Steady laminar forced convection heat transfer in the thermal entrance region of concentric annuli has been studied considering viscous dissipation characterized by the Brinkman number. The inner and outer pipes have been kept at constant and equal temperature. Two cases of entry temperatures have been considered, case 1: an entry temperature that varies with the radial coordinate, obtained by an adiabatically prepared fluid, i.e., attained by the fluid due to viscous dissipation in an adiabatic concentric annular duct and case 2: the conventional uniform entry temperature. The numerical results presented include the nondimensional temperature profiles, Nusselt numbers, and heat transferred from (or to) the inner and outer pipes. It has been shown from the numerical solutions that it is necessary to employ the dissipative entry temperature in place of conventional uniform entry temperature for higher Brinkman numbers. The results for circular pipes follow when the radius ratio takes the limiting value of zero.

References

1.
Graetz
,
L.
,
1883
, “
Uber die Wrmeleitungsfähigkeit von Flüssigkeiten
,”
Annu. Phys. Chem.
,
18
, pp.
79
94
.
2.
Graetz
,
L.
,
1885
, “
Uber die Wärmeleitungsfähigkeit von Flüssigkeiten
,”
Annu. Phys. Chem.
,
25
, pp.
337
357
.
3.
Nusselt
,
W.
,
1910
, “
Die Abhängigkeit der Wäreübergangszahl von der Rohrlänge
,”
VDIZ
,
54
, pp.
1154
1158
.
4.
Shah
,
R. K.
, and
London
,
A. L.
,
1978
,
Laminar Flow Forced Convection in Ducts, Advances in Heat Transfer
,
Academic
,
New York
.
5.
Kakac
,
S.
,
Shah
,
R. K.
, and
Aung
,
W.
,
1987
,
Handbook of Single-Phase Convective Heat Transfer
,
Wiley
,
New York
.
6.
Urbanovich
,
L. I.
,
1968
, “
Temperature Distribution and Heat Transfer in a Laminar Incompressible Annular-Channel Flow With Energy Dissipation
,”
J. Eng. Phys. (USSR)
,
14
(
4
), pp.
402
403
.
7.
Urbanovich
,
L. I.
,
1968
, “
The Transfer of Heat in the Laminar Flow of an Incompressible Liquid in an Annular Channel With Non Symmetric Boundary Conditions of the II-nd Kind Relative to the Axis of the Flow
,”
J. Eng. Phys. (USSR)
,
15
(
2
), pp.
753
754
.
8.
Avci
,
M.
, and
Aydin
,
O.
,
2006
, “
Laminar Forced Convection With Viscous Dissipation in a Concentric Annular Duct
,”
C. R. Mec.
,
334
(
3
), pp.
164
169
.
9.
Coelho
,
P. M.
, and
Pinho
,
F. T.
,
2006
, “
Fully-Developed Heat Transfer in Annuli With Viscous Dissipation
,”
Int. J. Heat Mass Transfer
,
49
(
19–20
), pp.
3349
3359
.
10.
Jambal
,
O.
,
Shigechi
,
T.
,
Davaa
,
G.
, and
Momoki
,
S.
,
2005
, “
Effects of Viscous Dissipation and Fluid Axial Heat Conduction on Heat Transfer for Non-Newtonian Fluids in Ducts With Uniform Wall Temperature Part II. Annular Ducts
,”
Int. Commun. Heat Mass Transfer
,
32
(
9
), pp.
1174
1183
.
11.
Barletta
,
A.
, and
Magyari
,
E.
,
2006
, “
Thermal Entrance Heat Transfer of an Adiabatically Prepared Fluid With Viscous Dissipation in a Tube With Isothermal Wall
,”
ASME J. Heat Transfer
,
128
(
11
), pp.
1185
1193
.
12.
Barletta
,
A.
, and
Magyari
,
E.
,
2007
, “
Forced Convection With Viscous Dissipation in the Thermal Entrance Region of a Circular Duct With Prescribed Wall Heat Flux
,”
Int. J. Heat Mass Transfer
,
50
(
1–2
), pp.
26
35
.
13.
Aydin
,
O.
, and
Avci
,
M.
,
2010
, “
On the Constant Wall Temperature Boundary Condition in Internal Convection Heat Transfer Studies Including Viscous Dissipation
,”
Int. Commun. Heat Mass Transfer
,
37
(
5
), pp.
535
539
.
14.
Satyamurty
,
V. V.
,
1984
, “
Successive Accelerated Replacement Scheme Applied to Study of Natural Convection Heat Transfer in Porous Cryogenic Insulations
,” ASME Paper No. 84-WA/HT-37.
15.
Marpu
,
D. R.
, and
Satyamurty
,
V. V.
,
1989
, “
Influence of Variable Fluid Density on Free Convection in Rectangular Porous Media
,”
ASME J. Energy Resour. Technol.
,
111
(
4
), pp.
214
220
.
16.
Satyamurty
,
V. V.
, and
Marpu
,
D. R.
,
1988
, “
Relative Effects of Variable Fluid Properties and Non-Darcy Flow on Convection in Porous Media
,”
ASME-HTD
,
96
, pp.
613
621
.
17.
Satyamurty
,
V. V.
, and
Bhargavi
,
D.
,
2010
, “
Forced Convection in Thermally Developing Region of a Channel Partially Filled With a Porous Material and Optimal Porous Fraction
,”
Int. J. Therm. Sci.
,
49
(
2
), pp.
319
332
.
18.
Repaka
,
R.
, and
Satyamurty
,
V. V.
,
2010
, “
Local and Average Heat Transfer in the Thermally Developing Region of an Asymmetrically Heated Channel
,”
Int. J. Heat Mass Transfer
,
53
(
9–10
), pp.
1654
1665
.
19.
Liu
,
C. Y.
,
Gooi
,
B. C.
,
Wong
,
Y. W.
, and
Yeo
,
J. H.
,
1994
, “
The Effect of Inlet Velocity Distribution on the Temperature Field of a Rotating Circular Pipe
,”
Int. Commun. Heat Mass Transfer
,
21
(
6
), pp.
829
837
.
20.
Kays
,
W. M.
,
Crawford
,
M. E.
, and
Weigand
,
B.
,
2005
,
Convective Heat and Mass Transfer
,
McGraw Hill International Edition
, New York.
21.
Antia
,
H. M.
,
1991
,
Numerical Methods for Scientists and Engineers
,
Tata McGraw-Hill
,
New Delhi
.
22.
Dellinger
,
T. C.
,
1971
, “
Computations on Non-Equilibrium Merged Shock Layer by Successive Accelerated Replacement Scheme
,”
AIAA J.
,
9
(2), pp.
262
269
.
23.
Kumar
,
M. M. J.
, and
Satyamurty
,
V. V.
,
2011
, “
Limiting Nusselt Numbers for Laminar Forced Convection in Asymmetrically Heated Annuli With Viscous Dissipation
,”
Int. Commun. Heat Mass Transfer
,
38
(
7
), pp.
923
927
.
You do not currently have access to this content.