scholarly journals Thermal impedance estimations by semi-derivatives and semi-integrals: 1-D semi-infinite cases

2013 ◽  
Vol 17 (2) ◽  
pp. 581-589 ◽  
Author(s):  
Jordan Hristov ◽  
Ganaoui El
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Boundary Conditions ◽  
Half Time ◽  
Thermal Impedance ◽  
Entire Domain ◽  
Various Boundary Conditions ◽  
Transient Thermal

Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances under various boundary conditions imposed at the interface (x=0). The approach is purely analytic and very effective because it uses only simple semi-derivatives (half-time) and semi-integrals and avoids development of entire domain solutions. 0x=

scholarly journals Thermal impedance at the interface of contacting bodies: 1-D examples solved by semi-derivatives

2012 ◽  
Vol 16 (2) ◽  
pp. 623-627 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Half Time ◽  
Thermal Impedance ◽  
Entire Domain ◽  
Transient Thermal ◽  
Two Bodies

Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances of two bodies with different initial temperatures contacting at the interface ( x = 0 ) at t = 0 . The approach is purely analytic and uses only semi-derivatives (half-time) and semi-integrals in the Riemann-Liouville sense. The example solved clearly reveals that the fractional calculus is more effective in calculation the thermal resistances than the entire domain solutions.

Determination of the stress concentration in the corner point of the wedge-shaped region reinforced by a more rigid thin coating

2020 ◽  
Vol 26 (1) ◽  
pp. 80-89
Author(s):  
AN Soloviev ◽  
BV Sobol ◽  
EV Rashidova ◽  
AI Novikova
Keyword(s):  
Boundary Conditions ◽  
Corner Point ◽  
Theory Of Elasticity ◽  
The Other ◽  
Thin Coating ◽  
Various Boundary Conditions ◽  
Singular Behaviour ◽  
Isotropic Theory ◽  
Made In

We analysed the problem of determining the exponents in the asymptotic solution of the isotropic theory of elasticity problem at the top of the wedge-shaped region where its sides (or one of them) are supported by a thin coating and lean without friction on the rigid bases. On the other side of the wedge-shaped region, it is assumed that there are various boundary conditions, including when there is a thin coating. Mathematically, the problem reduces to the problem of determining the roots of transcendental characteristic equations arising from the condition for the existence of a nontrivial solution of a system of the linear homogeneous equations. The characteristics of the stress tensor components have been determined for the various combinations of boundary conditions and physical and geometric parameters. The qualitative conclusions are made. In particular, we have established the combinations of the values of these parameters at which the singular behaviour of stresses arises.

Two-Dimensional Transient Thermal Behavior of Work Rolls in Rolling Process

1998 ◽  
Vol 120 (1) ◽  
pp. 28-33 ◽  
Author(s):  
Remn-Min Guo
Keyword(s):  
Boundary Conditions ◽  
Complete Solution ◽  
Work Roll ◽  
Rolling Process ◽  
Related Individual ◽  
Various Boundary Conditions ◽  
Cooling Behavior ◽  
Friction Energy ◽  
Transient Thermal ◽  
Work Rolls

In the rolling process, deformation and friction energy generated in the roll bite transfer to work rolls. Work rolls are cooled by the cooling medium in both entry and exit sides of the mill. The transient cooling behavior of the roll affects the temperature distribution and the thermal profile. This article proposes a semi-analytical solution to solve the temperature field of the work roll which is subjected to various cooling and heating boundary conditions during a rolling campaign. Laplace and inverse transforms are applied to pursue the unsteady solution for one particular boundary condition. The complete solution for various boundary conditions is superimposed by related individual solutions using Duhamel’s rule. Case studies as demonstrated in this paper show versatility of the developed model.

scholarly journals THE PROCESS OF HEAT TRANSFER IN TWO-LAYERED CYLINDRICAL BODY

2019 ◽  
Vol 20 (11-12) ◽  
pp. 93-98
Author(s):  
U. V. Vidin ◽  
R. V. Kazakov ◽  
V. S. Zlobin
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Analytical Method ◽  
Analytical Methods ◽  
Cylindrical Body ◽  
Characteristic Equations ◽  
The Third ◽  
Thermal Regimes

Determination of thermal regimes of composite cylindrical bodies by analytical methods leads to the appearance of complex characteristic equations, the solution of which is the determination of eigenvalues. The article considers a relatively simple approximate analytical method for determining the eigenvalues of characteristic equations for a two-layer cylindrical body under boundary conditions of the third kind. This method can also be easily used in more complex formulations of heat conduction problems.

A study of the diffusion analogy technique for the photoelastic determination of transient thermal stresses

1988 ◽  
Vol 23 (1) ◽  
pp. 33-45
Author(s):  
P Stanley ◽  
Y J Yip
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Isotropic Material ◽  
Heat Conduction Equation ◽  
Thermal Stresses ◽  
Conduction Equation ◽  
Formal Similarity ◽  
Photoelastic Study ◽  
Transient Thermal

The formal similarity between the equation governing the diffusion of a substance through a “porous” isotropic material and the heat conduction equation for the temperature distribution in an isotropic homogeneous solid is examined, and its use as a basis for the photoelastic study of transient thermal stresses is explored.

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