The combined thermal law of the wall and wake is used as the approximating sequence for the boundary layer temperature profile to solve an integral thermal energy equation for the local Stanton number distribution. The velocity profile in the turbulent boundary layer was taken to be the combined law of the wall and wake of Coles. This allows the solution of an integral form of the x-momentum equation to give the skin friction coefficient distribution. This, along with the velocity profile, is used to solve the thermal energy equation using inner coordinates. The strength of the thermal wake was found by analysis of earlier research results, in the literature, for equilibrium, constant property, turbulent boundary layers. Solutions for the Stanton number distribution with position are found for some adverse pressure gradient boundary layers as well as for those having zero pressure gradient. The zero pressure gradient results cover both fully heated plates and those with unheated starting lengths, including both isothermal surfaces and constant flux surfaces. Comparison of predictions of the present work is made with experimental data in the literature.

1.
So
,
R. M. C.
,
1994
, “
Pressure Gradient Effects on Reynolds Analogy for Constant Property Equilibrium Turbulent Boundary Layers
,”
Int. J. Heat Mass Transfer
,
37
, pp.
27
41
.
2.
Kader
,
B. A.
, and
Yaglom
,
A. M.
,
1972
, “
Heat and Mass Transfer Laws for Fully Turbulent Wall Flows
,”
Int. J. Heat Mass Transfer
,
15
, pp.
2329
2351
.
3.
Kader
,
B. A.
,
1981
, “
Temperature and Concentration Profiles in Fully Turbulent Boundary Layers
,”
Int. J. Heat Mass Transfer
,
24
, pp.
1541
1544
.
4.
Kader
,
B. A.
,
1991
, “
Heat and Mass Transfer in Pressure Gradient Boundary Layers
,”
Int. J. Heat Mass Transfer
,
34
, pp.
2837
2857
.
5.
Subramanian
,
C. S.
, and
Antonia
,
R. A.
,
1981
, “
Effect of Reynolds Number on a Slightly Heated Turbulent Boundary Layer
,”
Int. J. Heat Mass Transfer
,
24
, pp.
1833
1846
.
6.
Fridman, E., 1997, “Heat Transfer and Temperature Distribution in a Turbulent Flow Over a Flat Plate With an Unheated Starting Length,” HTD—Vol. 346, Proceedings of the 1997 National Heat Transfer Conference, 8, pp. 127–132.
7.
Faraco-Medeiros
,
M. A.
, and
Silva-Freire
,
A. P.
,
1992
, “
The Transfer of Heat in Turbulent Boundary Layers With Injection or Suction: Universal Laws and Stanton Number Equations
,”
Int. J. Heat Mass Transfer
,
35
, pp.
991
995
.
8.
Bell, D. M., and Ferziger, J. H., 1993, “Turbulent Boundary Layer DNS With Passive Scalars,” Near-Wall Turbulent Flows, edited by So, R. M. C., Speziale, C. G., and Launder, B. E., pp. 327–336.
9.
Mellor
,
G. L.
, and
Gibson
,
D. M.
,
1966
, “
Equilibrium Turbulent Boundary Layers
,”
J. Fluid Mech.
,
24
, pp.
255
274
.
10.
Das
,
D. K.
, and
White
,
F. M.
,
1986
, “
Integral Skin Friction Prediction for Turbulent, Separated Flows
,”
ASME J. Fluids Eng.
,
108
, pp.
476
482
.
11.
Sucec
,
J.
, and
Oljaca
,
M.
,
1995
, “
Calculation of Turbulent Boundary Layers With Transpiration and Pressure Gradient Effects
,”
Int. J. Heat Mass Transfer
,
38
, pp.
2855
2862
.
12.
Blackwell, B. F., 1972, “The Turbulent Boundary Layer on a Porous Plate: An Experimental Study of the Heat Transfer Behavior With Adverse Pressure Gradients,” Ph.D. thesis, Stanford University, Stanford California.
13.
Orlando, A. F., Moffat, R. J., and Kays, W. M., 1974, “Turbulent Transport of Heat and Momentum in a Boundary Layer Subject to Deceleration, Suction and Variable Wall Temperature,” Thermosciences Division Report No. HMT-17, Stanford University, Stanford, CA.
14.
Sucec
,
J.
, and
Lu
,
Y.
,
1990
, “
Heat Transfer Across Turbulent Boundary Layers With Pressure Gradient
,”
ASME J. Heat Transfer
,
112
, pp.
906
912
.
15.
Kays, W. M., and Crawford, M. E., 1993, Convective Heat and Mass Transfer, 3rd ed., McGraw–Hill, New York, pp. 278–284.
16.
Taylor, R. P., Love, P. H., Coleman, H. W., and Hosni, M. H., 1989, “The Effect of Step Changes in the Thermal Boundary Condition on Heat Transfer in the Incompressible Flat Plate Turbulent Boundary Layer,” HTD-Vol. 107, in Proceedings of the 1989 National Heat Transfer Conference, pp. 9–16.
17.
Kong
,
H.
,
Choi
,
H.
, and
Sik Lee
,
J.
,
2000
, “
Direct Numerical Simulation of Turbulent Thermal Boundary Layers
,”
Phys. Fluids
,
12
, pp.
2555
2568
.
18.
Moffat
,
R. J.
, and
Kays
,
W. M.
,
1968
, “
The Turbulent Boundary Layer on a Porous Plate: Experimental Heat Transfer With Uniform Blowing and Suction
,”
Int. J. Heat Mass Transfer
,
11
, pp.
1547
1566
.
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