Thermoelastic response of a fin exhibiting elliptic thickness profile: An analytical solution

A thermoelastic analytical solution of a variable thickness cooling fin problem is presented. A variable thickness annular fin mounted on a hot rotating rigid shaft is considered. The thickness of the fin is assumed to vary radially in a continuously variable nonlinear elliptic form. An energy equation that accounts for the conduction, convective heat loss from peripheral and edge surfaces, thickness variation and rotation is adopted. The thermoelastic equation is obtained under formal assumptions of plane stress and small strains. For given heat and centrifugal loads the temperature distribution in the fin and the corresponding state of stress are obtained by means of the analytical solutions of energy and thermoelastic equations, respectively.