Development of Shell Finite Element Formulation for combined heat and mass transfer from orthotropic material

Extended surfaces are widely used to enhance the rate of heat transfer between a solid and a surrounding fluid. Annular fins, spines (or pin fins) and longitudinal (plain) fins are commonly used types of extended surfaces for many types of thermal engineering applications. The other category of fin geometry is the one used in fin-and-tube heat exchangers; used for heating, ventilating, and air conditioning (HVAC) applications. In most applications, enhanced fin patterns (such as wavy, louver, slit, and convex-louver) are adopted. In a refrigeration and air conditioning equipment, if the fin surface temperature is lower than the dew point temperature of incoming moist air then the condensation of water vapor occurs on the fin surface; thus, heat and mass transfer occurs simultaneously. Therefore, the performance (or efficiency) of the fins is a governing parameter for the performance of the equipment. Composites have the potential to support a wider range of thermal and mechanical properties to meet requirements of high strength, stiffness, light in weight and resistance to hostile environments. Recently composite materials have been used for heat sink applications in electronic devices and they can also find their applications for HVAC applications. However the analytical solutions for composite material fins can become complex as the fin geometry becomes complicated. Some semi-analytical solutions are available in the literature to analyze the orthotropic material fin efficiency with combined heat and mass transfer. Therefore, finite element method can be used for the problems that contain variable geometry and orthotropic thermal conductivity. The proposed work deals with the design methodology using FEM simulation for orthotropic fins with combined heat and mass transfer from fins in a shell-tube heat exchanger. In the proposed study, a shell finite element will be developed having the capability of heat and mass transfer for orthotropic materials. The developed finite element will then be used for studying the heat and mass transfer rate predictions for orthotropic fins. The finite element formulation results will be first validated through some test case of studies by comparing them with experimental/numerical or analytical results. Effect of various parameters (such as fin geometry and orthotropic thermal conductivity, and operating conditions) on the resulting performance of the orthotropic material fins will be investigated.