scholarly journals Consideration of the nonlinear behavior of environmental material and a three-dimensional internal heat sources in mathematical modeling of heat conduction

2015 ◽  
Vol 2 (1) ◽  
pp. 107-113 ◽  
Author(s):  
L. Zhuravchak ◽  
◽  
O. Kruk ◽  
Keyword(s):  
Mathematical Modeling ◽  
Heat Conduction ◽  
Three Dimensional ◽  
Internal Heat ◽  
Nonlinear Behavior ◽  
Heat Sources ◽  
Environmental Material ◽  
Internal Heat Sources

scholarly journals A method for solving a boundary value problem in a multilayered area

2020 ◽  
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Boundary Value ◽  
Internal Heat ◽  
Electrical Machine ◽  
Problem Solution ◽  
Conductive Heat ◽  
Heat Sources ◽  
Internal Layers ◽  
Internal Heat Sources

A mathematical model of thermal process in an electrical machine was built as an example, presented as a three-layer cylinder where internal heat sources operate in one of the layers and heat is submitted to the other two by means of heat conduction. A method of solving the boundary-value problems for heat conduction equation in a complex area – a multi-layered cylinder with internal heat sources operating in one part of the layers and external ones in another part, is proposed. A method of problem solution in conditions of uncertainty of one of the boundary condition at the layers interface with conductive heat exchange between the layers is reviewed. The principle of method lies in the averaging of temperature distributions radially in the internal layers. As a result of transformations at the layers interface a boundary condition of the impedance-type conjugation appears. The analytical and numeric-analytical solutions of simplified problems were obtained.

scholarly journals Thermal constitutive matrix applied to asynchronous electrical machine using the cell method

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 27-30 ◽  
Author(s):  
Pablo Ignacio González Domínguez ◽  
José Miguel Monzón-Verona ◽  
Leopoldo Simón Rodríguez ◽  
Adrián de Pablo Sánchez
Keyword(s):  
Heat Conduction ◽  
Internal Heat ◽  
Conduction Equation ◽  
Equivalent Model ◽  
Electrical Machine ◽  
Heat Sources ◽  
Conduction Model ◽  
Cell Method ◽  
Internal Heat Sources ◽  
Constitutive Matrix

Abstract This work demonstrates the equivalence of two constitutive equations. One is used in Fourier’s law of the heat conduction equation, the other in electric conduction equation; both are based on the numerical Cell Method, using the Finite Formulation (FF-CM). A 3-D pure heat conduction model is proposed. The temperatures are in steady state and there are no internal heat sources. The obtained results are compared with an equivalent model developed using the Finite Elements Method (FEM). The particular case of 2-D was also studied. The errors produced are not significant at less than 0.2%. The number of nodes is the number of the unknowns and equations to resolve. There is no significant gain in precision with increasing density of the mesh.

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