Two-Dimensional Study of Heat Transfer and Fluid Flow in a Natural Convection Loop

Abstract

A study has been made of the heat transfer and fluid flow in a natural convection loop. Previous studies of these systems have utilized a one-dimensional approach which requires a priori specifications of the friction and the heat-transfer coefficients. The present work carries out a two-dimensional analysis for the first time. The results yield the friction and the heat-transfer coefficients and give their variation along the loop with the Graetz number as a parameter. Comparison is also made with experimental data for the heat flux and good agreement is obtained.

The onset of motion in a toroidal thermosyphon

“…The present work deals with the toroidal thermosyphon, whose steady state and its stability have been extensively investigated, [10,11,[13][14][15][16][17][18]. Similar to the results of [3], critical values are found for the Rayleigh number, associated with the onset of motion.…”

“…A two-dimensional analysis of this loop [13,14] indicates that the heat transfer and friction correlations approach, then, those for forced laminar flow in a tube: Nu = 3.66, f--16~Re. These results justify the use of a one-dimensional model with W and T denoting cross.sectional average velocity and temperature.…”

“…(11) and then finds R*(w; B) from eqs. (12,13). Figure 2 shows the results for the steady-state velocity w as a function of the modified Rayleigh number R* for various values of the Biot number B.…”

“…9) take the form Introducing these expressions into the momentum equation (4) (or using eqs. (12,13)), an algebraic equation for the velocity w is obtained whose solution is: w = (4R* -1) 1/2.…”

A Note on Convection in Fracture Loops

“…For these, of course, the primary topic of interest is heat transfer, and most publications have involved heating from the sides. Examples are the studies by Greif and colleagues, such as Greif et al (1979), Lavine et al (1986Lavine et al ( , 1987, Mertol et al (1982), Stern and Greif (1987) and Stern et al (1988), and those by Ridouane et al (2010Ridouane et al ( , 2011. The earlier work was reviewed by Mertol and Greif (1985).…”