Analysis of transient thermoelastic temperature distribution of a thin circular plate and its thermal deflection under uniform heat generation

Abstract

Analysis of transient thermoelastic temperature distribution of a thin circular plate and its thermal deflection under uniform internal heat generation is investigated. The upper and lower surfaces are thermally insulated, while the perimetric surface is subjected to convection heat transfer with convection coefficient h_c and fluid temperature $T_{\infty },$ while the plate is also subjected to uniform internal energy generation g₀ (W.m^–3). The integral transform method is used to obtain the analytical solution for the temperature field and thermal deflection. As a special case, the mathematical model is prepared for copper material, and temperature distribution is analyzed for two different initial conditions. The results for temperature changes and the thermal deflection are computed numerically and illustrated graphically.

Keywords:

• Thermal deflection
• thermoelastic problem
• thin circular plate
• uniform heat generation

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 35B07
• 35G30
• 35K05
• 44A10

Acknowledgment

The authors express their sincere thanks to Prof. Martin Ostoja-Starzewski and the reviewer of this article for their valuable suggestions.

Additional information

Funding

The authors are thankful to Council of Scientific and Industrial Research, Human Resource Development Group, New Delhi, India for providing partial financial assistance under Junior Research Fellowship [File No.:08/581(0003)2017-EMR-I].