scholarly journals GENERALIZED MAGNETO- THERMOELASTICITY AND HEAT CONDUCTION ON AN INFINITE MEDIUM WITH SPHERICAL CAVITY

2020 ◽  
Vol 14 (0) ◽  
Author(s):  
A.A. Abdelbary ◽  
Mahmoud A. Ismail ◽  
Shadia Fathi Mohamed El Sherif ◽  
Hamdy M. Youssef
Keyword(s):  
Heat Conduction ◽  
Spherical Cavity ◽  
Infinite Medium

scholarly journals Non-linear heat conduction with ramped surface heating ramp surface heating and approximate solution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 377-389
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Surface Temperature ◽  
Integral Method ◽  
Infinite Medium ◽  
Surface Heating ◽  
Integration Technique ◽  
Solution Approach ◽  
Linear Heat ◽  
Thermal Penetration Depth ◽  
Non Linear

Non-linear heat conduction with a power-law thermal diffusivity and ramped surface temperature has been solved by the double-integration technique of the integral-balance integral method. The case of a semi-infinite medium and infinite ramp of surface temperature has been considered as example demonstrating the versatility of the solution approach. The thermal penetration depth and solution behaviours with finite speeds have been analyzed.

Transient Conduction From Parallel Isothermal Cylinders

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Rajai S. Alassar
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Energy Equation ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Basis Functions ◽  
Cylindrical Coordinates ◽  
Transient Conduction ◽  
Isothermal Cylinders

The transient heat conduction from two parallel isothermal cylinders is studied using the naturally fit bipolar cylindrical coordinates system. The energy equation is expanded in a Fourier series using appropriate basis functions to eliminate one of the physical coordinates. The resulting modes of the expansion are solved using a finite difference scheme. It is shown that, as is the case with a single isothermal cylinder in an infinite medium, steady states for two isothermal cylinders are not possible and heat transfer changes indefinitely with time.

Axisymmetric Thermal Stresses in a Spherical Shell of Arbitrary Thickness

1957 ◽  
Vol 24 (3) ◽  
pp. 376-380
Author(s):  
E. L. McDowell ◽  
E. Sternberg
Keyword(s):  
Steady State ◽  
Spherical Shell ◽  
Spherical Cavity ◽  
Series Solution ◽  
Thermal Stresses ◽  
Solid Sphere ◽  
Theory Of Elasticity ◽  
Infinite Medium ◽  
Series Solutions ◽  
Arbitrary Thickness

Abstract This paper contains an explicit series solution, exact within the classical theory of elasticity, for the steady-state thermal stresses and displacements induced in a spherical shell by an arbitrary axisymmetric distribution of surface temperatures. The corresponding solutions for a solid sphere and for a spherical cavity in an infinite medium are obtained as limiting cases. The convergence of the series solutions obtained is discussed. Numerical results are presented appropriate to a solid sphere if two hemispherical caps of its boundary are maintained at distinct uniform temperatures.

scholarly journals Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
R. T. Al-Khairy ◽  
Z. M. AL-Ofey
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Closed Form Solution ◽  
Infinite Medium ◽  
Form Solution ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Laser Heat Source

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential) is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.

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