Minimization of entropy generation in U-bend tube heat exchanger during flow boiling of R134a

Abstract

The presence of a bend in a tube during two-phase flow boiling can improve heat transfer while also causing a pressure drop. The goal of this paper is to achieve an optimal geometry of the U-bend tube heat exchanger. The bend induces a high-pressure drop as well as increases heat transfer coefficient, striking a balance between pressure drop and heat transfer coefficient to obtain an optimal design can be achieved by minimizing entropy generation due to heat transfer and pressure drop. Hence, an entropy generation minimization during two-phase flow boiling of R134a was conducted using the constructal design method and the entropy generation techniques based on the second law of thermodynamics. The geometric optimization was subjected to the following constraints: the volume of the tube was constant with bending radius, and the tube's outer surface area was subjected to a uniform constant heat flux of 10 kW/m2. Geometric parameters such as total length Lt, internal diameter di and external diameter do of the tube were free to morph with respect to the degree of freedom until an optimal geometrical configuration was obtained at minimum entropy generation. The bend's curvature ratio was taken as a function of internal (hydraulic) diameter. The numerical computations were conducted with the mass fluxes from 100 to 500 kg/m2s and quality of 0.2 at the tube's inlet for downward-oriented flow. The results obtained were consistent with those found in the open literature. Furthermore, the optimal parameters of the tube heat exchanger were found to vary slightly as the minimum entropy generation rises with an increase in mass flux. The stability was achieved as minimum entropy generation increased which demonstrates the robustness of the optimized U-bend tube.