Heat transfer within an eccentric annulus containing heat generating fluid

Abstract

In this paper, the heat transfer within an eccentric annulus containing heat-generating fluid is investigated. The inner cylinder of the annulus is heated and kept at constant temperature, while the outer cylinder is cooled and maintained at a constant temperature lower than that of the inner cylinder. The full governing equations of mass, momentum, and energy have been solved to investigate the characteristics of flow and thermal fields within the annulus. Besides considering the numerical solution in the case of natural convection at moderate Rayleigh number of 104, the study also considered the numerical and analytical solutions in case of pure heat conduction within the annulus. Moreover, the study discussed the effect of annulus radius ratio Rr, the eccentricity e, and the heat generation parameter S on the heat transfer process. The study considered the range of Rr from 1.4 to 3.2, the range of e from −0.6 to 0.6, and the range of S up to 5. The study manifests that the numerical results for the case of pure conduction are in excellent agreement with the corresponding analytical results. The results for both pure conduction and natural convection cases showed that the average dimensionless temperature of the heat generation fluid increases with the increase in S. Similarly, the heat rejected from the outer cylinder increases with the increase in S for a given Rr. On the contrary, the heat added to the annulus through the inner cylinder decreases as S increases and changes to heat rejection if S exceeds a certain critical value S∗. The value of S∗ is found to decrease with the increase in Rr for both pure conduction and natural convection cases. Moreover, the heat transfer rates at inner and outer walls of the annulus decrease for a given Rr as the inner cylinder moves upward from negative eccentricity to positive eccentricity until both start increasing again at a certain positive eccentricity.