A new hybrid analytical/numerical method for transient heat conduction in composite hollow cylinders applied to plug and abandonment of oil wells

2021 ◽  
Vol 168 ◽  
pp. 106981
Author(s):  
Gabriel S. de Andrade ◽  
Marcelo J.S. de Lemos ◽  
Danilo Colombo
Keyword(s):  
Heat Conduction ◽  
Numerical Method ◽  
Transient Heat Conduction ◽  
Oil Wells ◽  
Hollow Cylinders

Taylor Series Numerical Method in Transient Heat Conduction Analysis

2013 ◽  
Vol 275-277 ◽  
pp. 677-680
Author(s):  
Li Bin Zhao ◽  
Yuan Wei Li ◽  
Feng Rui Liu
Keyword(s):  
Heat Conduction ◽  
Numerical Method ◽  
Taylor Series ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Theoretical Description ◽  
Fiber Optic Gyro ◽  
Lumped Mass ◽  
Transient Heat Conduction Problem ◽  
Capacity Matrix

Taylor series numerical method (TSNM) is extended to the field of transient heat conduction. Theoretical description of TSNM for transient heat conduction problems is presented. Furthermore, the algorithm is realized and embedded in commercial software ANSYS®. If a lumped mass heat capacity matrix provided, the governing equation of transient heat conduction problems, which is a differential equation, will be solved by a series of recursion calculation of Taylor expanding coefficients. A typical transient heat conduction problem with analytical solution was discussed to verify the TSNM. At last, the TSNM is applied in the transient heat analysis of an all-solid fiber optic gyro (FOG).

Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Conduction Theory ◽  
Hollow Cylinders ◽  
Fourier Heat Conduction ◽  
Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

scholarly journals Analytic Solutions for Heat Conduction in Functionally Graded Circular Hollow Cylinders with Time-Dependent Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Sen-Yung Lee ◽  
Chih-Cheng Huang
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Integral Transformation ◽  
Transient Heat Conduction ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Time Dependent ◽  
Power Functions ◽  
Hollow Cylinders

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.

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