scholarly journals Influence of extended heat sources on the temperature distribution in profiled polar-orthotropic annular plates with heat-insulated bases

2021 ◽  
pp. 99-104
Author(s):  
Uladzimir V. Karalevich ◽  
Dmitrij G. Medvedev
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Anisotropic Plate ◽  
Heat Conduction Problem ◽  
Heat Sources ◽  
Stationary Heat ◽  
Annular Plates ◽  
Outer Border ◽  
Stationary Heat Conduction ◽  
Polar Orthotropic

The solution of the stationary heat conduction problem for profiled polar-orthotropic annular plates with heat-insulated bases from N extended heat sources at their external border is presented. The temperature distribution in such plates will be non-axisymmetric. The solution of the stationary heat conduction problem for anisotropic annular plates of an random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conduction problem for polar-orthotropic annular plate of an exponential profile is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.

scholarly journals The influence of the length of heat sources on the external border on the temperature distribution in profiled polar-orthotropic ring plates taking into account there heat exchange with the external environment

2020 ◽  
pp. 86-91
Author(s):  
Uladzimir V. Karalevich ◽  
Dmitrij G. Medvedev
Keyword(s):  
Heat Exchange ◽  
Temperature Distribution ◽  
Heat Conduction Problem ◽  
External Environment ◽  
Heat Sources ◽  
Stationary Heat ◽  
Annular Plates ◽  
Outer Border ◽  
Polar Orthotropic ◽  
Account Heat

We study the influence of N extended heat sources at external boundaries on the nonaxisymmetric temperature distribution on profiled polar-orthotropic ring plates and take into account heat exchange with the external environment. The solution of the stationary heat conduction problem for anisotropic annular plates of a random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conductivity problem for a reverse conical polar-orthotropic ring plate is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.

scholarly journals The inverse stationary heat conduction problem for a cuboid

2016 ◽  
Vol 91 ◽  
pp. 01008
Author(s):  
Konstantin M. Yacenko ◽  
Yri Y. Rakov ◽  
Konstantin V. Slyusarskiy
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Stationary Heat ◽  
Stationary Heat Conduction

scholarly journals Determination of quasi-static thermoelastic state of layered thermosensitive plates

2019 ◽  
pp. 162-165
Author(s):  
B. V. Protsiuk
Keyword(s):  
Heat Conduction ◽  
Numerical Solutions ◽  
Heat Conduction Problem ◽  
Temperature Fields ◽  
Thermoelastic State ◽  
Algebraic Equations ◽  
Temperature Conductivity ◽  
Stationary Heat ◽  
Kirchhoff Transformation ◽  
Stationary Heat Conduction

The technique of determining the quasistatic thermoelastic state of the layered thermosensitive plates free of load is illustrated. Much attention is paid to finding analytical-numerical solutions of one-dimensional non-stationary heat conduction problems taking into account the temperature dependences of the thermal and temperature conductivity coefficients. Their finding involves use of the Kirchhoff transformation, generalized functions, Green's functions of the corresponding linear heat conduction problem, exact sums of the series, in particular those for which the Gibbs effect takes place, linear splines and solving the received recurrent systems of nonlinear algebraic equations relative to the values in the nodes of the spline of the Kirchhoff variable on the layer division surfaces and the derivative in time on inner flat-parallel surfaces of layers. The results of numerical calculations of temperature fields in two-layer plates with different thicknesses of layers and the external surface heated by a constant heat flux are presented. The accuracy of the found solution is investigated. The comparison of the temperature fields, which are determined assuming simple nonlinearity, stable thermophysical characteristics with the ones based on the exact solution of the corresponding nonlinear stationary heat conduction problem is fulfilled.

scholarly journals An Extended Analytical Solution of the Non-Stationary Heat Conduction Problem in Multi-Track Thick-Walled Products during the Additive Manufacturing Process

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7291
Author(s):  
Dmitrii Mukin ◽  
Ekaterina Valdaytseva ◽  
Gleb Turichin ◽  
Artur Vildanov
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Heat Conduction Problem ◽  
Deposition Process ◽  
Relative Difference ◽  
Temperature Fields ◽  
Transient Temperature ◽  
Stationary Heat ◽  
Direct Deposition ◽  
Stationary Heat Conduction

An analytical model has been developed for calculating three-dimensional transient temperature fields arising in the direct deposition process to study the thermal behavior of multi-track walls with various configurations. The model allows the calculation of all characteristics of the temperature fields (thermal cycles, cooling rates, temperature gradients) in the wall during the direct deposition process at any time. The solution of the non-stationary heat conduction equation for a moving heat source is used to determine the temperature field in the deposited wall, taking into account heat transfer to the environment. The method considers the size of the wall and the substrate, the change in power from layer to layer, the change in the cladding speed, the interpass dwell time (pause time), and the heat source trajectory. Experiments on the deposition of multi-track block samples are carried out, as a result of which the values of the temperatures are obtained at fixed points. The proposed model makes it possible to reproduce temperature fields at various values of the technological process parameters. It is confirmed by comparisons with experimental thermocouple data. The relative difference in the interlayer temperature does not exceed 15%.

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