scholarly journals Fractional order heat conduction and thermoelastic response of a thermally sensitive rectangular parallelopiped

2021 ◽  
Vol 24 (1) ◽  
pp. 62-73
Author(s):  
V. B. SRİNİVAS ◽  
V R MANTHENA ◽  
Jaya BİKRAM ◽  
G. D. KEDAR
Keyword(s):  
Heat Conduction ◽  
Fractional Order ◽  
Thermoelastic Response ◽  
Rectangular Parallelopiped

Fractional lumped capacitance

2018 ◽  
Vol 21 (4) ◽  
pp. 1104-1119 ◽  
Author(s):  
Andrew W. Wharmby
Keyword(s):  
Heat Conduction ◽  
Fractional Order ◽  
Transient Heat Conduction ◽  
Temperature Profiles ◽  
Cooling Temperature ◽  
Heating And Cooling ◽  
Capacitance Model

Abstract A new lumped capacitance model that employs fractional order operators is proposed for use on transient heat conduction problems. Details and implications of the fractional lumped capacitance model’s development and application are discussed. The model is shown to agree with observed heating and cooling temperature profiles of laser aiming paper being heated by a laser under various conditions.

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.

Damage Analysis of Internal Surface Flaws Using Thermoelastic Stress Analysis

2005 ◽  
Vol 293-294 ◽  
pp. 279-288 ◽  
Author(s):  
N. Sathon ◽  
Janice M. Dulieu-Barton
Keyword(s):  
Heat Conduction ◽  
Stress Analysis ◽  
Phase Variation ◽  
Thermoelastic Stress ◽  
Internal Surface ◽  
Thermoelastic Stress Analysis ◽  
Element Simulation ◽  
Surface Flaws ◽  
Thermoelastic Response ◽  
Phase Data

Thermoelastic Stress Analysis (TSA) has been used to detect and evaluate the severity of damage on a flat metallic plate. The damage takes the form of a semi-circular notch that represents a surface flaw. Thermoelastic data was gathered from the undamaged side of the plate. The experimental results show that shallow surface flaws can be detected by using phase information from thermoelastic data. This information can then be used to indicate the flaw severity in terms of the notch depth. It is shown that the phase data is dependent on the heat conduction effects around the notch, which enable an assessment of the damage. This is modelled using a simple finite element simulation of the effects of heat conduction on the thermoelastic response. A discussion on the potential of using phase variation across damaged regions to analyse damage severity is provided.

scholarly journals A Novel Method for Solution of Fractional Order Two-Dimensional Nonlocal Heat Conduction Phenomena

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Hammad Khalil ◽  
Ishak Hashim ◽  
Waqar Ahmad Khan ◽  
Abuzar Ghaffari
Keyword(s):  
Heat Conduction ◽  
Fractional Order ◽  
Operational Matrix ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Test Problems ◽  
Operational Matrices ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Operational Matrix Method

In this paper, we have extended the operational matrix method for approximating the solution of the fractional-order two-dimensional elliptic partial differential equations (FPDEs) under nonlocal boundary conditions. We use a general Legendre polynomials basis and construct some new operational matrices of fractional order operations. These matrices are used to convert a sample nonlocal heat conduction phenomenon of fractional order to a structure of easily solvable algebraic equations. The solution of the algebraic structure is then used to approximate a solution of the heat conduction phenomena. The proposed method is applied to some test problems. The obtained results are compared with the available data in the literature and are found in good agreement.Dedicated to my father Mr. Sher Mumtaz, (1955-2021), who gave me the basic knowledege of mathematics.

Time-Fractional Hygrothermoelastic Problem for a Sphere Subjected to Heat and Moisture Flux

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Xue-Yang Zhang ◽  
Yi Peng ◽  
Xian-Fang Li
Keyword(s):  
Heat Conduction ◽  
Fractional Order ◽  
Integral Transform ◽  
Moisture Diffusion ◽  
Moisture Flux ◽  
Moisture Distribution ◽  
Order Derivative ◽  
Transform Method ◽  
Stress Components ◽  
Heat And Moisture

In this paper, a non-Fourier model of heat conduction and moisture diffusion coupling is proposed. We study a hygrothermal elastic problem within the framework of time-fractional calculus theory for a centrally symmetric sphere subjected to physical heat and moisture flux at its surface. Analytic expressions for transient response of temperature change, moisture distribution, displacement, and stress components in the sphere are obtained for heat/moisture flux pulse and constant heat/moisture flux at the sphere's surface, respectively, by using the integral transform method. Numerical results are calculated and the effects of fractional order on temperature field, moisture distribution, and hygrothermal stress components are illustrated graphically. Subdiffusive and super-diffusive transport coupling behavior as well as wave-like behavior are shown. When fractional-order derivative reduces to first-order derivative, the usual heat and moisture coupling is recovered, which obeys Fourier heat conduction and Fick's moisture diffusion.

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