This research concentrates on melting heat transfer in magnetohydrodynamics (MHD) flow of Sisko fluid bounded by a sheet with nonlinear stretching velocity. Modeling and analysis have been carried out in the presence of heat generation/absorption and magnetic field. Transformation procedure is implemented in obtaining nonlinear differential system. Convergence series solutions are developed. The solution for different influential parameters is analyzed. Skin friction coefficient and heat transfer rate are analyzed. It is observed that the qualitative results of magnetic field and melting heat transfer on velocity are similar.

References

References
1.
Sakiadis
,
B. C.
,
1961
, “
Boundary Layer Behavior on Continuous Solid Surfaces—Part I: Boundary Layer Equations for Two-Dimensional and Axisymmetric Flow
,”
AIChE J.
,
7
(
1
), pp.
26
28
.
2.
Chamkha
,
A. J.
, and
Khaled
,
A. R. A.
,
2000
, “
Hydromagnetic Combined Heat and Mass Transfer by Natural Convection From a Permeable Surface Embedded in a Fluid-Saturated Porous Medium
,”
Int. J. Numer. Methods Heat Fluid Flow
,
10
(
5
), pp.
455
477
.
3.
Takhar
,
H. S.
,
Chamkha
,
A. J.
, and
Nath
,
G.
,
2001
, “
Unsteady Three-Dimensional MHD-Boundary-Layer Flow Due to the Impulsive Motion of a Stretching Surface
,”
Acta Mech.
,
146
(
1–2
), pp.
59
71
.
4.
Hayat
,
T.
,
Ullah
,
I.
,
Alsaedi
,
A.
, and
Ahmad
,
B.
,
2017
, “
Radiative Flow of Carreau Liquid in Presence of Newtonian Heating and Chemical Reaction
,”
Results Phys.
,
7
, pp.
715
722
.
5.
Mudhaf
,
A. A.
, and
Chamkha
,
A. J.
,
2005
, “
Similarity Solutions for MHD Thermo-Solutal Marangoni Convection Over a Flat Surface in the Presence of Heat Generation or Absorption Effects
,”
Heat Mass Transfer
,
42
(
2
), pp.
112
121
.
6.
Chamkha
,
A. J.
, and
Mudhaf
,
A. A.
,
2005
, “
Unsteady Heat and Mass Transfer From a Rotating Vertical Cone With a Magnetic Field and Heat Generation or Absorption Effects
,”
Int. J. Therm. Sci.
,
44
(
3
), pp.
267
276
.
7.
Hayat
,
T.
,
Ullah
,
I.
,
Alsaedi
,
A.
, and
Ahmad
,
B.
,
2017
, “
Modeling Tangent Hyperbolic Nanoliquid Flow With Heat and Mass Flux Conditions
,”
Eur. Phys. J. Plus
,
132
(
3
), p.
112
.
8.
Khedr
,
M. E. M.
,
Chamkha
,
A. J.
, and
Bayomi
,
M.
,
2009
, “
MHD Flow of a Micropolar Fluid Past a Stretched Permeable Surface With Heat Generation or Absorption
,”
Nonlinear Anal.-Model.
,
14
(
1
), pp.
27
40
.https://www.mii.lt/na/issues/NA_1401/NA14103.pdf
9.
Hayat
,
T.
,
Ullah
,
I.
,
Muhammad
,
T.
, and
Alsaedi
,
A.
,
2017
, “
Thermal and Solutal Stratification in Mixed Convection Three-Dimensional Flow of an Oldroyd-B Nanofluid
,”
Results Phys.
,
7
, pp.
3797
3805
.
10.
Chamkha
,
A. J.
, and
Aly
,
A. M.
,
2010
, “
MHD Free Convection Flow of a Nanofluid Past a Vertical Plate in the Presence of Heat Generation or Absorption Effects
,”
Chem. Eng. Commun.
,
198
(
3
), pp.
425
441
.
11.
Chamkha
,
A. J.
,
1997
, “
MHD-Free Convection From a Vertical Plate Embedded in a Thermally Stratified Porous Medium With Hall Effects
,”
Appl. Math. Model
,
21
(
10
), pp.
603
609
.
12.
Hayat
,
T.
,
Ullah
,
I.
,
Alsaedi
,
A.
,
Waqas
,
M.
, and
Ahmad
,
B.
,
2017
, “
Three-Dimensional Mixed Convection Flow of Sisko Nanoliquid
,”
Int. J. Mech. Sci.
,
133
, pp.
273
282
.
13.
Chamkha
,
A. J.
,
Abbasbandy
,
S.
, and
Rashad
,
A. M.
,
2015
, “
Non-Darcy Natural Convection Flow for Non-Newtonian Nanofluid Over Cone Saturated in Porous Medium With Uniform Heat and Volume Fraction Fluxes
,”
Int. J. Numer. Methods Heat Fluid Flow
,
25
(
2
), pp.
422
437
.
14.
Hayat
,
T.
,
Ullah
,
I.
,
Ahmed
,
B.
, and
Alsaedi
,
A.
,
2017
, “
MHD Mixed Convection Flow of Third Grade Liquid Subject to Non-Linear Thermal Radiation and Convective Condition
,”
Results Phys.
,
7
, pp.
2804
2811
.
15.
Mustafa
,
M.
,
Mushtaq
,
A.
,
Hayat
,
T.
, and
Alsaedi
,
A.
,
2015
, “
Radiation Effects in Three-Dimensional Flow Over a Bi-Directional Exponentially Stretching Sheet
,”
J. Taiwan Inst. Chem. Eng.
,
47
, pp.
43
49
.
16.
Hayat
,
T.
,
Ullah
,
I.
,
Muhammad
,
T.
, and
Alsaedi
,
A.
,
2016
, “
Magnetohydrodynamic (MHD) Three-Dimensional Flow of Second Grade Nanofluid by a Convectively Heated Exponentially Stretching Surface
,”
J. Mol. Liq.
,
220
, pp.
1004
1012
.
17.
Hayat
,
T.
,
Ullah
,
I.
,
Alsaedi
,
A.
, and
Ahmad
,
B.
,
2018
, “
Numerical Simulation for Homogeneous–Heterogeneous Reactions in Flow of Sisko Fluid
,”
J. Braz. Soc. Mech. Sci. Eng.
,
40
(
2
), p. 73.
18.
Vajravelu
,
K.
,
2001
, “
Viscous Flow Over a Nonlinearly Stretching Sheet
,”
Appl. Math. Comput.
,
124
(
3
), pp.
281
288
.
19.
Cortell
,
R.
,
2008
, “
Effects of Viscous Dissipation and Radiation on the Thermal Boundary Layer Over a Nonlinearly Stretching Sheet
,”
Phys. Lett. A
,
372
(
5
), pp.
631
636
.
20.
Rana
,
P.
, and
Bhargava
,
R.
,
2012
, “
Flow and Heat Transfer of a Nanofluid Over a Nonlinearly Stretching Sheet: A Numerical Study
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
1
), pp.
212
226
.
21.
Mukhopadhyay
,
S.
,
2013
, “
Analysis of Boundary Layer Flow Over a Porous Nonlinearly Stretching Sheet With Partial Slip at the Boundary
,”
Alex. Eng. J
,
52
(
4
), pp.
563
569
.
22.
Mabood
,
F.
,
Khan
,
W. A.
, and
Ismail
,
A. I. M.
,
2015
, “
MHD Boundary Layer Flow and Heat Transfer of Nanofluids Over a Nonlinear Stretching Sheet: A Numerical Study
,”
J. Magn. Magn. Mater.
,
374
, pp.
569
576
.
23.
Hayat
,
T.
,
Aziz
,
A.
,
Muhammad
,
T.
, and
Ahmad
,
B.
,
2016
, “
On Magnetohydrodynamic Flow of Second Grade Nanofluid Over a Nonlinear Stretching Sheet
,”
J. Magn. Magn. Mater.
,
408
, pp.
99
106
.
24.
Das
,
K.
,
Acharya
,
N.
, and
Kundu
,
P. K.
,
2015
, “
Radiative Flow of MHD Jeffrey Fluid Past a Stretching Sheet With Surface Slip and Melting Heat Transfer
,”
Alex. Eng. J.
,
54
(
4
), pp.
815
821
.
25.
Epstein
,
M.
, and
Cho
,
D. H.
,
1976
, “
Melting Heat Transfer in Steady Laminar Flow Over a Flat Plate
,”
ASME J. Heat Transfer
,
98
(
3
), pp.
531
533
.
26.
Ishak
,
A.
,
Nazar
,
R.
,
Bachok
,
N.
, and
Pop
,
I.
,
2010
, “
Melting Heat Transfer in Steady Laminar Flow Over a Moving Surface
,”
Heat Mass Transfer
,
46
(
4
), pp.
463
468
.
27.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2010
, “
Melting Heat Transfer in Boundary Layer Stagnation-Point Flow Towards a Stretching/Shrinking Sheet
,”
Phys. Lett. A
,
374
(
40
), pp.
4075
4079
.
28.
Hayat
,
T.
,
Khan
,
M. I.
,
Waqas
,
M.
,
Alsaedi
,
A.
, and
Farooq
,
M.
,
2017
, “
Numerical Simulation for Melting Heat Transfer and Radiation Effects in Stagnation Point Flow of Carbon-Water Nanofluid
,”
Comput. Methods Appl. Mech. Eng.
,
315
, pp.
1011
1024
.
29.
Hiemenz
,
K.
,
1911
, “
Die Grenzschicht an Einem in Den Gleichformingen Flussigkeitsstrom Eingetauchten Graden Kreiszylinder
,”
Dinglers Polytech. J.
,
326
, pp.
321
324
.
30.
Mabood
,
F.
, and
Khan
,
W. A.
,
2014
, “
Approximate Analytic Solutions for Influence of Heat Transfer on MHD Stagnation Point Flow in Porous Medium
,”
Comput. Fluids
,
100
, pp.
72
78
.
31.
Chamkha
,
A. J.
, and
Ahmed
,
S. E.
,
2011
, “
Similarity Solution for Unsteady MHD Flow Near a Stagnation Point of a Three-Dimensional Porous Body With Heat and Mass Transfer, Heat Generation/Absorption and Chemical Reaction
,”
J. Appl. Fluid Mech.
,
4
(
2
), pp.
87
94
.http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=C6DB4994C572F81C77482F3405C7A20D?doi=10.1.1.679.5931&rep=rep1&type=pdf
32.
Hayat
,
T.
,
Shafiq
,
A.
, and
Alsaedi
,
A.
,
2016
, “
Characteristics of Magnetic Field and Melting Heat Transfer in Stagnation Point Flow of Tangent-Hyperbolic Liquid
,”
J. Magn. Magn. Mater.
,
405
, pp.
97
106
.
33.
Sisko
,
A. W.
,
1958
, “
The Flow of Lubricating Greases
,”
Ind. Eng. Chem.
,
50
(
12
), pp.
1789
1792
.
34.
Wang
,
Y.
,
Hayat
,
T.
,
Ali
,
N.
, and
Oberlack
,
M.
,
2008
, “
Magnetohydrodynamic Peristaltic Motion of a Sisko Fluid in a Symmetric or Asymmetric Channel
,”
Physics A
,
387
(
2–3
), pp.
347
362
.
35.
Abelman
,
S.
,
Hayat
,
T.
, and
Momoniat
,
E.
,
2009
, “
On the Rayleigh Problem for a Sisko Fluid in a Rotating Frame
,”
Appl. Math. Comput.
,
215
(
7
), pp.
2515
2520
.
36.
Khan
,
M.
, and
Shahzad
,
A.
,
2012
, “
On Axisymmetric Flow of Sisko Fluid Over a Radially Stretching Sheet
,”
Int. J. Nonlinear Mech.
,
47
(
9
), pp.
999
1007
.
37.
Mekheimer
,
K. S.
, and
El Kot
,
M. A.
,
2012
, “
Mathematical Modelling of Unsteady Flow of a Sisko Fluid Through an Anisotropically Tapered Elastic Arteries With Time-Variant Overlapping Stenosis
,”
Appl. Math. Model.
,
36
(
11
), pp.
5393
5407
.
38.
Malik
,
R.
,
Khan
,
M.
,
Munir
,
A.
, and
Khan
,
W. A.
,
2014
, “
Flow and Heat Transfer in Sisko Fluid With Convective Boundary Condition
,”
PLos One
,
9
(
10
), p.
e107989
.
39.
Liao
,
S.
,
2003
,
Beyond Perturbation: Introduction to the Homotopy Analysis Method
,
CRC Press
, Boca Raton, FL.
40.
Turkyilmazoglu
,
M.
,
2012
, “
Solution of the Thomas-Fermi Equation With a Convergent Approach
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
11
), pp.
4097
4103
.
41.
Abbasbandy
,
S.
,
Hashemi
,
M. S.
, and
Hashim
,
I.
,
2013
, “
On Convergence of Homotopy Analysis Method and Its Application to Fractional Integro-Differential Equations
,”
Quaest. Math.
,
36
(
1
), pp.
93
105
.
42.
Hayat
,
T.
,
Shehzad
,
S. A.
, and
Alsaedi
,
A.
,
2012
, “
Soret and Dufour Effects on Magnetohydrodynamic (MHD) Fow of Casson Fuid
,”
Appl. Math. Mech.
,
33
(
10
), pp.
1301
1312
.
43.
Hayat
,
T.
,
Ullah
,
I.
,
Muhammad
,
T.
,
Alsaedi
,
A.
, and
Shehzad
,
S. A.
,
2016
, “
Three-Dimensional Flow of Powell-Eyring Nanofluid With Heat and Mass Flux Boundary Conditions
,”
Chin. Phys. B
,
25
(
7
), p.
074701
.
44.
Lin
,
Y.
,
Zheng
,
L.
, and
Chen
,
G.
,
2015
, “
Unsteady Flow and Heat Transfer of Pseuodoplastic Nanofluid in a Finite Thin Flim on a Stretching Surface With Variable Thermal Conductivity and Viscous Dissipation
,”
Powder Technol.
,
274
, pp.
342
332
.
45.
Hayat
,
T.
,
Ullah
,
I.
,
Alsaedi
,
A.
, and
Farooq
,
M.
,
2017
, “
MHD Flow of Powell-Eyring Nanofluid Over a Non-Linear Stretching Sheet With Variable Thickness
,”
Results Phys.
,
7
, pp.
189
196
.
46.
Keimanesh
,
M.
,
Rashidi
,
M. M.
,
Chamkha
,
A. J.
, and
Jafari
,
R.
,
2011
, “
Study of a Third Grade Non-Newtonian Fluid Flow Between Two Parallel Plates Using the Multi-Step Differential Transform Method
,”
Comput. Math. Appl.
,
62
(
8
), pp.
2871
2891
.
47.
Hayat
,
T.
,
Ullah
,
I.
,
Muhammad
,
T.
, and
Alsaedi
,
A.
,
2017
, “
Radiative Three-Dimensional Flow With Soret and Dufour Effects
,”
Int. J. Mech. Sci.
,
133
, pp.
829
837
.
48.
Schilchting
,
H.
,
1964
,
Boundary Layer Theory
,
McGraw-Hill
,
New York
.
49.
Hayat
,
T.
,
Ullah
,
I.
,
Muhammad
,
T.
, and
Alsaedi
,
A.
,
2017
, “
A Revised Model for Stretched Flow of Third Grade Fluid Subject to Magneto Nanoparticles and Convective Condition
,”
J. Mol. Liq.
,
230
, pp.
608
615
.
50.
Zaigham Zia
,
Q. M.
,
Ullah
,
I.
,
Waqas
,
M.
,
Alsaedi
,
A.
, and
Hayat
,
T.
,
2018
, “
Cross Diffusion and Exponential Space Dependent Heat Source Impacts in Radiated Three-Dimensional (3D) Flow of Casson Fluid by Heated Surface
,”
Results Phys.
,
8
, pp.
1275
1282
.
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