Thermal stresses and Temperature Profile in Functionally Graded Material with Internal Heat Generation in Rectangular Plate

Abstract

    The physical parameters such as temperature distribution and induced stresses are always characterized by the influence of propagation of heat through any solid. Many researchers have contributed in development of study and analysis of such properties of solids. The material in nature exhibit different behavior regarding their temperature dependent property. The functionally graded material is one of the interesting compositions of solid. Present research emphasizes on determination of stresses and temperature distribution through a solid. In present research paper, attempt is being made to reveal temperature distribution and induced thermal stresses in a rectangular thin slab of thermo sensitive functionally graded material. The plate was kept at surrounding temperature and the effect of temperature on a plate is analyzed for evaluation of thermal stresses. The conversion of a nonlinear heat equation into linear heat equation is performed to design the mathematical treatment of the problem. Kirchhoff’s variable transformation has been introduced and results are obtained by using integral transform technique with hyperbolic varying point heat source. A mathematical modeling is performed by considering ceramic metal-based material which is composed of alumina as ceramic and nickel as metal. Temperature distribution and induced stresses have been calculated in homogeneous as well as non-homogeneous specimen. The final output of temperature and stresses have been represented graphically and numerically. It has been reported that the variation in stresses occurred on account of changes in homogeneity parameters.