The surface temperature of a tube of outer radius is The tube is cooled with a porous annular fin of porosity P, inner radius and outer radius Coolant at mass flow rate and temperature flows axially normal to the fin’s surface. The specific heat of the coolant is and the conductivity of the fluid-solid matrix is Ri and Ro. The fin exchanges heat by convection along its upper and lower surfaces. The heat transfer coefficient is h and the ambient temperature is T∞. The fin equation is
Use the integral method to determine the heat transfer rate from the fin. Assume a second-degree polynomial temperature profile.