The steady-state three-dimensional flow and heat transfer of a viscous, compressible fluid in the vicinity of stagnation point region on a flat plate with constant wall temperature is investigated by similarity solution approach, taking into account the variation of density of the fluid with respect to temperature. The free stream, along z-direction, impinges on the flat plate to produce a flow with different velocity components. An exact solution of the problem is obtained for the three dimensional case by the reduction of the Navier–Stokes and energy equations using appropriate similarity transformations introduced for the first time. The nonlinear ordinary differential equations are solved numerically using a finite difference scheme. Computations have been conducted for different values of the parameters characterizing the problem. The obtained results show that increasing the value of compressibility factor and wall temperature both cause the value of the velocity components and temperature gradients and pressure gradients in the vicinity of the plate to increase.

References

References
1.
Howarth
,
L.
,
1951
, “
The Boundary Layer in Three-Dimensional Flow—Part II: The Flow Near a Stagnation Point
,”
Philos. Mag.
,
42
(
7
), pp.
1433
1440
.
2.
Wang
,
C. Y.
,
1973
, “
Axisymmetric Stagnation Flow Towards a Moving Plate
,”
AIChE J.
,
19
, pp.
1080
1081
.10.1002/aic.690190540
3.
Kumari
,
M.
, and
Nath
,
G.
,
1978
, “
Unsteady Laminar Compressible Boundary-Layer Flow at a Three-Dimensional Stagnation Point
,”
J. Fluid Mech.
,
87
, pp.
705
717
.10.1017/S0022112078001834
4.
Vasantha
,
R.
, and
Nath
,
G.
,
1989
, “
Semi-Similar Solutions of the Unsteady Compressible Second-Order Boundary Layer Flow at the Stagnation Point
,”
Int. J. Heat Mass Transfer
,
32
, pp.
435
444
.10.1016/0017-9310(89)90131-2
5.
Chiriac
, V
. A.
, and
Ortega
,
A.
,
2002
, “
A Numerical Study of the Unsteady Flow and Heat Transfer in a Transitional Confined Slot Jet Impinging on an Isothermal Surface
,”
Int. J. Heat Mass Transfer
,
45
, pp.
1237
1248
.10.1016/S0017-9310(01)00224-1
6.
Saleh
,
R.
, and
Rahimi
,
A. B.
,
2004
, “
Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity and Uniform Transpiration
,”
ASME J. Fluids Eng.
,
126
, pp.
997
1005
.10.1115/1.1845556
7.
Rahimi
,
A. B.
, and
Saleh
,
R.
,
2007
, “
Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration
,”
ASME J. Fluids Eng.
,
129
, pp.
107
115
.10.1115/1.2375132
8.
Rahimi
,
A. B.
, and
Saleh
,
R.
,
2008
, “
Similarity Solution of Un-Axisymmetric Heat Transfer in Stagnation-Point Flow on a Cylinder With Simultaneous Axial and Rotational Movements
,”
ASME J. Heat Transfer
,
130
, p.
054502
.10.1115/1.2885173
9.
Baris
,
S.
,
2003
, “
Steady Three-Dimensional Flow of a Second Grade Fluid Towards a Stagnation Point at a Moving Flat Plate
,”
Turk. J. Eng. Environ. Sci.
,
27
, pp.
21
29
.
10.
Zuccher
,
S.
,
Tumin
,
A.
, and
Reshotko
,
E.
,
2006
, “
Parabolic Approach to Optimal Perturbations in Compressible Boundary Layers
,”
J. Fluid Mech.
,
556
, pp.
189
216
.10.1017/S0022112006009451
11.
Rahimi
,
A. B.
, and
Esmaeilpour
,
M.
,
2011
, “
Axisymmetric Stagnation Flow Obliquely Impinging on a Moving Circular Cylinder With Uniform Transpiration
,”
Int. J. Numer. Methods Fluids
,
65
, pp.
1084
1095
.10.1002/fld.2230
12.
Abbasi
,
A. S.
, and
Rahimi
,
A. B.
,
2009
, “
Non-Axisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate
,”
ASME J. Fluids Eng.
,
131
, p.
074501
.10.1115/1.3153366
13.
Abbasi
,
A. S.
, and
Rahimi
,
A. B.
,
2009
, “
Three-Dimensional Stagnation Flow and Heat Transfer on a Flat Plate With Transpiration
,”
J. Thermophys. Heat Transfer
,
23
, pp.
513
521
.10.2514/1.41529
14.
Abbasi
,
A. S.
,
Rahimi
,
A. B.
, and
Niazman
,
H.
,
2011
, “
Exact Solution of Three-Dimensional Unsteady Stagnation Flow on a Heated Plate
,”
J. Thermodyn. Heat Transfer
,
25
, pp.
55
58
.10.2514/1.48702
15.
Abbasi
,
A. S.
, and
Rahimi
,
A. B.
,
2012
, “
Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate
,”
ASME J. Heat Transfer
,
134
, p.
064501
.10.1115/1.4005742
16.
Mohammadiun
,
H.
, and
Rahimi
,
A. B.
,
2012
, “
Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous, Compressible Fluid on a Cylinder With Constant Wall Temperature
,”
J. Thermophys. Heat Transfer
,
26
(
3
), pp.
494
502
.
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