scholarly journals An Interface Anticrack in a Periodic Two–Layer Piezoelectric Space under Vertically Uniform Heat Flow

2020 ◽  
Vol 22 (3) ◽  
pp. 667-682
Author(s):  
Andrzej Kaczyński ◽  
Bartosz Kaczyński
Keyword(s):  
Heat Flow ◽  
Complete Solution ◽  
Laminated Composite ◽  
Circular Inclusion ◽  
Oscillatory Behavior ◽  
Boundary Integral ◽  
Elementary Functions ◽  
Uniform Heat ◽  
Homogenized Model ◽  
Stress Discontinuity

AbstractThis paper aims to investigate 3D static thermoelectroelastic problem of a uniform heat flow in a bi-material periodically layered space disturbed by a thermally and electrically-insulated rigid sheet-like inclusion (so-called anticrack) situated at one of the interfaces. An approximate analysis of the considered laminated composite is given in the framework of the homogenized model with microlocal parameters. Accurate results are obtained by constructing suitable potential solutions and reducing to the corresponding homogeneous thermoelectromechanical (or thermomechanical) anticrack problems. The governing boundary integral equation for a planar interface anticrack of arbitrary shape is derived in terms of a normal stress discontinuity. As an illustration, a complete solution for a rigid circular inclusion is obtained in terms of elementary functions and interpreted from the failure perspective. Unlike existing solutions for defects at the interface of materials, the solution obtained displays no oscillatory behavior.

Thermal Stresses Due to Disturbance of Uniform Heat Flow by an Insulated Ovaloid Hole

1960 ◽  
Vol 27 (4) ◽  
pp. 635-639 ◽  
Author(s):  
A. L. Florence ◽  
J. N. Goodier
Keyword(s):  
Heat Flow ◽  
Closed Form ◽  
Thermal Stresses ◽  
Thermoelastic Problem ◽  
Uniform Heat ◽  
Special Cases

The linear thermoelastic problem is solved for a uniform heat flow disturbed by a hole of ovaloid form, which includes the ellipse and circle as special cases. Results for stress and displacement are found in closed form, by reducing the problem to one of boundary loading solvable by a method of Muskhelishvili.

scholarly journals On the Thermal Stresses of an Infinite Plate with an Infinite Row of Circular Inclusions under Uniform Heat Flow

1980 ◽  
Vol 23 (180) ◽  
pp. 849-856 ◽  
Author(s):  
Hidekazu ARAKI ◽  
Shunsuke SHIOYA ◽  
Mitsumasa MATSUDA
Keyword(s):  
Heat Flow ◽  
Thermal Stresses ◽  
Infinite Plate ◽  
Uniform Heat

Interfacial Stresses of a Coated Square Hole Induced by a Remote Uniform Heat Flow

2020 ◽  
Vol 12 (06) ◽  
pp. 2050063
Author(s):  
S. C. Tseng ◽  
C. K. Chao ◽  
F. M. Chen
Keyword(s):  
Heat Flow ◽  
Shape Factor ◽  
Coating Layer ◽  
Infinite Plate ◽  
Interfacial Stress ◽  
Graphical Form ◽  
Shear Stresses ◽  
Interfacial Stresses ◽  
Uniform Heat ◽  
Square Hole

This paper presents an analytical solution of a coated square hole embedded in an isotropic infinite plate under a remote uniform heat flow. Based on conformal mapping, analytic continuation theorem and the alternation technique, temperature and stress functions are derived in a compact series form. Results of temperature contours and interfacial stresses are validated using the finite element method. The comparison indicates the high accuracy of the proposed method. Numerical results of both the interfacial normal and shear stresses for different properties and geometric parameters of a coated layer are provided in a graphical form. The results indicate that the interfacial stresses are highly dependent on the thermal expansion coefficient, thickness of the coating layer and shape factor of the coated square hole. In conclusion, the interfacial shear stresses exhibit a significant increase at the corners with abrupt geometrical changes, which would cause the delamination of the coating layer system. Furthermore, increasing the thickness of the coating layer and the shape factor results in a higher interfacial stress.

Numerical Visualization of Heat Flow and Thermal Mixing in Various Differentially Heated Square Cavities Using Bejan’s Heatlines

2011 ◽  
Author(s):  
Ram Satish Kaluri ◽  
Tanmay Basak
Keyword(s):  
Heat Flow ◽  
Bottom Wall ◽  
Temperature Fields ◽  
Heat Distribution ◽  
Heat Sources ◽  
Large Area ◽  
Thermal Mixing ◽  
Uniform Heat ◽  
High Heat Transfer ◽  
Lower Corner

A comprehensive analysis of heat distribution and thermal mixing in steady laminar natural convective flow in discretely heated square cavities has been carried out via Bejan’s heatlines. Heatlines are analogous to streamlines and heat energy flow may be visualized by heatlines similar to streamlines which display fluid flow. The trajectories of heatlines indicate direction and magnitude of heat flow and zones of high heat transfer. The heatline approach is implemented to study heat flow in the following three different square cavities which are filled with water (Pr = 7): (1) uniformly heated bottom wall (2) distributed heating with heat sources present on central portions of the walls and (3) multiple heat sources on the walls of the cavity. Top wall is maintained adiabatic in all the cases. Galerkin finite element method with penalty parameter has been used to solve non-linear coupled partial differential equations for flow and temperature fields over a range of Rayleigh numbers (Ra = 103–105). The Galerkin method is further employed to solve the Poisson equation for streamfunctions and heatfunctions. Finite discontinuity exists at the junction of hot and cold walls leading to mathematical singularity. Solution of heatfunction for such type of situation demands implementation of non-homogeneous Dirichlet conditions. Heatlines illustrate that in uniformly heated bottom wall case, the heat from the bottom wall is not adequately distributed to the lower portion of side walls which leads to low temperature in those regions (case 1). In order to improve the heat distribution, the uniform heat sources is divided into three parts and are applied along the central regimes of the walls (case 2). It is observed that, heat distribution and thermal mixing in the cavity is significantly enhanced. However, the lower corner portions are still retained cold. In case 3, multiple heat sources are placed along the walls of the cavity along with heat sources at lower corner regions of the cavity. Heatlines indicate that, the temperature at the core is reduced compared to case 2, but uniform heat distribution results in uniformity of temperature across large area of cavity.

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