Transient analysis of a circular foil gage in a convective and radiative environment

An analysis of a circular thin-foil gage is presented that includes transient effects, convective heat transfer, and an arbitrary time-varying boundary condition at the foil edge to account for fluctuations in cooling water temperature. The governing energy equation is solved using Laplace transform to obtain the temporal and spatial temperature distributions of the foil. Under constant temperature at the foil edge and constant thermal radiative heat flux, closed-form response curves for the gage under various modes of heat transfer are provided. Steady-state results are also presented as limiting cases.