Time fractional heat transfer analysis in thermally sensitive functionally graded thick hollow cylinder with internal heat source and its thermal stresses

Abstract

The aim of this work is to investigate the time fractional thermoelastic state of a thermally sensitive functionally graded thick hollow cylinder subjected to internal heat source. Convection boundary conditions are applied on the curved surface of cylinder also sectional heating is assumed on the lower surface. The material properties except density and Poisson’s ratio are assumed to be dependent on temperature. Kirchhoff’s variable transformation is used to reduce the nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity to linear form. Further the solution of linear form is obtained by using integral transform technique in the form of Bessel’s and trigonometric functions. All physical and mechanical quantities are taken as dimensional for the theoretical analysis whereas for numerical computations non-dimensional parameters are assumed. Numerical results of temperature change and stress distribution are illustrated graphically for ceramic-metal-based functionally graded materials and shown in figures with the help of Mathematica software.

Fractional Thermal Analysis in a Generalized two Dimensional Infinite half Space with Heat Source

“…The thermoelastic theory which deals with concept of two relaxation times or having temperature dependency is known as second generalization. The thermoelastic theory with two relaxation times was developed by Green and Lindsay [3].From last few years, a lot of research work has developed in theory of fractional [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Generalized Cattaneo’s Law over a Vertical Cylinder on Casson Fluids

“…Zhang et al, [15] applied the fractional derivative scheme to present the simulations for a bio-convective problem with heat conduction model and able to predict thermal response between diffusion and wave behavior. Thakare and Warbhe [16] have discussed the time fractional thermoelastic state of a thermally sensitive functionally graded thick hollow cylinder subjected to internal heat source. Xu and Wang [17] successfully implemented analytical solution of time fractional Catteno heat equation for finite slab under pulse heat flux.…”

Thermosensitive Response of a Functionally Graded Cylinder with Fractional Order Derivative

“…Therefore, an analysis of time fractional thermo-sensitivity is very important in various cylindrical structures which are made of FGMs. Recently, Thakare and Warbhe [23] studied the time fractional order thermoelastic problem of a thermally sensitive functionally graded thick hollow cylinder with the effect of internal heat source. Thakre et al [24] solved a two dimensional thermoelastic problem and determined temperature and associated stresses for a non-homogeneous thick hollow cylinder within the context of fractional order theory.…”

“…The article presented here is related to the extension of our own work [23,24] by assuming the time fractional governing temperature and spatial variable dependent heat conduction problem for a thick functionally graded hollow cylinder with an internal heat source (geometry as shown in Fig. 1).…”