Abstract
An analytic solution method, without integral transformation, is developed to find the exact solutions for transient heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions. By introducing suitable shifting functions, the governing second-order regular singular differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions. The exact solution of the system with thermal conductivity and specific heat in power functions with different orders is developed. Finally, limiting studies and numerical analyses are given to illustrate the efficiency and the accuracy of the analysis.
Highlights
IntroductionThe applications of heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions can be widely found in many engineering fields, such as cannon barrels, heat exchanger tubes, time varied heating on walls of circular structure, and heat treatment on hollow cylinders
By introducing suitable shifting functions, the governing second-order regular singular differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions
The applications of heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions can be widely found in many engineering fields, such as cannon barrels, heat exchanger tubes, time varied heating on walls of circular structure, and heat treatment on hollow cylinders
Summary
The applications of heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions can be widely found in many engineering fields, such as cannon barrels, heat exchanger tubes, time varied heating on walls of circular structure, and heat treatment on hollow cylinders. For the problem of heat conduction in circular hollow uniform cylinders with time-dependent boundary conditions, the associated governing differential equation is a secondorder Bessel differential equation with constant coefficients. Ootao et al [10] studied the transient temperature and thermal stress distribution in an infinitely long nonhomogeneous hollow cylinder due to Mathematical Problems in Engineering a moving heat source in the axial direction from the inner and/or outer surfaces using the layerwise theory in conjunction with the method of Fourier cosine and the Laplace transformations. Asgari and Akhlaghi [13] employed the finite element method to study the transient thermal stresses in a thick hollow cylinder with finite length mad of 2D-FGM that its material properties are varied in the radial and axial directions with a power law function. Limiting studies and numerical analysis are given to illustrate the efficiency and accuracy of the solution method
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