scholarly journals An External Circular Crack in an Infinite Solid Under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 70
Author(s):  
Yuriy Povstenko ◽  
Tamara Kyrylych ◽  
Bożena Woźna-Szcześniak ◽  
Renata Kawa ◽  
Andrzej Yatsko
Keyword(s):  
Heat Flux ◽  
Thermal Stresses ◽  
Time Derivative ◽  
Circular Crack ◽  
Constant Heat Flux ◽  
Circular Ring ◽  
Different Types ◽  
External Circular Crack ◽  
Fractional Heat Conduction ◽  
Real Solid

In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R<r<ρ. The stress intensity factor is calculated as a function of the order of time-derivative, time, and the size of a circular ring and is presented graphically.

scholarly journals A Study of Temperature Distribution and Thermal Stresses in a Hot Rock Due to Rapid Cooling

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Tran X. Phuoc ◽  
Mehrdad Massoudi ◽  
Ping Wang ◽  
Mark L. McKoy
Keyword(s):  
Heat Flux ◽  
Temperature Distribution ◽  
Thermal Stresses ◽  
Initial Temperature ◽  
Constant Heat Flux ◽  
Surface Heat ◽  
Uniform Temperature ◽  
Constant Heat ◽  
Thermoelastic Response ◽  
Unit Depth

Abstract Thermal stresses may be induced in a hot dry rock when a cold fluid is injected in the well. To study this problem, we look at the thermoelastic response of a hot rock that is suddenly cooled. The cooling is assumed to be either at a constant temperature or at a constant heat flux per unit depth. Our approach is to nondimensionalize the equations and perform a parametric study and look at the temperature distribution and the induced-thermal stresses. The results indicate that depending on the extent of cooling and the cooling time, thermal stresses can be induced. Numerical simulations on sandstone, with an initial uniform temperature of 473 K, are also carried out. The results show that if the cooling is due to the surface temperature maintained at 463 K (10 °C lower than the initial temperature of the hot rock), thermal stresses that are larger than the rock tensile strength could be induced. When the cooling is due to a constant surface heat flux, this temperature can be reached after about 777 days of cooling with a minimum value of a heat flux of −20 W/m.

The Initial Phase of Transient Thermal Stresses Due to General Boundary Thermal Loads in Orthotropic Hollow Cylinders

1990 ◽  
Vol 57 (3) ◽  
pp. 719-724 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Heat Flux ◽  
Initial Phase ◽  
Bessel Functions ◽  
Thermal Stresses ◽  
Constant Heat Flux ◽  
Hollow Cylinders ◽  
Temperature Constant ◽  
The One ◽  
Transient Thermal ◽  
Bounding Surfaces

The stresses and displacements in the initial phase of applying a thermal load on the bounding surfaces of an orthotropic hollow circular cylinder are obtained using the Hankel asymptotic expansions for the Bessel functions of the first and second kind. Such a load may be constant temperature, constant heat flux, zero heat flux, or heat convection to a different medium at either surface. The material properties are assumed to be independent of temperature. A constant applied temperature at the one surface and convection into a medium at a different temperature at the other surface is used to illustrate the variation of stresses with time and through the thickness in the initial transient phase.

Thermoelastic Interaction in an Infinite Long Hollow Cylinder with Fractional Heat Conduction Equation

2017 ◽  
Vol 9 (2) ◽  
pp. 378-392
Author(s):  
Ahmed. E. Abouelregal
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
Hollow Cylinder ◽  
Heat Conduction Equation ◽  
Thermal Stresses ◽  
Generalized Thermoelasticity ◽  
Constant Heat Flux ◽  
Conduction Equation ◽  
The Laplace Transform ◽  
Fractional Heat Conduction

AbstractIn this work, we introduce a mathematical model for the theory of generalized thermoelasticity with fractional heat conduction equation. The presented model will be applied to an infinitely long hollow cylinder whose inner surface is traction free and subjected to a thermal and mechanical shocks, while the external surface is traction free and subjected to a constant heat flux. Some theories of thermoelasticity can extracted as limited cases from our model. Laplace transform methods are utilized to solve the problem and the inverse of the Laplace transform is done numerically using the Fourier expansion techniques. The results for the temperature, the thermal stresses and the displacement components are illustrated graphically for various values of fractional order parameter. Moreover, some particular cases of interest have also been discussed.

Rate of Sublimation of Ice by Radiative Heating in Freeze-Etching

1980 ◽  
Vol 38 ◽  
pp. 618-619
Author(s):  
Yeshayahu Talmon
Keyword(s):  
Heat Flux ◽  
Freeze Fracture ◽  
Constant Heat Flux ◽  
Radiative Heating ◽  
Constant Heat ◽  
Entire Sample ◽  
Simplified Method ◽  
Freeze Etching ◽  
Sublimation Rates ◽  
Fractured Surface

To bring out details in the fractured surface of a frozen sample in the freeze fracture/freeze-etch technique,the sample or part of it is warmed to enhance water sublimation.One way to do this is to raise the temperature of the entire sample to about -100°C to -90°C. In this case sublimation rates can be calculated by using plots such as Fig.1 (Talmon and Thomas),or by simplified formulae such as that given by Menold and Liittge. To achieve higher rates of sublimation without heating the entire sample a radiative heater can be used (Echlin et al.). In the present paper a simplified method for the calculation of the rates of sublimation under a constant heat flux F [W/m2] at the surface of the sample from a heater placed directly above the sample is described.

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