A novel analysis for calculating the smallest envelope shape of wet fins with a nonlinear mode of surface transport

A solely analytical method is investigated to determine the minimum fin shape of wet fins subject to variable heat transfer coefficients. The analysis is applicable to any surface condition, including dry, fully wet and partially wet. An optimization procedure based on the variational principle is derived to develop an analytical formulation. The effects of various design parameters, including base temperature, relative humidity, surrounding temperature and surrounding pressure, are studied to identify the dependent variables affecting the minimum envelope shape to transfer energy efficiently. The analysis also shows the influence of the variable heat transfer coefficient on the temperature distribution and profile shape with the intention of optimizing the envelope shape criterion. A convergent optimum profile shape is established for the constant heat transfer coefficient or the temperature-dependent heat transfer coefficient with a decreasing function along the length of the fin. On the other hand, divergent profiles under wet conditions may transfer heat optimally for an increasing heat transfer coefficient from the fin base to the fin tip. A simple method is highlighted to produce a new profile by choosing a constraint tip temperature to improve the shape near the tip in order to have an ease in manufacturing process.