Unsteady Temperature Distribution in a Sphere Subjected to Time-Dependent Surface Heat Flux and Internal Heat Source

1969 ◽  
Vol 91 (1) ◽  
pp. 45-50 ◽  
Author(s):  
N. Y. O¨lc¸er
Keyword(s):  
Heat Flux ◽  
Temperature Distribution ◽  
Heat Source ◽  
Surface Heat Flux ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Surface Heat ◽  
Initial Temperature Distribution ◽  
Unsteady Temperature ◽  
Special Cases

General expressions are derived for the three-dimensional unsteady heating of a solid sphere under the influence of a variable internal heat source and an arbitrary initial temperature distribution when the entire surface is subjected to a variable heat flux. Both the volume heat source and the surface heat flux are prescribed in terms of arbitrary functions of space and time. Various forms of solutions are noted. These expressions, not available hitherto, contain the solutions of many special problems of technological importance. The results presented in two recent studies on the arbitrary heating of spheres are shown to be special cases of the general sphere problem treated here and the errors appearing in these studies are corrected. Other special cases are also discussed.

scholarly journals Plane Strain Deformation In A Thermoelastic Microelongated Solid With Internal Heat Source

2015 ◽  
Vol 20 (4) ◽  
pp. 717-731
Author(s):  
P. Ailawalia ◽  
S.K. Sachdeva ◽  
D.S. Pathania
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Normal Mode Analysis ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Displacement Component ◽  
Mode Analysis ◽  
Plane Strain Deformation ◽  
Gl Theory ◽  
Component Force

Abstract The purpose of this paper is to study the two dimensional deformation due to an internal heat source in a thermoelastic microelongated solid. A mechanical force is applied along an overlaying elastic layer of thickness h. The normal mode analysis has been applied to obtain the exact expressions for the displacement component, force stress, temperature distribution and microelongation. The effect of the internal heat source on the displacement component, force stress, temperature distribution and microelongation has been depicted graphically for Green-Lindsay (GL) theory of thermoelasticity.

scholarly journals Two-Temperature Generalized Thermoviscoelasticity with Fractional Order Strain Subjected to Moving Heat Source: State Space Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Renu Yadav ◽  
Kapil Kumar Kalkal ◽  
Sunita Deswal
Keyword(s):  
Heat Source ◽  
State Space ◽  
Fractional Order ◽  
Mechanical Load ◽  
Generalized Thermoelasticity ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Conductive Temperature ◽  
Special Cases ◽  
Two Temperature

The theory of generalized thermoelasticity with fractional order strain is employed to study the problem of one-dimensional disturbances in a viscoelastic solid in the presence of a moving internal heat source and subjected to a mechanical load. The problem is in the context of Green-Naghdi theory of thermoelasticity with energy dissipation. Laplace transform and state space techniques are used to obtain the general solution for a set of boundary conditions. To tackle the expression of heat source, Fourier transform is also employed. The expressions for different field parameters such as displacement, stress, thermodynamical temperature, and conductive temperature in the physical domain are derived by the application of numerical inversion technique. The effects of fractional order strain, two-temperature parameter, viscosity, and velocity of internal heat source on the field variables are depicted graphically for copper material. Some special cases of interest have also been presented.

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