This communication studies the effect of melting heat transfer on the stagnation-point flow of a Jeffrey fluid over a stretching sheet. Heat transfer analysis is carried out in the presence of viscous dissipation. The arising differential system has been solved by the homotopy analysis method (HAM). The results indicate an increase in the velocity and the boundary layer thickness with an increase in the values of the elastic parameter (Deborah number) for a Jeffrey fluid which are opposite to those accounted for in the literature for the other subclasses of rate type fluids. Furthermore, an increase in the melting process corresponds to an increase in the velocity and a decrease in the temperature. A comparative study between the current computations and the previous studies is also presented in a limiting sense.

References

References
1.
Al-Nimr
,
M. A.
,
Khadrawi
,
A. F.
, and
Othman
,
A.
, 2005, “
Basic Viscoelastic Fluid Flow Problems Using Jeffrey’s Model
,”
Chem. Eng. Sci.
,
60
, pp.
7131
7136
.
2.
Hayat
,
T.
,
Ahmad
,
N.
, and
Ali
,
N.
, 2008, “
Effects of an Endoscope and Magnetic Field on the Peristalsis Involving Jeffrey Fluid
,”
Commun. Nonlinear Sci. Numer. Simul.
,
13
, pp.
1581
1591
.
3.
Kothandapani
,
M.
and
Srinivas
,
S.
, 2008, “
Peristaltic Transport of a Jeffrey Fluid Under the Effect of Magnetic Field in an Asymmetric Channel
,”
Int. J. Nonlinear Mech.
,
43
, pp.
915
924
.
4.
Hayat
,
T.
and
Ali
,
N.
, 2008, “
Peristaltic Motion of a Jeffrey Fluid Under the Effect of a Magnetic Field in a Tube
,”
Commun. Nonlinear Sci. Numer. Simul.
,
13
, pp.
1343
1352
.
5.
Hayat
,
T.
and
Mustafa
,
M.
, 2010, “
Influence of Thermal Radiation on the Unsteady Mixed Convection Flow of a Jeffrey Fluid Over a Stretching Sheet
,”
Z. Naturforsch. A: Phys. Sci.
,
65
, pp.
711
719
.
6.
Crane
,
L. J.
, 1970, “
Flow Past a Stretching Plate
,”
Z. Angew. Math. Phys.
,
21
, pp.
645
647
.
7.
Kiwan
,
S.
and
Al-Nimr
,
M. A.
, 2009, “
Flow and Heat Transfer Over a Stretched Micro-Surface
,”
ASME J. Heat Transfer
,
131
, pp.
1
8
.
8.
Kiwan
,
S.
and
Al-Nimr
,
M. A.
, 2010, “
Investigation into the Similarity Solution for Boundary Layer Flows in Microsystems
,”
ASME J. Heat Transfer
,
132
, pp.
1
9
.
9.
T. C.
Chiam
, T. C., 1994, “
Stagnation-Point Flow Towards a Stretching Plate
,”
J. Phys. Soc. Jpn.
,
63
, pp.
2443
2444
.
10.
Mahapatra
,
T. R.
,
Nandy
,
S. K.
, and
Gupta
,
A. S.
, “
Magnetohydrodynamic Stagnation-Point Flow of a Power-Law Fluid Towards a Stretching Surface
,”
Int. J. Non–Linear Mech.
,
44
, pp.
124
129
.
11.
Lapropulu
,
F.
and
Li
,
D.
, 2008, “
Stagnation-Point Flow of a Second Grade Fluid With Slip
,”
Int. J. Non-Linear Mech.
,
43
, pp.
941
947
.
12.
Hayat
,
T.
,
Abbas
,
Z.
, and
Sajid
,
M.
, 2009, “
MHD Stagnation-Point Flow of an Upper-Convected Maxwell Fluid Over a Stretching Surface
,”
Chaos, Soliton Fractals
,
39
, pp.
840
848
.
13.
Epstein
,
M.
, 1975, “
The Effect of Melting on Heat Transfer to Submerged Bodies
,”
Heat Mass Transfer
,
2
, pp.
97
104
.
14.
M.
Epstein
,
M.
and
Cho
,
D. H.
, 1976, “
Melting Heat Transfer in Steady Laminar Flow Over a Flat Plate
,”
ASME J. Heat Transfer
,
98
, pp.
531
533
.
15.
Liao
,
S. J.
, 2009, “
Notes on the Homotopy Analysis Method: Some Definitions and Theorems
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
, pp.
983
997
.
16.
Xu
,
X.
,
Liao
,
S. J.
, and
You
,
X. C.
, 2009, “
Analysis of Nonlinear Fractional Partial Differential Equations with Homotopy Analysis Method
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
, pp.
1152
1156
.
17.
Bataineh
,
A. S.
,
Noorani
,
M. S. M.
, and
Hashim
,
I.
, 2009, “
Homotopy Analysis Method for Singular IVPs of Emden—Fowler Type
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
, pp.
1121
1131
.
18.
Abbasbandy
,
S.
, 2010, “
Homotopy Analysis Method for the Kawahara Equation
,”
Nonlinear Anal.: Real World Appl.
,
11
, pp.
307
312
.
19.
Hayat
,
T.
,
Mustafa
,
M.
, and
Mesloub
,
S.
, 2010, “
Mixed Convection Boundary Layer Flow Over a Stretching Surface Filled With a Maxwell Fluid in Presence of Soret and Dufour Effects
,”
Z. Naturforsch. A: Phys. Sci.
,
65
, pp.
401
410
.
20.
Hayat
,
T.
,
Mustafa
,
M.
,
Shehzad
,
S. A.
, and
Obaidat
,
S.
, 2012, “
Melting Heat Transfer in the Stagnation-Point Flow of an Upper-Convected Maxwell (UCM) Fluid Past a Stretching Sheet
,”
Int. J. Numer. Methods Fluids
,
68
, pp.
233
243
.
21.
Mahapatra
,
T. R.
and
Gupta
,
A. S.
, 2002, “
Heat Transfer in the Stagnation-Point Flow Towards a Stretching Surface
,”
Heat Mass Transfer
,
38
, pp.
517
521
.
22.
Ishak
,
A.
,
Nazar
,
R.
,
Amin
,
N.
,
Filip
,
D.
, and
Pop
,
I.
, 2007, “
Mixed Convection in the StagnaTion-Point Flow Towards a Stretching Vertical Permeable Sheet
,”
Malaysian J. Math. Sci.
,
2
, pp.
217
226
.
23.
Schlichting
,
H.
,
Gersten
,
K.
, and
Gersten
,
K.
, 2000,
Boundary Layer Theory
,
Springer
,
New York.
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