In the present investigation, the steady state performance of a rectangular single phase natural circulation loop (NCL) with end heat exchangers is studied. One-dimensional governing equations are considered in developing the mathematical model. Analytical expressions are derived for the circulation rate and temperature profile. However, the individual performance parameters are to be computed iteratively as the equations are strongly coupled. A suitable iterative procedure is given to evaluate the important loop parameters such as steady state flow rate, and riser and downcomer temperatures. Few special cases are discussed where analytical expressions for circulation rate and temperature distribution can be obtained directly without any iterative procedure. It is also shown that both the hot and cold end heat exchangers should have equal conductance $(UA)$ for maximization of circulation rate. This feature of NCL is identical with heat power cycle and can be explained in light of equipartition principle.

1.
Creveling
,
H. F.
,
De Paz
,
J. F.
,
,
J. Y.
, and
Schoenhals
,
R. J.
, 1975, “
Stability Characteristics of a Single Phase Free Convection Loop
,”
J. Fluid Mech.
0022-1120,
67
, pp.
65
84.
.
2.
Greif
,
R.
,
Zvirin
,
Y.
, and
Mertol
,
A.
, 1979, “
The Transient and Stability Behavior of a Natural Convection Loop
,”
ASME J. Heat Transfer
0022-1481,
101
, pp.
684
688
.
3.
Vijayan
,
P. K.
, 2002, “
Experimental Observations on the General Trends of the Steady State and Stability Behaviour of Single-Phase Natural Circulation Loops
,”
Nucl. Eng. Des.
0029-5493,
215
, pp.
139
152
.
4.
Jiang
,
Y. Y.
, and
Shoji
,
M.
, 2003, “
Flow Stability in a Natural Circulation Loop: Influences of Wall Thermal Conductivity
,”
Nucl. Eng. Des.
0029-5493,
222
, pp.
16
28
.
5.
Mousavian
,
S. K.
,
Misale
,
M.
,
D’Auria
,
F.
, and
Salehi
,
M. A.
, 2004, “
Transient and Stability Analysis in Single-Phase Natural Circulation
,”
Ann. Nucl. Energy
0306-4549,
31
, pp.
1177
1198
.
6.
Rao
,
N. M.
,
Maiti
,
B.
, and
Das
,
P. K.
, 2005, “
Stability Behaviour of a Natural Circulation Loop With End Heat Exchangers
,”
ASME J. Heat Transfer
0022-1481,
127
, pp.
749
759
.
7.
Bejan
,
A.
, 1988,
,
Wiley
,
New York
.
8.
Holmberg
,
R. B.
, 1975, “
Heat Transfer in Liquid-Coupled Indirect Heat Exchanger Systems
,”
ASME J. Heat Transfer
0022-1481,
97
, pp.
499
503
.
9.
Sauar
,
E.
,
Ratkje
,
S. K.
, and
Lien
,
K. M.
, 1996, “
Equipartition of Forces: A New Principle for Process Design and Optimization
,”
Ind. Eng. Chem. Res.
0888-5885,
35
, pp.
4147
4153
.
10.
Pramanick
,
A. K.
, and
Das
,
P. K.
, 2005, “
Heuristics as an Alternative to Variational Calculus for Optimization of a Class of Thermal Insulation Systems
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
1851
1857
.