Abstract

In this work the similarity solution of the thermal boundary layer for a laminar axisymmetric jet with viscous dissipation is derived and solved numerically, using a fourth-order Runge-Kutta method. The results are compared with the existing solutions, in which viscous dissipation is neglected. After that the effects of Reynolds and Prandtl numbers of the incoming hot jet on the temperature profile of the jet is investigated. It is seen that inclusion of viscous dissipation term results in a more rapid heat exchange between the incoming jet and quiescent fluid than the case where the viscous dissipation term is neglected. Also, it is observed that by increasing the Reynolds and Prandtl numbers of the jet, the heat penetrates better in locations near the symmetry line, whereas in locations farther from the symmetry axis the penetration is less.

1.
Schlichting
,
H.
, and
Gersten
,
K.
, 2000,
Boundary Layer Theory
, 8th revised and enlarged edition (English),
Springer
, New York, pp.
222 and 331
334
.
2.
White
,
F. M.
, 1991,
Viscous Fluid Flow
, 2nd ed.,
McGraw-Hill
, New York, pp.
301
302
.
3.
Fang
,
T.
, 2002, “
Similarity Solution of Thermal Boundary Layers for Laminar Narrow Axisymmetric Jets
,”
Int. J. Heat Fluid Flow
0142-727X,
23
, pp.
840
843
.
4.
Pai
,
S. I.
, 1954,
Fluid Dynamics of Jets
,
D. Van Nostrand Company
, pp.
78
79
.
5.
Fujii
,
T.
, 1963, “
Theory of the Steady Laminar Natural Convection Above a Horizontal Line Heat Source and a Point Heat Source
,”
Int. J. Heat Mass Transfer
0017-9310,
6
, pp.
597
606
.
6.
Zhang
,
X.
, and
Zheng
,
L.
, 2004, “
Similarity Solution of Momentum and Energy Equations for an Axi-symmetric Laminar Jet
,”
J. Therm. Sci.
1003-2169,
13
(
4
), pp.
334
337
.
7.
Rankin
,
G. W.
, and
Sridhar
,
K.
, 1978, “
Developing Region of Laminar Jets With Uniform Exit Velocity Profiles
,”
J. Fluids Eng.
0098-2202,
100
, pp.
55
59
.
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