We investigate the thermoelastic stress generation and temperature distribution in a thin circular plate using the integral transform method. The initial temperature distribution in the plate follows a parabolic profile along the z-axis, with insulation at  and  The surface  of the circular plate is subjected to thermal heat transfer at different temperatures, followed by convection with a fluid at temperature  and a convection coefficient  The analytical solution for thermal stress, displacement, and temperature is derived using the integral transform method and implemented using PTC Mathcad software.

fluid temperature, fractional derivative, thermoelasticity, heat generation, circular plate.