Unsteady-state temperature distribution in a convecting fin of constant area

A solution for the unsteady-state temperature distribution in a fin of constant area dissipating heat only by convection to an environment of constant temperature, is obtained. The partial differential equation is separated into an ordinary differential equation with position as the independent variable, and a partial differential equation with position and time as the independent variables. The problem is solved for either a step function in temperature or a step function in heat flow rate, for zero time, at one boundary while the other boundary is insulated. The initial condition is taken as an arbitrary constant. The unspecified boundary values (temperature or heat flow rate) are presented for both cases by utilizing dimensionless plots. Experimental verification is presented for the case of constant heat flow rate boundary condition.