Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 1): Numerical Method

Abstract

In this research, unsteady three-dimensional incompressible Navier–Stokes equations are solved to simulate experiments with the Boussinesq approximation and validate the proposed numerical model for the design of a circular fin-tube heat exchanger. Unsteady time marching is proposed for a time sweeping analysis of various Rayleigh numbers. The accuracy of the natural convection data of a single horizontal circular tube with the proposed numerical method can be guaranteed when the Rayleigh number based on the tube diameter exceeds 400, which is regarded as the limitation of numerical errors due to instability. Moreover, the effective limit for a circular fin-tube heat exchanger is reached when the Rayleigh number based on the fin gap size ( Ra s ) is equal to or exceeds 100. This is because at low Rayleigh numbers, the air gap between the fins is isolated and rarely affected by natural convection of the outer air, where the fluid provides heat resistance. Thus, the fin acts favorably when Ra s exceeds 100.

Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 2): Correlations for Limiting Cases

“…The errors of the results of the computational fluid dynamics presented in this paper against the correlation of Kang and Chang [9] are shown in Table 4. For D15-D18, the mean errors are limited to 18.5%, namely within the error levels reported in Part 1 [1]. However, for the limiting cases of D50 and D100, the errors tend to deviate to a greater extent because these diameter ratios do not fit within the correlation range of Kang and Chang [9].…”

“…These results are due to the fact that the computational data underpredict experimental data in Kang and Chang [9] by approximately 16% -20%. This reason has already been mentioned in Part 1 [1].…”

“…Accordingly, in this paper, we report on the application of the numerical method presented in Part 1 [1] by considering a single circular fin-tube heat exchanger model as a counterpart of the model in Kang and Chang [9]. Additionally, we analyzed the limiting cases in Figure 1 which were not elaborated upon by Kang and Chang [9], or the main idea presented in Equation (11) using the numerical technique.…”

“…Unsteady and laminar flow conditions are assumed for the entire computation. The details of the numerical method are elucidated in Part 1 [1] of this paper.…”

“…In Part 1 [1] of this paper, a numerical method was proposed for the natural convection heat transfer in circular fin-tube heat exchangers. The results validate the accuracy of the proposed computation method and its ability to serve as a suitable design reference.…”