An investigation toward the existence of a complete similarity solution for boundary layer flows under the velocity slip and temperature jump conditions is carried out. The study is limited to the boundary layer flows resulting from an arbitrary freestream velocity $U(x)=Uoxm$ and wall temperature given by $Tw−T∞=Cxn$. It is found that a similar solution exists only for $m=1$ and $n=0$, which represents stagnation flow on isothermal surface. This case has been thoroughly investigated. The analysis showed that three parameters control the flow and heat transfer characteristics of the problem. These parameters are the velocity slip parameter $K1$, the temperature jump parameter $K2$, and Prandtl number. The effect of these parameters on the flow and heat transfer of the problem has been studied and presented. It is found that the slip velocity parameter affects both the flow and heat transfer characteristics of the problem. It is found that the skin friction coefficient decreases with increasing $K1$ and most of changes in the skin friction takes place in the range $0. The skin friction coefficient is found to be related to $K1$ and $Rex$ according to the relation: $Cf=3.38Rex−0.5(K1+1.279)−0.8$ for $0 with an error of $±4%$. On the other hand, the correlation between Nu, $K1$, $K2$, and Pr has been found by the equation $Nu=[(0.449+1.142K11.06)∕(0.515+K11.06)](K2+1.489Pr−0.44)−1$, for $0, $K2<5$, $0.7≤Pr≤5$ within a maximum error of $±3%$.

1.
Duncan
,
G. P.
, and
Peterson
,
G. P.
, 1994, “
Review of Microscale Heat Transfer
,”
Appl. Mech. Rev.
0003-6900,
47
(
9
), pp.
397
428
.
2.
,
M.
, 1999, “
The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture
,”
ASME J. Fluids Eng.
0098-2202,
121
, pp.
5
33
.
3.
,
M.
, 2002, “
Flow Physics in Microdevices
,”
The Handbook of MEMS
,
CRC
,
Boca Raton, FL
.
4.
Barron
,
R. F.
,
Wang
,
X.
,
Ameel
,
T. A.
, and
Warrington
,
R. O.
, 1997, “
The Graetz Problem Extended to Slip-Flow
,”
Int. J. Heat Mass Transfer
0017-9310,
40
(
8
), pp.
1817
1823
.
5.
Guo
,
Z. Y.
, and
Li
,
Z. X.
, 2003, “
Size Effect on Single-Phase Channel Flow and Heat Transfer at Microscale
,”
Int. J. Heat Fluid Flow
0142-727X,
24
(
3
), pp.
284
298
.
6.
Chakraborty
,
S.
,
Som
,
S. K.
, and
Rahul
, 2008, “
A Boundary Layer Analysis for Entrance Region Heat Transfer in Vertical Microchannels With the Slip Flow Regime
,”
Int. J. Heat Mass Transfer
0017-9310,
51
, pp.
3245
3250
.
7.
Aydın
,
O.
, and
Avcı
,
M.
, 2006, “
Heat and Flow Characteristics of Gases in Micropipes
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
1723
1730
.
8.
Aydın
,
O.
, and
Avcı
,
M.
, 2007, “
Analysis of Laminar Heat Transfer in Micro-Poiseuille Flow
,”
Int. J. Therm. Sci.
1290-0729,
46
, pp.
30
37
.
9.
Avcı
,
M.
, and
Aydın
,
O.
, 2008, “
Laminar Forced Convection Slip-Flow in a Micro-Annulus Between Two Concentric Cylinders
,”
Int. J. Heat Mass Transfer
0017-9310,
51
, pp.
3460
3467
.
10.
Kiwan
,
S.
, and
Al-Nimr
,
M. A.
, 2009, “
Flow and Heat Transfer Over a Stretched Micro-Surface
,”
ASME Trans. J. Heat Transfer
0022-1481,
131
(
6
), p.
061703
.
11.
Martin
,
M. J.
, and
Boyd
,
I. D.
, 2006, “
Momentum Heat Transfer in a Laminar Boundary Layer With Slip Flow
,”
J. Thermophys. Heat Transfer
0887-8722,
20
(
4
), pp.
710
719
.
12.
Pereyra
,
V.
, 1978, “
PASVA3: An Adaptive Finite-Difference FORTRAN Program for First Order Nonlinear Boundary Value Problems
,”
Lecture Notes in Computer Science
,
Springer-Verlag
,
Berlin
, p.
76
.
13.
Schlichting
,
H.
, 1987,
Boundary Layer Theory
, 7th ed.,
McGraw-Hill
,
New York
.