Effective temperature of an expanding tube with a radial temperature gradient over the wall

By using the finite-strain theory, an effective temperature, defined as a uniform temperature producing the same deformation rates as the actual temperature gradient, of a thick-walled internally pressurized closed-end tube with an over-the-wall radial temperature gradient, is expressed in terms of original tube geometry, strain, temperature distribution, and creep properties of the tube material. For a stainless-steel cladding tube of a fission reactor fuel pin, with a radial temperature gradient of 500C over the wall, the effective temperature equals the average of the instantaneous inner and outer surface temperatures to within 10C