Heat transfer from a horizontal fin array by natural convection and radiation-A conjugate analysis

The problem of natural convection heat transfer from a horizontal fin array is theoretically formulated by treating the adjacent internal fins as two-fin enclosures. A conjugate analysis is carried out in which the mass, momentum and energy balance equations for the fluid in the two-fin enclosure are solved together with the heat conduction equations in both the fins. The numerical solutions by using alternating direction implicit (ADI) method yield steady state temperature and velocity fields in the fluid, and temperatures along the fins. Each end fin of the array is exposed to limited enclosure on one side and to infinite fluid medium on the other side. Hence a separate analysis is carried out for the problem of end fin exposed to infinite fluid medium with appropriate boundary conditions. From the numerical results, the heat fluxes from the fins and the base of the two-fin enclosure, and the heat flux from the end fin are calculated. Making use of the heat fluxes the total heat transfer rate and average heat transfer coefficient for a fin array are estimated. Heat transfer by radiation is also considered in the analysis. The results obtained for a four-fin array are compared with the experimental data available in literature, which show good agreement. Numerical results are obtained to study the effectiveness for different values of fin heights, emissivities, number of fins in a fixed base, fin base temperature and fin spacing. The numerical results are subjected to non-linear regression and equations are obtained for heat fluxes from the two-fin enclosure and single fin as functions of Rayleigh number, aspect ratio and fin emissivity. Also regression equations are obtained to readily calculate the average Nusselt number, heat transfer rate and effectiveness for a fin array.