Kishor Gaikwad - Department of Mathematics, N. E. S., Science College, Nanded, Maharashtra, ۴۳۱۶۰۵, India
Yogesh Naner - Department of Mathematics, Shri Vitthal Rukhmini Art&#۰۳۹;s, Commerce and Science College, Sawana, Yavatmal, Maharashtra, India
Satish Khavale - Department of Mathematics, N. E. S., Science College, Nanded, Maharashtra, ۴۳۱۶۰۵, India

The aim of the current research is to analyze the transient thermoelastic bending analysis of a rectangular plate with a simply supported edge under the heat source.  Initially, the plate is kept at a constant temperature. For t > ۰, the heat is produced in the plate at the rate g (W.m^{-۳}) and the surfaces at x = ۰, a and y = ۰,  b are kept at zero temperature, while the surfaces z = ۰, c are subjected to heat convection. Using Green’s function approach and integral transform technique, the analytical solution of the rectangular plate with the simply supported edge is derived. As a preeminent finding from this investigation, it can be deduced that the accuracy,  reliability, and simplicity of these methods are excellent. Accurate bending solutions to title problems are then obtained using the transform technique. The approach used in this paper is more reasonable than conventional methods. Numerical results are presented to demonstrate the validity and efficiency of the approach as compared with those reported in other literature. The outcomes demonstrate that the temperature profile and the thermal deflection are maximum at the middle part of the plate, due to the heat source located in the middle, however, the direction of heat flow and the body deformation is the same.

Green’s Function, Rectangular plate, Heat source, Thermal Bending, Thermal Stresses