Stagnation-point flow toward a stretching sheet with slip effects has been investigated. Unlike most classical works, Cattaneo–Christov heat flux model is utilized for the formulation of the energy equation instead of Fourier's law of heat conduction. A similarity transformation technique is adopted to reduce partial differential equations into a system of nonlinear ordinary differential equations. Numerical solutions are obtained by using shooting method to explore the features of various parameters for the velocity and temperature distributions. The obtained results are graphically presented and analyzed. It is found that fluid temperature has a converse relationship with the thermal relaxation time. A comparison of Cattaneo–Christov heat flux model and Fourier's law is also presented.

References

1.
Hiemenz
,
K.
,
1911
, “
Die Grenzschicht an einem in den Gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszlynder
,”
Dinglers J.
,
326
, pp.
321
324
.
2.
Crane
,
L. J.
,
1970
, “
Flow Past a Stretching Plate
,”
J. Appl. Math. Phys.
,
21
, pp.
645
647
.
3.
Chiam
,
T. C.
,
1996
, “
Heat Transfer With Variable Conductivity in a Stagnation-Point Flow Towards a Stretching Sheet
,”
Int. Commun. Heat Mass Transfer
,
23
, pp.
239
248
.
4.
Mahapatra
,
T. R.
, and
Gupta
,
A. S.
,
2002
, “
Heat Transfer in Stagnation-Point Flow Towards a Stretching Sheet
,”
Heat Mass Transfer
,
38
, pp.
517
521
.
5.
Nazar
,
R.
,
Amin
,
N.
,
Flip
,
D.
, and
Pop
,
I.
,
2004
, “
Unsteady Boundary Layer Flow in the Region of the Stagnation-Point on a Stretching Sheet
,”
Int. J. Eng. Sci.
,
42
, pp.
1241
1253
.
6.
Ishak
,
A.
,
Nazar
,
R.
, and
Pop
,
I.
,
2006
, “
Mixed Convection Boundary Layers in the Stagnation-Point Flow Toward a Stretching Vertical Sheet
,”
Meccanica
,
41
, pp.
509
518
.
7.
Layek
,
G. C.
,
Mukhopadhyay
,
S.
, and
Samad
,
S. A.
,
2007
, “
Heat and Mass Transfer Analysis for Boundary Layer Stagnation-Point Flow Towards a Heated Porous Stretching Sheet With Heat Absorption/Generation and Suction/Blowing
,”
Int. Commun. Heat Mass Transfer
,
34
, pp.
347
356
.
8.
Mahapatra
,
T. R.
, and
Gupta
,
A. S.
,
2001
, “
Magnetohydrodynamic Stagnation-Point Flow Towards a Stretching Sheet
,”
Acta Mech.
,
152
, pp.
191
196
.
9.
Lok
,
Y. Y.
,
Ishak
,
A.
, and
Pop
,
I.
,
2011
, “
MHD Stagnation-Point Flow Towards a Shrinking Sheet
,”
Int. J. Numer. Methods Heat Fluid Flow
,
2
, pp.
61
72
.
10.
Jafar
,
K.
,
Ishak
,
A.
, and
Nazar
,
R.
,
2013
, “
MHD Stagnation-Point Flow Over a Nonlinearly Stretching/Shrinking Sheet
,”
J. Aerosp. Eng.
,
26
, pp.
829
834
.
11.
Mahapatra
,
T. R.
,
Dholey
,
S.
, and
Gupta
,
A. S.
,
2007
, “
Momentum and Heat Transfer in the Magnetohydrodynamics Stagnation-Point Flow of a Viscoelastic Fluid Towards a Stretching Surface
,”
Meccanica
,
42
, pp.
263
272
.
12.
Ishak
,
A.
,
Lok
,
Y. Y.
, and
Pop
,
I.
,
2010
, “
Stagnation-Point Flow Over a Shrinking Sheet in a Micropolar Fluid
,”
Chem. Eng. Commun.
,
197
, pp.
1417
1427
.
13.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2011
, “
On the Stagnation-Point Flow Towards a Stretching Sheet With Homogeneous–Heterogeneous Reactions Effects
,”
Commun. Nonlinear Sci. Numer. Simul.
,
16
, pp.
4296
4302
.
14.
Bhattacharyya
,
K.
, and
Layek
,
G. C.
,
2011
, “
Effects of Suction/Blowing on Steady Boundary Layer Stagnation-Point Flow and Heat Transfer Towards a Shrinking Sheet With Thermal Radiation
,”
Int. J. Heat Mass Transfer
,
54
, pp.
302
307
.
15.
Boutros
,
Y. Z.
,
Abdel-Malek
,
M. B.
,
Badran
,
N. A.
, and
Hassan
,
H. S.
,
2006
, “
Lie-Group Method of Solution for Steady Two-Dimensional Boundary Layer Stagnation-Point Flow Towards a Heated Stretching Sheet Placed in a Porous Medium
,”
Meccanica
,
41
, pp.
681
691
.
16.
Nadeem
,
S.
,
Hussain
,
A.
, and
Khan
,
M.
,
2010
, “
HAM Solutions for Boundary Layer Flow in the Region of the Stagnation Point Towards a Stretching Sheet
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
, pp.
475
481
.
17.
Bhattacharyya
,
K.
,
Mukhopadhyay
,
S.
, and
Layek
,
G. C.
,
2011
, “
Slip Effects on Boundary Layer Stagnation-Point Flow and Heat Transfer Towards a Shrinking Sheet
,”
Int. J. Heat Mass Transfer
,
54
, pp.
308
313
.
18.
Andersson
,
H. I.
,
2002
, “
Slip Flow Past a Stretching Surface
,”
Acta Mech.
,
158
, pp.
121
125
.
19.
Wang
,
C. Y.
,
2002
, “
Flow Due to a Stretching Boundary With Partial Slip—An Exact Solution of the Navier-–Stokes Equations
,”
Chem. Eng. Sci.
,
57
, pp.
3745
3747
.
20.
Wang
,
C. Y.
,
2006
, “
Stagnation Slip Flow and Heat Transfer on a Moving Plate
,”
Chem. Eng. Sci.
,
61
, pp.
7668
7672
.
21.
Ariel
,
P. D.
,
Hayat
,
T.
, and
Asghar
,
S.
,
2006
, “
The Flow of an Elastic-Viscous Fluid Past a Stretching Sheet With Partial Slip
,”
Acta Mech.
,
187
, pp.
29
35
.
22.
Abbas
,
Z.
,
Wang
,
Y.
,
Hayat
,
T.
, and
Oberlack
,
M.
,
2009
, “
Slip Effects and Heat Transfer Analysis in a Viscous Fluid Over an Oscillatory Stretching Surface
,”
Int. J. Numer. Methods Fluids
,
59
, pp.
443
458
.
23.
Fang
,
T.
,
Zhang
,
J.
, and
Yao
,
S.
,
2009
, “
Slip MHD Viscous Flow Over a Stretching Sheet—An Exact Solution
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
, pp.
3731
3737
.
24.
Fang
,
T.
,
Yao
,
S.
,
Zhang
,
J.
, and
Aziz
,
A.
,
2010
, “
Viscous Flow Over a Shrinking Sheet With a Second Order Slip Flow Model
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
, pp.
1831
1842
.
25.
Mehmood
,
A.
, and
Ali
,
A.
,
2007
, “
The Effect of Slip Condition on Unsteady MHD Oscillatory Flow of a Viscous Fluid in a Planer Channel
,”
Rom. J. Phys.
,
52
(1), pp.
85
91
.https://www.researchgate.net/publication/241582115_The_effect_of_slip_condition_on_unsteady_MHD_oscillatory_flow_of_a_viscous_fluid_in_a_planer_channel
26.
Murthy
,
J. V. R.
, and
Kumar
,
M. P.
,
2014
, “
Effect of Slip Parameter on the Flow of Viscous Fluid Past an Impervious Sphere
,”
Int. J. Appl. Sci. Eng.
,
12
(3), pp.
203
223
.https://pdfs.semanticscholar.org/9a63/30e7e0d59bdfac1389d5d2743a5eaa95631a.pdf
27.
Khairy
,
Z.
, and
Ishak
,
A.
,
2016
, “
Stagnation-Point Flow Towards a Stretching Vertical Sheet With Slip Effects
,”
Mathematics
,
4
(
2
), p.
27
.
28.
Fourier
,
J. B. J.
,
1822
,
Thorie Analytique de la Chaleur
, J Gabay,
Paris, France
.
29.
Cattaneo
,
C.
,
1948
, “
Sulla Conduzione del Calore
,”
Atti Semin. Mat. Fis. Univ. Modena
,
3
, pp.
83
101
.
30.
Layek
,
G. C.
, and
Pati
,
N. C.
,
2017
, “
Bifurcations and Chaos in Convection Taking Non-Fourier Heat Flux
,”
Phys. Lett. A
,
381
, pp.
3568
3575
.
31.
Christov
,
C. I.
,
2009
, “
On Frame Indifferent Formulation of the Maxwell-Cattaneo Model of Finite Speed Heat Conduction
,”
Mech. Res. Commun.
,
36
, pp.
481
486
.
32.
Ciarletta
,
M.
, and
Straughan
,
B.
,
2010
, “
Uniqueness and Structural Stability for the Cattaneo-Christov Equations
,”
Mech. Res. Commun.
,
37
, pp.
445
447
.
33.
Straughan
,
B.
,
2010
, “
Thermal Convection With the Cattaneo-Christov Model
,”
Int. J. Heat Mass Transfer
,
53
, pp.
95
98
.
34.
Straughan
,
B.
,
2010
, “
Acoustic Waves in a Cattaneo-Christov Gas
,”
Phys. Lett. A
,
374
, pp.
2667
2669
.
35.
Han
,
S.
,
Zheng
,
L.
,
Li
,
C.
, and
Zhang
,
X.
,
2014
, “
Coupled Flow and Heat Transfer in Viscoelastic Fluid With Cattaneo-Christov Heat Flux Model
,”
Appl. Math. Lett.
,
38
, pp.
87
93
.
36.
Khan
,
J. A.
,
Mustafa
,
M.
,
Hayat
,
T.
, and
Alsaedi
,
A.
,
2015
, “
Numerical Study of Cattaneo-Christov Heat Flux Model for Viscoelastic Flow Due to an Exponentially Stretching Surface
,”
PLoS One
,
10
, p.
e0137363
.
37.
Hayat
,
T.
,
Qayyum
,
S.
,
Imtiaz
,
M.
, and
Alsaedi
,
A.
,
2016
, “
Impact of Cattaneo-Christov Heat Flux in Jeffrey Fluid Flow With Homogeneous-Heterogeneous Reactions
,”
PLoS One
,
11
(
2
), p.
e0148662
.
38.
Li
,
J.
,
Zheng
,
L.
, and
Liu
,
L.
,
2016
, “
MHD Viscoelastic Flow and Heat Transfer Over a Vertical Stretching With Cattaneo-Christov Heat Flux
,”
J Mol. Liq.
,
221
, pp.
19
25
.
39.
Mustafa
,
M.
,
2015
, “
Cattaneo-Christov Heat Flux Model for Rotating Flow and Heat Transfer of Upper Convected Maxwell Fluid
,”
AIP Adv.
,
5
(
4
), p.
047109
.
40.
Hayat
,
T.
,
Muhammad
,
T.
,
Alsaedi
,
A.
, and
Mustafa
,
M.
,
2016
, “
A Comparative Study for Flow of Viscoelastic Fluids With Cattaneo-Christov Heat Flux
,”
PLoS One
,
11
(
5
), p.
e0155185
.
41.
Hayat
,
T.
,
Muhammad
,
T.
,
Alsaedi
,
A.
, and
Ahmad
,
B.
,
2016
, “
Three-Dimensional Flow of Nanofluid With Cattaneo-Christov Double Diffusion
,”
Results Phys.
,
6
, pp.
897
903
.
42.
Hayat
,
T.
,
Muhammad
,
T.
, and
Alsaedi
,
A.
,
2017
, “
On Three-Dimensional Flow of Couple Stress Fluid With Cattaneo-Christov Heat Flux
,”
Chin. J. Phys.
,
55
(
3
), pp.
930
938.
43.
Shehzad
,
S. A.
,
Abbasi
,
F. M.
,
Hayat
,
T.
, and
Alsaedi
,
A.
,
2016
, “
Cattaneo-Christov Heat Flux Model for Darcy-Forchheimer Flow of an Oldroyd-B Fluid With Variable Conductivity and Non-Linear Convection
,”
J. Mol. Liq.
,
224
, pp.
274
278
.
44.
Hayat
,
T.
,
Muhammad
,
T.
,
Al-Mezal
,
S.
, and
Liao
,
S. J.
,
2016
, “
Darcy-Forchheimer Flow With Variable Thermal Conductivity and Cattaneo-Christov Heat Flux
,”
Int. J. Numer. Methods Heat Fluid Flow
,
26
(
8
), pp.
2355
2369
.
45.
Hayat
,
T.
,
Haider
,
F.
,
Muhammad
,
T.
, and
Alsaedi
,
A.
,
2017
, “
Darcy-Forchheimer Flow With Cattaneo-Christov Heat Flux and Homogeneous-Heterogeneous Reactions
,”
PLoS One
,
12
(
4
), p.
e0174938
.
46.
Haddad
,
S. A. M.
,
2014
, “
Thermal Instability in Brinkman Porous Media With Cattaneo-Christov Heat Flux
,”
Int. J. Heat Mass Transfer
,
68
, pp.
659
668
.
47.
Hayat
,
T.
,
Farooq
,
M.
,
Alsaedi
,
A.
, and
Al-Solamy
,
F.
,
2015
, “
Impact of Cattaneo-Christov Heat Flux in the Flow Over a Stretching Sheet With Variable Thickness
,”
AIP Adv.
,
5
(
8
), p.
087159
.
48.
Waqas
,
M.
,
Hayat
,
T.
,
Farooq
,
M.
,
Shehzad
,
S. A.
, and
Alsaedi
,
A.
,
2016
, “
Cattaneo-Christov Heat Flux Model for Flow of Variable Thermal Conductivity Generalized Burgers Fluid
,”
J. Mol. Liq.
,
220
, pp.
642
648
.
49.
Cantwell
,
B. J.
,
2002
,
Introduction to Symmetry Analysis
,
Cambridge University Press
, Cambridge, UK.
50.
Layek
,
G. C.
,
2015
,
An Introduction to Dynamical Systems and Chaos
,
Springer
, NewDelhi, India.
You do not currently have access to this content.