The research work aims at investigating the performance of functionally graded annular fin. The work involves computation of efficiency and effectiveness of such fins and compares the fin performances for different geometry and grading parameters. It is also assumed that the temperature gradient only exists in one direction i.e. along the radius. A general second order governing differential equation has been derived for all the profiles and grading. The thickness of fin is considered to be a power function of radial co-ordinate. The functional grading of thermal conductivity is assumed to be a power function of radial co-ordinate and also consists of parameters, namely grading parameters, varying which different grading combinations can be carried out. The efficiency and effectiveness of the annular fin of different geometry and grading combinations have been calculated and plotted. The performance analysis reveals the dependence of thermal behaviour of annular fins on geometry and grading parameter.
TopBackground
Although there are abundant reports available on thermal performance of annular fin made of isotropic material, the studies of fin made of materials having varying thermal conductivity is scare. Jensen et. al. (1999) presented the work for finding the efficiency of annular fin made of two materials using Gardner's expression. Bahadur and Bar-cohen (2004) gave an optimization methodology for a thermally conductive polyphenylene sulphide (PPS) polymer staggered pin fin heat sink, for an advanced natural convection cooled microprocessor application. The coefficient of thermal performance, COP, that relates cooling capability to the energy invested in the formation of the heat sink, has been determined and compared with conventional aluminium heat sinks.
An analytical equation to optimize thermally conductive PPS polymer fins used in electronic heat sink of microprocessor application has been described by Bahadur and Bar-cohen (2005) the geometric dependence of heat dissipation and relationships between the pin fin height, pin diameter, horizontal spacing, and pin fin density for a fixed base area and excess temperature has been discussed. The thermal calculation of composite metallic fins of variable thickness has been obtained by Campo et. al. (2008) wherein analytical solution for the two-dimensional, two-material conduction problem, under the form of an infinite series of orthogonal eigen functions has been obtained and Bi number limitation has been checked to express the fin efficiency in closed form.
The effects of radiation and convection heat transfer in porous media have been discussed by Gorla and Bakier (2011). The effects of the porosity parameter (Sh), radiation parameter (G) and temperature ratio (CT) on the dimensionless temperature distribution and heat transfer rate discussed in detail. Results show that the radiation transfers more heat compared to a similar model without radiation. Heat transfer and temperature distribution equations for longitudinal convective–radiative porous fins have been presented by Hatami and Ganji (2014). Al,SiC and Si3N4 has been considered ceramic porous materials, and it has been observed that exponential section fin with Si3N4 material has the maximum amount of transferred heat.
Turkyilmazoglu (2014) reported the combined heat and mass transfer mechanisms owing to the temperature and humidity ratio differences considering their influence on the efficiency of different exponential type porous fin configurations. A comparison with the traditional straight porous fins proves that the fin tip temperature and efficiency of the exponential porous wet fins are much better than those corresponding to the straight porous wet fins.
Lee et. al. (2004) reported the solution for estimating the unknown heat flux at the pin fin base by the conjugate gradient method. The accuracy of the inverse analysis has been examined by simulated exact and inexact measurements of temperature at interior locations of the pin fin.
Recursive numerical formulation technique has been applied by Kou et. al. (2005) to analyze the longitudinal fin of variable thermal properties with discrete model dividing the singular into many sections. Finally combining each section together, the complete solution of the fin has been obtained.