Film flow coupled with heat and mass transfer is a widely open domain due to the range of its applications. However, the coupling between the different phenomena makes the analytical resolution difficult, and thus, coerces most authors into performing numerical studies. Although efficient, the numerical approach does not reveal the real link between the different parameters when studying heat transfer. This lack of meaningful formulation motivates the present paper, which proposes a semi-analytical solution for the establishment of the thermal boundary layer of a film flowing down an inclinated heated plane. The formula is obtained by a truncated sum of Whittaker’s functions, and is validated by comparison with a full numerical solution of the problem (assuming the same hypotheses). The semi-analytical nature of the equation provides better understanding of the physical phenomena and could help in reducing numerical computational time.

1.
Nusselt
,
W.
, 1926, “Die Oberflächenkondensation des Wasserdampfes,” VDI Zeitschrift, 60, pp. 541–546.
2.
Wu
,
C. W.
, and
Lin
,
T.
, 2007, “
Full-Scale Evaluations on Heat Resistance of Glass Panes Incorporated With Water Film or Sprinkler in a Room Fire
,”
Build. Environ.
0360-1323,
42
(
9
), pp.
3277
3284
.
3.
Ben Jabrallah
,
S.
,
Belghith
,
A.
, and
Corriou
,
J. P.
, 2002, “
Study of Heat and Mass Transfer in a Rectangular Cavity: Application to a Distillation Cell
,”
Int. J. Heat Mass Transfer
0017-9310,
45
(
4
), pp.
891
904
.
4.
Raach
,
H.
, and
Mitrovic
,
J.
, 2005, “
Seawater Falling Film Evaporation on Vertical Plates With Turbulence Wires
,”
Desalination
0011-9164,
183
(
1–3
), pp.
307
316
.
5.
Cui
,
X. -Y.
,
Shi
,
J. -Z.
,
Tan
,
C.
, and
Xu
,
Z. -P.
, 2009, “
Investigation of Plate Falling Film Absorber With Film-Inverting Configuration
,”
ASME J. Heat Transfer
0022-1481,
131
(
7
), p.
072001
.
6.
Killion
,
J. D.
, and
Garimella
,
S.
, 2001, “
A Critical Review of Models of Coupled Heat and Mass Transfer in Falling-Film Absorption
,”
Int. J. Refrig.
0140-7007,
24
(
8
), pp.
755
797
.
7.
Nakoryakov
,
V. E.
, and
Grigor’eva
,
N. I.
, 1977, “
Combined Heat and Mass Transfer During Absorption in Drops and Films
,”
J. Eng. Phys. Thermophys.
1062-0125,
32
(
3
), pp.
243
247
.
8.
Grossman
,
G.
, 1987, “
Analysis of Interdiffusion in Film Absorption
,”
Int. J. Heat Mass Transfer
0017-9310,
30
(
1
), pp.
205
208
.
9.
Conlisk
,
A. T.
, 1995, “
Analytical Solutions for the Heat and Mass Transfer in a Falling Film Absorber
,”
Chem. Eng. Sci.
0009-2509,
50
(
4
), pp.
651
660
.
10.
Ren
,
C.
, 2006, “
An Analytical Approach to the Heat and Mass Transfer Processes in Counterflow Cooling Towers
,”
ASME J. Heat Transfer
0022-1481,
128
(
11
), pp.
1142
1148
.
11.
Gradshteyn
,
I. S.
, and
Ryzhik
,
I. M.
, 2000,
Table of Integrals, Series, and Products
,
6th ed.
,
Academic
,
New York
.
You do not currently have access to this content.