Equation (14) has shown that simulation of the steady state behaviour is possible by simulating Grm/NG for any natural circulation loop. The transient and stability behaviour, however, are described by equations (8) and (10). Substituting the steady state solution, the transient momentum equation can be rewritten as

From equations (17) and (8), it is obvious that the transient and stability behaviours are governed by the physical parameters Grm, St and the geometric parameters of NG, g, Vt/Vh, PcLt/Ac and the area ratio ai. To reduce the number of independent parameters, it is customary to combine St and PcLt / Ac into a single dimensionless parameter called Stm. Similarly, Grm and NG can be combined as Grmb/3-b/NG3/3-b so that the transient and stability behaviour can be expressed as

Further reduction in the number of independent parameters is possible for special cases. For example, with a uniform diameter loop, (Vt / Vh ) = (Lt / Lh), ai=1 and NG = Lt / D so that

In addition to Lt/Lh other length scales also affect the stability behaviour. This can be established by carrying out a linear stability analysis. In this method, the loop flow rate and temperature are perturbed as

ю = rnss + rose111 and 9 = 9ss + 9senx

Where e is a small quantity, w and в are the amplitudes of the flow and temperature disturbances respectively, and n is the growth rate of the perturbations. Substituting Eq. (20) in equations (10) and (17), and using the continuity of temperature perturbation in various segments as the boundary condition, the characteristic equation for the stability behaviour can be derived. The characteristic equation for a uniform diameter loop with horizontal heat source and sink can be expressed as Y(n)=0 (Vijayan and Austregesilo (1994)), where

-L{p(- nLh/Lt)-1} + (exp{- n(sc — St — Sh)h )Lt}-1

nLh

and D = ex p{StmLc/Lt}- exp(- n) Where St=Lt/H and Sx =sx/H. Sc, St and Sx are the

dimensionless distances from the origin (i. e. S=0 in Fig. 1) in anticlockwise direction. It is obvious from equation (21) that, apart from the parameters listed in (19), the ratios of the lengths are also required to be preserved to simulate the stability behaviour.