scholarly journals Fractional Heat Conduction Models and Thermal Diffusivity Determination

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Monika Žecová ◽  
Ján Terpák
Keyword(s):  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Numerical Methods ◽  
Fractional Order ◽  
Experimental Verification ◽  
Heat Conduction Equation ◽  
Historical Overview ◽  
One Dimensional ◽  
The One ◽  
Fractional Heat Conduction

The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.

scholarly journals An analysis of heat conduction in polar bear hairs using one-dimensional fractional model

2016 ◽  
Vol 20 (3) ◽  
pp. 785-788 ◽  
Author(s):  
Wei-Hong Zhu ◽  
Shao-Tang Zhang ◽  
Zheng-Biao Li
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Polar Bear ◽  
Thermal Protection ◽  
Polar Bears ◽  
Cold Environment ◽  
Membrane Pore ◽  
One Dimensional ◽  
Fractional Heat Conduction ◽  
Maintain Body Temperature

Hairs of a polar bear are of superior properties such as the excellent thermal protection. The polar bears can perennially live in an extremely cold environment and can maintain body temperature at around 37 ?C. Why do polar bears can resist such cold environment? Its membrane-pore structure plays an important role. In the previous work, we established a 1-D fractional heat conduction equation to reveal the hidden mechanism for the hairs. In this paper, we further discuss solutions and parameters of the equation established and analyze heat conduction in polar bear hairs.

Reconstruction of the Robin boundary condition and order of derivative in time fractional heat conduction equation

2018 ◽  
Vol 13 (1) ◽  
pp. 5 ◽  
Author(s):  
Rafał Brociek ◽  
Damian Słota
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Fractional Order ◽  
Heat Conduction Equation ◽  
Robin Boundary Condition ◽  
Conduction Equation ◽  
Additional Information ◽  
Bee Colony ◽  
Robin Boundary ◽  
Fractional Heat Conduction

This paper describes an algorithm for reconstruction the boundary condition and order of derivative for the heat conduction equation of fractional order. This fractional order derivative was applied to time variable and was defined as the Caputo derivative. The heat transfer coefficient, occurring in the boundary condition of the third kind, was reconstructed. Additional information for the considered inverse problem is given by the temperature measurements at selected points of the domain. The direct problem was solved by using the implicit finite difference method. To minimize functional defining the error of approximate solution an Artificial Bee Colony (ABC) algorithm and Nelder-Mead method were used. In order to stabilize the procedure the Tikhonov regularization was applied. The paper presents examples to illustrate the accuracy and stability of the presented algorithm.

Numerical solutions for the one-dimensional heat-conduction equation using a spreadsheet

1996 ◽  
Vol 22 (10) ◽  
pp. 1147-1158 ◽  
Author(s):  
Zohar Gvirtzman ◽  
Zvi Garfunkel
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Conduction Equation ◽  
One Dimensional ◽  
The One

scholarly journals Transition from Diffusion to Wave Propagation in Fractional Jeffreys-Type Heat Conduction Equation

2020 ◽  
Vol 4 (3) ◽  
pp. 32
Author(s):  
Emilia Bazhlekova ◽  
Ivan Bazhlekov
Keyword(s):  
Heat Conduction ◽  
Fundamental Solution ◽  
Heat Conduction Equation ◽  
Constitutive Law ◽  
Conduction Equation ◽  
Diffusion Regime ◽  
One Dimensional ◽  
Different Types ◽  
Propagation Regime ◽  
The One

The heat conduction equation with a fractional Jeffreys-type constitutive law is studied. Depending on the value of a characteristic parameter, two fundamentally different types of behavior are established: diffusion regime and propagation regime. In the first case, the considered equation is a generalized diffusion equation, while in the second it is a generalized wave equation. The corresponding memory kernels are expressed in both cases in terms of Mittag–Leffler functions. Explicit representations for the one-dimensional fundamental solution and the mean squared displacement are provided and analyzed analytically and numerically. The one-dimensional fundamental solution is shown to be a spatial probability density function evolving in time, which is unimodal in the diffusion regime and bimodal in the propagation regime. The multi-dimensional fundamental solutions are probability densities only in the diffusion case, while in the propagation case they can have negative values. In addition, two different types of subordination principles are formulated for the two regimes. The Bernstein functions technique is extensively employed in the theoretical proofs.

scholarly journals A Cubic Spline Technique for the One Dimensional Heat Conduction Equation

1973 ◽  
Vol 11 (1) ◽  
pp. 111-113 ◽  
Author(s):  
N. PAPAMICHAEL ◽  
J. R. WHITEMAN
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Cubic Spline ◽  
Conduction Equation ◽  
One Dimensional ◽  
The One

Research on the Issue of LED’s Cooling Based on Heat Conduction Equations

2012 ◽  
Vol 507 ◽  
pp. 137-141
Author(s):  
Zhi Qin Huang ◽  
Pei Ying Quan ◽  
Yong Qing Pan
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Heat Conduction Equation ◽  
Rapid Development ◽  
Three Dimensional ◽  
Conduction Equation ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
The One

With the rapid development of power type LED, the issue of the cooling of LED has been prominent. How to make the heat generated by LED chip go out quickly in order to cool the LED chip has become an urgent problem. The form of heat goes through the substrate has been widely used and has become the best way to solve the heat problem. There are three types of LED substrate. They are metal substrate, ceramic substrate and composite substrate. At first, In this paper I analyze the theoretical of three-dimensional non-steady state and steady state heat conduction equation, then the three-dimensional model is simplified as one-dimensional model and I get the results of heat conduction equation under the one-dimensional stationary and non-steady state.

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