scholarly journals NONSTATIONARY HEAT CONDUCTION IN MULTILAYER GLAZING SUBJECTED TO DISTRIBUTED HEAT SOURCES

2020 ◽  
Vol 10 (2) ◽  
pp. 28-31
Author(s):  
Natalia Smetankina ◽  
Oleksii Postnyi
Keyword(s):  
Heat Conduction ◽  
Laplace Transformation ◽  
Heat Conduction Equation ◽  
Constant Thickness ◽  
Heat Sources ◽  
Nonstationary Heat Conduction ◽  
Multilayer Plate ◽  
Expansion Theorem ◽  
Thermal Fields ◽  
Transformation Series

A method for calculation of nonstationary thermal fields in a multilayer glazing of vehicles under the effect of impulse film heat sources is offered. The glazing is considered as a rectangular multilayer plate made up of isotropic layers with constant thickness. Film heat sources are arranged on layers' interfaces. The heat conduction equation is solved using the Laplace transformation, series expansion and the second expansion theorem. The method offered can be used for designing a safe multilayer glazing under operational and emergency thermal and force loading in vehicles.

scholarly journals Calculation of Temperature Fields in Multilayer Plates and Shells with Distributed Heat Sources

2019 ◽  
pp. 75-77
Author(s):  
Natalia Smetankina ◽  
Oleksii Postnyi
Keyword(s):  
Heat Transfer ◽  
Functional Equation ◽  
Heat Conduction Equation ◽  
Side Surface ◽  
Temperature Fields ◽  
Heat Sources ◽  
Multilayer Plate ◽  
Expansion Theorem ◽  
Plates And Shells ◽  
Three Space

The aircraft multilayer glazing is considered as arectangular multilayer plate made up of isotropic layers withconstant thickness. The temperature on the side surface of theplate is zero. Convective heat transfer occurs on outer surfaces ofthe plate; on layers' interfaces film heat sources are arranged.The heat conduction equation for an arbitrary plate layer isreduced to the functional equation. A solution of the functionalequation we search in the form of three space functions product.We get the system of ordinary differential equations. Seriesexpansion factors are determined from a system of linearalgebraic equations. A transform of the required function isfound by the second expansion theorem, and the problemsolution has the form of double trigonometrical series.The comparative analysis of the results is carried out with theresults of other method. The method offered can be used fordesigning a safe multilayer glazing under operational andemergency thermal and force loading in different vehicles.

scholarly journals Construction and investigation of new numerical algorithms for the heat equation : Part 2

2020 ◽  
Vol 10 (4) ◽  
pp. 339-348
Author(s):  
Mahmoud Saleh ◽  
Ádám Nagy ◽  
Endre Kovács
Keyword(s):  
Heat Conduction ◽  
Numerical Methods ◽  
Heat Conduction Equation ◽  
Space Dimension ◽  
Numerical Test ◽  
Numerical Algorithms ◽  
Heat Conducting ◽  
Heat Sources ◽  
Test Results ◽  
New Algorithms

This paper is the second part of a paper-series in which we create and examine new numerical methods for solving the heat conduction equation. Now we present numerical test results of the new algorithms which have been constructed using the known, but non-conventional UPFD and odd-even hopscotch methods in Part 1. Here all studied systems have one space dimension and the physical properties of the heat conducting media are uniform. We also examine different possibilities of treating heat sources.

INTEGRAL METHOD OF SOLVING HEAT-CONDUCTION PROBLEMS WITH THE SECOND-KIND BOUNDARY CONDITION. 1. BASIC STATEMENTS

2018 ◽  
Vol 63 (2) ◽  
pp. 201-213 ◽  
Author(s):  
V. A. Kot
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Boundary Value ◽  
Integral Operators ◽  
Heating Process ◽  
Nonstationary Heat Conduction ◽  
Integral Boundary ◽  
Boundary Characteristics ◽  
Two Stages

On the basis of systems of identical equalities and integral boundary characteristics, a new algorithm of solving a boundary-value problem on the nonstationary heat conduction in a canonical body with boundary condition of the second kind has been developed. The scheme proposed for finding approximate analytical solutions of boundary-value problems on nonstationary heat conduction with boundary conditions of the second kind involves the introduction into consideration of a temperature-disturbance front and separation of the whole heating process into two stages. For the first stage of this process, on the basis of the differentiation of the heat-conduction equation over a space variable and the application of symmetric integral and differential operators to the expressions obtained, two sequences of integral and differential identical equalities have been constructed. Each of these sequences includes integral or differential limiting characteristics for a definite boundary condition of the second kind. For the second stage, by way of introduction of a boundary function, differentiation of the heat-conduction equation with respect to a spatial coordinate, and application of integral operators to the expression obtained, a sequence of integral identical equalities involving integral boundary characteristics for the second-kind boundary condition has been constructed. On the basis of the integral and differential identical equalities obtained, closed systems of equations, allowing one to find polynomial coefficients of the temperature profile for the first and second stages of the heating process, have been constructed. A general scheme of determining approximate eigenvalues of boundary-value problems with boundary conditions of the second kind on the basis of construction of an ordinary differential equation and transformation of it into the characteristic equation is proposed. For each of the two stages of the heating process, special integral operators, reducing the boundary-value heat-conduction problem to the ordinary differential equation, are proposed.

Nonstationary Heat Conduction in Complex-Shape Laminated Plates

2006 ◽  
Vol 129 (3) ◽  
pp. 335-341 ◽  
Author(s):  
Alexander N. Shupikov ◽  
Natalia V. Smetankina ◽  
Yevgeny V. Svet
Keyword(s):  
Heat Conduction ◽  
Convective Heat Exchange ◽  
Laminated Plates ◽  
Temperature Fields ◽  
Nonstationary Heat ◽  
Heat Sources ◽  
Nonstationary Heat Conduction ◽  
Immersion Method ◽  
Heating Systems ◽  
Plate Plane

Based on the immersion method, an analytical solution has been obtained for the problem of nonstationary heat conduction in laminated plates of complex plan shape when they are heated with interlayer film heat sources. The temperature distribution over the thickness of each layer is represented in the form of an expansion in a system of the orthonormal Legendre polynomials and, in the plate plane, it is represented as trigonometric series expansions. Temperature fields were investigated in a five-layer plate for conditions of convective heat exchange with the environment. The method suggested can be applied for designing heating systems and determining temperature stresses in laminated glazing for different vehicles

Error Estimates for the Finite Difference Solution of the Heat Conduction Equation: Consideration of Boundary Conditions and Heat Sources

2013 ◽  
Vol 336 ◽  
pp. 195-207
Author(s):  
Mohammad Mahdi Davoudi ◽  
Andreas Öchsner
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Heat Conduction Equation ◽  
Exact Result ◽  
Numerical Approach ◽  
Conduction Equation ◽  
Heat Sources ◽  
Numerical Implementation ◽  
Dependent Sources

This contribution investigates the numerical solution of the steady-state heat conduction equation. The finite difference method is applied to simple formulations of heat sources where still analytical solutions can be derived. Thus, the results of the numerical approach can be related to the exact solutions and conclusions on the accuracy obtained. In addition, the numerical implementation of different forms of boundary conditions, i.e. temperature and flux condition, is compared to the exact solution. It is found that the numerical implementation of coordinate dependent sources gives the exact result while temperature dependent sources are only approximately represented. Furthermore, the implementation of the mentioned boundary conditions gives the same results as the analytical reference solution.

Thermoelastic response of a one-dimensional semi-infinite rod heated by a moving laser pulse

2016 ◽  
Vol 94 (10) ◽  
pp. 953-959 ◽  
Author(s):  
Yuxin Sun ◽  
Jingxuan Ma ◽  
Xin Wang ◽  
Ai Kah Soh ◽  
Jialing Yang
Keyword(s):  
Heat Conduction ◽  
Laser Pulse ◽  
Laplace Transformation ◽  
Heat Conduction Equation ◽  
Axial Direction ◽  
Transformation Method ◽  
Governing Equations ◽  
One Dimensional ◽  
Thermoelastic Response ◽  
Laplace Transformation Method

In the present study, thermoelastic behavior of a semi-infinite rod, which is subjected to a time exponentially decaying laser pulse, is formulated. The rod is free at the left end and the laser pulse moves along the axial direction from the left end. The non-Fourier effect of the heat conduction equation is considered and the Laplace transformation method is employed in solving the governing equations. The temperature, displacement, strain, and stress in the rod are derived and the distributions of the parameters at different positions are analyzed. Also the influence of the laser speed is investigated.

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