An equilibrium thermal wake strength parameter is developed for a two-dimensional turbulent boundary layer flow and is then used in the combined thermal law of the wall and the wake to give an approximate temperature profile to insert into the integral form of the thermal energy equation. After the solution of the integral x momentum equation, the integral thermal energy equation is solved for the local Stanton number as a function of position x for accelerating turbulent boundary layers. A simple temperature distribution in the thermal “superlayer” is part of the present modeling. The analysis includes a dependence of the hydrodynamic and thermal wake strengths on the momentum thickness and enthalpy thickness Reynolds numbers, respectively. An approximate dependence of the turbulent Prandtl number, in the “log” region, on the strength of the favorable pressure gradient is proposed and incorporated into the solution. The resultant solution for the Stanton number distribution in accelerated turbulent flows is compared with experimental data in the literature. A comparison of the present predictions is also made to a finite difference solution, which uses the turbulent kinetic energy—turbulent dissipation model of turbulence, for a few cases of accelerating flows.

1.
Moretti
,
P. M.
, and
Kays
,
W. M.
, 1964, “
Heat Transfer Through an Incompressible Turbulent Boundary Layer With Varying Free-Stream Velocity and Varying Surface Temperature
,” Thermosciences Division Report No. PG-1, Stanford University, Stanford, CA.
2.
Kearney
,
D. W.
,
Moffat
,
R. J.
, and
Kays
,
W. M.
, 1970, “
The Turbulent Boundary Layer: Experimental Heat Transfer With Strong, Favorable Pressure Gradients and Blowing
,” Thermosciences Division Report No. HMT-12, Stanford University, Stanford, CA.
3.
Thielbahr
,
W. H.
,
Kays
,
W. M.
, and
Moffat
,
R. J.
, 1972, “
The Turbulent Boundary Layer on a Porous Plate: Experimental Heat Transfer With Uniform Blowing and Suction, With Moderately Strong Acceleration
,”
ASME J. Heat Transfer
0022-1481,
94
, pp.
111
118
.
4.
Jones
,
W. P.
, and
Launder
,
B. E.
, 1972, “
The Prediction of Laminarization With a Two-Equation Model of Turbulence
,”
Int. J. Heat Mass Transfer
0017-9310,
15
, pp.
301
314
.
5.
Sucec
,
J.
, and
Lu
,
Y.
, 1990, “
Heat Transfer Across Turbulent Boundary Layers With Pressure Gradient
,”
ASME J. Heat Transfer
0022-1481,
112
, pp.
906
912
.
6.
Wang
,
X.
,
Castillo
,
L.
, and
Araya
,
G.
, 2008, “
Temperature Scalings and Profiles in Forced Convection Turbulent Boundary Layers
,”
ASME J. Heat Transfer
0022-1481,
130
, pp.
021701
-01–021701-
17
.
7.
So
,
R. M. C.
, 1994, “
Pressure Gradient Effects on Reynolds Analogy for Constant Property Equilibrium Turbulent Boundary Layers
,”
Int. J. Heat Mass Transfer
0017-9310,
37
, pp.
27
41
.
8.
Sucec
,
J.
, 2005, “
Calculation of Turbulent Boundary Layers Using Equilibrium Thermal Wakes
,”
ASME J. Heat Transfer
0022-1481,
127
, pp.
159
164
.
9.
Sucec
,
J.
, 2006, “
Modern Integral Method Calculation of Turbulent Boundary Layers
,”
J. Thermophys. Heat Transfer
0887-8722,
20
, pp.
552
557
.
10.
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, Department of Mechanical Engineering, Stanford University, Stanford, CA.
11.
Mellor
,
G. L.
, and
Gibson
,
D. M.
, 1966, “
Equilibrium Turbulent Boundary Layers
,”
J. Fluid Mech.
0022-1120,
24
, pp.
255
274
.
12.
Sucec
,
J.
, and
Oljaca
,
M.
, 1995, “
Calculation of Turbulent Boundary Layers With Transpiration and Pressure Gradient Effects
,”
Int. J. Heat Mass Transfer
0017-9310,
38
, pp.
2855
2862
.
13.
Cebeci
,
T.
, and
Bradshaw
,
P.
, 1984,
Physical and Computational Aspects of Convective Heat Transfer
,
Springer-Verlag
,
New York
, p.
188
.
14.
Fridman
,
E.
, 1997, “
Heat Transfer and Temperature Distribution in a Turbulent Flow Over a Flat Plate With an Unheated Starting Length
,”
Proceedings of the 1997 National Heat Transfer Conference
, HTD-Vol.
346
, Chap. 8, pp.
127
132
.
15.
Kays
,
W. M.
, 1994, “
Turbulent Prandtl Number—Where Are We?
ASME J. Heat Transfer
0022-1481,
116
, pp.
284
295
.
16.
Roganov
,
P. S.
,
Zabolotsky
,
V. P.
,
Shishov
,
E. V.
, and
Leontiev
,
A. I.
, 1984, “
Some Aspects of Turbulent Heat Transfer in Accelerated Flows on Permeable Surfaces
,”
Int. J. Heat Mass Transfer
0017-9310,
27
, pp.
1251
59
.
17.
Launder
,
B. E.
, and
Lockwood
,
F. C.
, 1969, “
An Aspect of Heat Transfer in Accelerating Turbulent Boundary Layers
,”
ASME J. Heat Transfer
0022-1481,
91
, pp.
229
234
.
18.
Kays
,
W. M.
,
Moffat
,
R. J.
, and
Thielbahr
,
W. H.
, 1970, “
Heat Transfer to the Highly Accelerated Turbulent Boundary Layer With and Without Mass Addition
,”
ASME J. Heat Transfer
0022-1481,
92
, pp.
499
505
.
19.
Kays
,
W. M.
,
Crawford
,
M. E.
, and
Weigand
,
B.
, 2005,
Convective Heat and Mass Transfer
,
4th ed.
,
McGraw-Hill
,
New York
.
20.
Kearney
,
D. W.
,
Kays
,
W. M.
, and
Moffat
,
R. J.
, 1973, “
Heat Transfer to a Strongly Accelerated Turbulent Boundary Layer: Some Experimental Results, Including Transpiration
,”
Int. J. Heat Mass Transfer
0017-9310,
16
, pp.
1289
1305
.
21.
El-Hawary
,
M. A.
, and
Nicoll
,
W. B.
, 1979, “
The Prediction of Highly Accelerating Flows Near Smooth Walls
,”
Proceedings of the Joint ASME-CSME Applied Mechanics, Fluids Engineering and Bioengineering Conference
,
H. E.
Weber
, ed., pp
93
106
.
22.
Kreskovsky
,
J. P.
,
Shamroth
,
S. J.
, and
McDonald
,
H.
, 1975, “
Application of a General Boundary Layer Analysis to Turbulent Boundary Layers Subjected to Strong Favorable Pressure Gradients
,”
ASME J. Fluids Eng.
0098-2202,
97
, pp.
217
224
.
23.
Shishov
,
E. V.
, 1991, “
Turbulent Heat and Momentum Transfer in Boundary Layers Under Strong Pressure Gradient Conditions: Analysis of Experimental Data and Numerical Predictions
,”
Exp. Therm. Fluid Sci.
0894-1777,
4
, pp.
389
398
.
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