The paper considers heat transfer characteristics of thin film flow over a hot horizontal flat plate resulting from a cold vertical jet of liquid falling onto the surface. A numerical solution of high accuracy is obtained for large Reynolds numbers using the modified Keller box method. For the flat plate, solutions for axisymmetric jets are obtained. In a parallel approximation theory, an advanced polynomial approximation for the velocity and temperature distribution is employed and results are in good agreement with those obtained using a simple Pohlhausen polynomial and the numerical solutions.

1.
Shu
,
J.-J.
, and
Wilks
,
G.
, 2007, “
Heat Transfer in the Flow of a Cold, Two-Dimensional Draining Sheet Over a Hot, Horizontal Cylinder
,”
Eur. J. Mech. B/Fluids
0997-7546,
26
(
6
), pp.
1
5
.
2.
Watson
,
E. J.
, 1964, “
The Radial Spread of a Liquid Jet Over a Horizontal Plane
,”
J. Fluid Mech.
0022-1120,
20
(
3
), pp.
481
499
.
3.
Chaudhury
,
Z. H.
, 1964, “
Heat Transfer in a Radial Liquid Jet
,”
J. Fluid Mech.
0022-1120,
20
(
3
), pp.
501
511
.
4.
Shu
,
J.-J.
, and
Wilks
,
G.
, 1996, “
Heat Transfer in the Flow of a Cold, Two-Dimensional Vertical Liquid Jet Against a Hot, Horizontal Plate
,”
Int. J. Heat Mass Transfer
0017-9310,
39
(
16
), pp.
3367
3379
.
5.
Zhao
,
Y. H.
,
Masuoka
,
T.
,
Tsuruta
,
T.
, and
Ma
,
C. F.
, 2002, “
Conjugated Heat Transfer on a Horizontal Surface Impinged by Circular Free-Surface Liquid Jet
,”
JSME Int. J., Ser. B
1340-8054,
45
(
2
), pp.
307
314
.
6.
Shu
,
J.-J.
, 2004, “
Microscale Heat Transfer in a Free Jet Against a Plane Surface
,”
Superlattices Microstruct.
0749-6036,
35
(
3–6
), pp.
645
656
.
7.
Guerra
,
D. R. S.
,
Su
,
J.
, and
Freire
,
A. P. S.
, 2005, “
The Near Wall Behavior of an Impinging Jet
,”
Int. J. Heat Mass Transfer
0017-9310,
48
(
14
), pp.
2829
2840
.
8.
Rice
,
J.
,
Faghri
,
A.
, and
Cetegen
,
B.
, 2005, “
Analysis of a Free Surface Film From a Controlled Liquid Impinging Jet Over a Rotating Disk Including Conjugate Effects, With and Without Evaporation
,”
Int. J. Heat Mass Transfer
0017-9310,
48
(
25–26
), pp.
5192
5204
.
9.
Shu
,
J.-J.
, and
Wilks
,
G.
, 2007, “
Heat Transfer in the Flow of a Cold, Axisymmetric Jet Over a Hot Sphere
,”
Int. J. Therm. Sci.
1290-0729,
46
(
12
), pp.
1
5
.
10.
Shu
,
J.-J.
, 2004, “
Impact of an Oblique Breaking Wave on a Wall
,”
Phys. Fluids
1070-6631,
16
(
3
), pp.
610
614
.
11.
Shu
,
J.-J.
, 2004, “
Slamming of a Breaking Wave on a Wall
,”
Phys. Rev. E
1063-651X,
70
(
6
), p.
066306
.
12.
Rosenhead
,
L.
, 1963,
Laminar Boundary Layers
,
Oxford University Press
,
New York
.
13.
Shu
,
J.-J.
, and
Wilks
,
G.
, 1995, “
An Accurate Numerical Method for Systems of Differentio-Integral Equations Associated With Multiphase Flow
,”
Comput. Fluids
0045-7930,
24
(
6
), pp.
625
652
.
14.
Shu
,
J.-J.
, and
Wilks
,
G.
, 1995, “
Mixed-Convection Laminar Film Condensation on a Semi-Infinite Vertical Plate
,”
J. Fluid Mech.
0022-1120,
300
, pp.
207
229
.
15.
Shu
,
J.-J.
, and
Pop
,
I.
, 1997, “
Inclined Wall Plumes in Porous Media
,”
Fluid Dyn. Res.
0169-5983,
21
(
4
), pp.
303
317
.
16.
Shu
,
J.-J.
, and
Pop
,
I.
, 1998, “
Transient Conjugate Free Convection from a Vertical Flat Plate in a Porous Medium Subjected to a Sudden Change in Surface Heat Flux
,”
Int. J. Eng. Sci.
0020-7225,
36
(
2
), pp.
207
214
.
17.
Shu
,
J.-J.
, and
Pop
,
I.
, 1998, “
On Thermal Boundary Layers on a Flat Plate Subjected to a Variable Heat Flux
,”
Int. J. Heat Fluid Flow
0142-727X,
19
(
1
), pp.
79
84
.
18.
Shu
,
J.-J.
, and
Pop
,
I.
, 1999, “
Thermal Interaction Between Free Convection and Forced Convection Along a Conducting Plate Embedded in a Porous Medium
,”
Hybrid Methods in Engineering: ---Modeling, Programming, Analysis, Animation
,
1
(
1
), pp.
55
66
.
19.
Shu
,
J.-J.
, and
Pop
,
I.
, 1999, “
Thermal Interaction Between Free Convection and Forced Convection Along a Vertical Conducting Wall
,”
Heat Mass Transfer
0947-7411,
35
(
1
), pp.
33
38
.
You do not currently have access to this content.