Analytical Approach to Solve an Inverse Problem for One-Dimensional Heat Conduction Based on Laplace Transformation. Application to Cylindrical and Spherical Coordinates.

In the present study, thermoelastic behavior of a semi-infinite rod, which is subjected to a time exponentially decaying laser pulse, is formulated. The rod is free at the left end and the laser pulse moves along the axial direction from the left end. The non-Fourier effect of the heat conduction equation is considered and the Laplace transformation method is employed in solving the governing equations. The temperature, displacement, strain, and stress in the rod are derived and the distributions of the parameters at different positions are analyzed. Also the influence of the laser speed is investigated.

Download Full-text

Efficient Technique for the Numerical Solution of the One-Dimensional Inverse Problem of Heat Conduction

Numerical Heat Transfer Part B Fundamentals ◽

10.1080/10407798108547046 ◽

1981 ◽

Vol 4 (2) ◽

pp. 229-238

Author(s):

B. F. Blackwell

Keyword(s):

Inverse Problem ◽

Heat Conduction ◽

Numerical Solution ◽

Efficient Technique ◽

One Dimensional ◽

The One

Download Full-text

Heat conduction in one-dimensional functionally graded media based on the dual-phase-lag theory

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406212456651 ◽

2012 ◽

Vol 227 (4) ◽

pp. 744-759 ◽

Cited By ~ 19

Author(s):

AH Akbarzadeh ◽

ZT Chen

Keyword(s):

Heat Conduction ◽

Analytical Solution ◽

Functionally Graded ◽

Hyperbolic Heat Conduction ◽

Phase Lag ◽

Dual Phase ◽

Spherical Coordinates ◽

One Dimensional ◽

Phase Lags ◽

Functionally Graded Media

In this article, heat conduction in one-dimensional functionally graded media is investigated based on the dual-phase-lag theory to consider the microstructural interactions in the fast transient process of heat conduction. All material properties of the media are assumed to vary continuously according to a power-law formulation with arbitrary non-homogeneity indices except the phase lags which are taken constant for simplicity. The one-dimensional heat conduction equations based on the dual-phase-lag theory are derived in a unified form which can be used for Cartesian, cylindrical, and spherical coordinates. A semi-analytical solution for temperature and heat flux is presented using the Laplace transform to eliminate the time dependency of the problem. The results in the time domain are then given by employing a numerical Laplace inversion technique. The semi-analytical solution procedure leads to exact expressions for the thermal wave speed in one-dimensional functionally graded media with different geometries based on the dual-phase-lag and hyperbolic heat conduction theories. The transient temperature distributions have been found for various types of dynamic thermal loading. The numerical results are shown to reveal the effects of phase lags, non-homogeneity indices, and thermal boundary conditions on the thermal responses for different temporal disturbances. The results are verified with those reported in the literature for hyperbolic heat conduction in cylindrical and spherical coordinates.

Download Full-text

An Initial Value Approach to the Inverse Heat Conduction Problem

Journal of Heat Transfer ◽

10.1115/1.3246912 ◽

1986 ◽

Vol 108 (2) ◽

pp. 248-256 ◽

Cited By ~ 31

Author(s):

E. Hensel ◽

R. G. Hills

Keyword(s):

Inverse Problem ◽

Heat Conduction ◽

Heat Conduction Problem ◽

Noisy Data ◽

Inverse Heat Conduction Problem ◽

Inverse Heat Conduction ◽

Initial Value ◽

Surface Conditions ◽

One Dimensional ◽

The One

The one-dimensional linear inverse problem of heat conduction is considered. An initial value technique is developed which solves the inverse problem without need for iteration. Simultaneous estimates of the surface temperature and heat flux histories are obtained from measurements taken at a subsurface location. Past and future measurement times are inherently used in the analysis. The tradeoff that exists between resolution and variance of the estimates of the surface conditions is discussed quantitatively. A stabilizing matrix is introduced to the analysis, and its effect on the resolution and variance of the estimates is quantified. The technique is applied to “exact” and “noisy” numerically simulated experimental data. Results are presented which indicate the technique is capable of handling both exact and noisy data.

Download Full-text

Numerical Simulation of 1D Unsteady Heat Conduction-Convection in Spherical and Cylindrical Coordinates by Fourth-Order FDM

Engineering, Technology & Applied Science Research ◽

10.48084/etasr.1724 ◽

2018 ◽

Vol 8 (1) ◽

pp. 2389-2392

Author(s):

E. C. Romao ◽

L. H. P. De Assis

Keyword(s):

Numerical Simulation ◽

Heat Conduction ◽

Finite Difference ◽

Finite Difference Method ◽

Fourth Order ◽

Spherical Coordinates ◽

Cylindrical Coordinates ◽

One Dimensional ◽

Unsteady Heat Conduction ◽

The One

This paper aims to apply the Fourth Order Finite Difference Method (FDM) to solve the one-dimensional unsteady conduction-convection equation with energy generation (or sink) in cylindrical and spherical coordinates. Two applications were compared through exact solutions to demonstrate the accuracy of the proposed formulation.

Download Full-text