The Effect of Combined Flow and Temperature Maldistribution on Heat Exchangers: Characteristics of Deterioration Factor Ratio, Y

Abstract

The magnitude of thermal performance degradation factor Dc for a heat exchanger as a result of combining the flow and temperature maldistribution is shown to depend on the magnitude of the shape index, S, and the statistical moments of probability density function for the flow maldistribution. In this paper, the theoretical basis describing the translational behavior of Dc with respect to S, and the influence of the statistical moments on the deterioration factor ratio Y, are given. The analysis is performed on a discretized model of an arbitrary heat exchanger. The flow distribution profile is also discretized to reveal the influence of statistical moments on Dc. The numerical calculations reveal that the combined thermal degradation factor, Dc, is a simple summation of the thermal degradation factor due to flow maldistribution alone, D, and a translational factor, XT. The value of S depends on the distribution profiles of flow and temperature. Large values of S, i.e., greater than the number N of discretized elements of the heat exchanger, and low standard deviation and high skew of the flow distribution are desirable for good thermal performance, as these reduce the magnitude of Dc and increase Y. At large values of S, maldistribution can lead, not to degradation but to augmentation of thermal performance in the heat exchanger. A critical normalized standard deviation, σ′cr, is used to characterize the transition to heat transfer augmentation for a given magnitude of S > N and skew. For any imposed flow and temperature maldistribution profiles defined by their statistical moments, these results allow development of correlation equations with the shape index and statistical moments, and enable prediction of the deterioration factor ratio Y to aid in the design of heat exchangers.