In this study, Prandtl’s transposition theorem is used to stretch the ordinary coordinate-system in certain direction. The small wavy surface can be transferred into a calculable plane coordinate-system. The new governing equations of turbulent forced convection along wavy surface are derived from complete Navier–Stokes equations. A simple transformation is proposed to transform the governing equations into boundary layer equations for solution by the cubic spline collocation method. The effects such as the wavy geometry, the local skin-friction and Nusselt number are studied. The results of the simulation show that it is more significant to increase heat transfer with small wavy surface than plat surface.

References

References
1.
Yao
,
L. S.
, 1983, “
Natural Convection Along a Vertical Wavy Surface
,”
ASME J. Heat Transfer
,
105
, pp.
465
468
.
2.
Yao
,
L. S.
, 1988, “
A Note on Prandtl’s Transposition Theorem
,”
ASME J. Heat Transfer
,
100
, pp.
507
508
.
3.
Moulic
,
S. G.
, and
Yao
,
L. S.
, 1989, “
Natural Convection Along a Vertical Wavy Surface With Uniform Heat Flux
,”
ASME J. Heat Transfer
,
111
, pp.
1106
1108
.
4.
Moulic
,
S. G.
, and
Yao
,
L. S.
, 1989, “
Mixed Convection Along a Vertical Wavy Surface
,”
ASME J. Heat Transfer
,
111
, pp.
974
978
.
5.
Yao
,
L. S
, 2006, “
Natural Convection Along a Vertical Complex Wavy Surface
,”
Int. J. Heat Mass Transfer
,
49
, pp.
281
286
.
6.
Wang
,
C. C.
, and
Chen
,
C. K.
, 2002, “
Forced Convection in a Wavy-Wall Channel
,”
Int. J. Heat Mass Transfer
,
45
, pp.
2587
2595
.
7.
Wang
,
C. C.
, and
Chen
,
C. K.
, 2000, “
Forced Convection in Micropolar Fluid Flow Over a Wavy Surface
,”
Numer. Heat Transfer
,
37
, pp.
271
279
.
8.
Wang
,
C. C.
, and
Chen
,
C. K.
, 2001, “
Transient Force and Free Convection Along a Vertical Wavy Surface in Micropolar Fluids
,”
Int. J. Heat Mass Transfer
,
44
, pp.
3241
3251
.
9.
Lien
,
F. S.
,
Chen
,
T. M.
, and
Chen
,
C. K.
, 1990, “
Analysis of a Free-Convection Micropolar Boundary Layer About a Horizontal Permeable Cylinder at a Non-Uniform Thermal Condition
,”
ASME J. Heat Transfer
,
112
, pp.
504
506
.
10.
Lien
,
F. S.
,
Chen
,
C. K.
, and
Cleaver
,
J. W.
, 1986, “
Analysis of Natural Convection Flow of Micropolar Fluid About a Sphere With Blowing and Suction
,”
ASME J. Heat Transfer
,
108
, pp.
967
970
.
11.
Yang
,
Y. T.
,
Chen
,
C. K.
, and
Lin
,
M. T.
, 1996, “
Natural Convection of Non-Newtonian Fluids Along a Wavy Vertical Plate Including the Magnetic Field Effect
,”
Int. J. Heat Mass Transfer
,
39
, pp.
2831
2842
.
12.
Chen
,
C. K.
,
Yang
,
Y. T.
, and
Lin
,
M. T.
, 1996, “
Transient Free Convection of Non-Newtonian Fluids Along a Wavy Vertical Plate Including the Magnetic Field Effect
,”
Int. J. Heat Fluid Flow
,
17
, pp.
604
612
.
13.
Char
,
M. I.
, and
Chen
,
C. K.
, 1988, “
Temperature Field in Non-Newtonian Flow Over a Stretching Plate With Variable Heat Flux
,”
Int. J. Heat Mass Transfer
,
31
, pp.
917
921
.
14.
Wang
,
C. C.
, and
Chen
,
C. K.
, 2002, “
Mixed Convection Boundary Layer Flow of Non-Newtonian Fluids Along Vertical Wavys Plates
,”
Int. J. Heat Fluid Flow
,
23
, pp.
831
839
.
15.
Rubin
,
S. G.
, and
Graves
,
R. A.
, 1975, “
Viscous Flow Solution With a Cubic Spline Approximation
,”
Comput. Fluids
,
1
, pp.
1
36
.
16.
Wang
,
P.
, and
Kahawita
,
R.
, 1983, “
Numerical Integration of Partial Differential Equations Using Cubic Spline
,”
Int. J. Comput. Math.
,
13
, pp.
271
286
.
You do not currently have access to this content.