. F.
,
2016
, “
Entropy Generation Case Studies of Two Immiscible Fluids Under the Influence of a Uniform Magnetic Field in an Inclined Channel
,”
J. Mech.
,
32
(6), pp. 749–757.
32.
Jangili
,
S.
, and
Bég
,
O. A.
,
2018
, “
Homotopy Study of Entropy Generation in Magnetized Micropolar Flow in a Vertical Parallel Plate Channel With Buoyancy Effect
,”
Heat Transfer Res.
,
49
(
6
), pp.
529
553
.
33.
Liao
,
S. J.
,
2003
,
Beyond Perturbation: Introduction to Homotopy Analysis Method
,
Chapman & Hall/CRC Press
,
Boca Raton, FL
.
34.
Bird
,
R. B.
,
Stewart
,
W. E.
, and
Lightfoot
,
E. N.
,
1960
,
Transport Phenomena
,
Wiley
,
New York
.
35.
Bejan
,
A.
,
1982
, “
Second Law Analysis in Heat Transfer and Thermal Design
,”
Adv. Heat Transfer
,
15
, pp.
1
58
.
36.
Paoletti
,
S.
,
Rispoli
,
F.
, and
Sciubba
,
E.
,
1989
, “
Calculation of Exergetic Losses in Compact Heat Exchanger Passages
,”
Adv. Energy Syst. Div.
,
10
(2), pp.
21
29
.
37.
Ramana Murthy
,
J. V.
,
Srinivas
,
J.
, and
Chamkha
,
A. J.
,
2016
, “
Analysis of Entropy Generation in an Inclined Channel Flow Containing Two Immiscible Micropolar Fluids Using HAM
,”
Int. J. Numer. Methods Heat Fluid Flow
,
26
(3/4), pp.
1
24
.
38.
Fatih
,
S.
, and
Oztop
,
H. F.
,
2016
, “
MHD Mixed Convection and Entropy Generation of Power Law Fluids in a Cavity With a Partial Heater Under the Effect of a Rotating Cylinder
,”
Int. J. Heat Mass Transfer
,
98
, pp.
40
51
.
39.
Adesanya
,
S. O.
,
Falade
,
J. A.
,
Jangili
,
S.
, and
Beg
,
O. A.
,
2017
, “
Irreversibility Analysis for Reactive Third-Grade Fluid Flow and Heat Transfer With Convective Wall Cooling
,”
Alexandria Eng. J.
,
56
(
1
), pp.
153
160
.
40.
Gardner
,
R. A.
,
1968
, “
Laminar Pipe Flow in a Transverse Magnetic Field With Heat Transfer
,”
Int. J. Heat Mass Transfer
,
11
(
6
), pp.
1076
1081
.
41.
Cunha
,
F. R.
, and
Sobral
,
Y. D.
,
2005
, “
Asymptotic Solution for Pressure-Driven Flows of Magnetic Fluids in Pipes
,”
J. Magnet. Magn. Mater.
,
289
, pp.
314
317
.
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