The non-stationary temperature field of the fracturing fluid during the propagation of planar 3D hydraulic crack

2020 ◽  
Author(s):  
Mikhail B. Babenkov ◽  
Egor B. Starobinskii
Keyword(s):  
Temperature Field ◽  
Fracturing Fluid ◽  
Stationary Temperature Field

scholarly journals Analytical study of the non-stationary temperature field of a thermally thin plate

2021 ◽  
Vol 1155 (1) ◽  
pp. 012007
Author(s):  
I I Latypov ◽  
L A Bigaeva ◽  
G S Mukhametshina ◽  
N A Shaikhutdinova ◽  
A Y Gilev
Keyword(s):  
Temperature Field ◽  
Thin Plate ◽  
Analytical Study ◽  
Stationary Temperature Field

scholarly journals NUMERICAL MODELING OF GAS TURBINE COOLED BLADES

Aviation ◽  
2005 ◽  
Vol 9 (3) ◽  
pp. 9-18
Author(s):  
Arif Pashayev ◽  
Djakhangir Askerov ◽  
Ramiz Ali Cabar oqlu Sadiqov
Keyword(s):  
Numerical Modeling ◽  
Temperature Field ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Gas Turbine ◽  
Point Of View ◽  
Theoretical Substantiation ◽  
Stationary Temperature Field ◽  
Methods Of Calculation ◽  
Effective Combination

In contrast to methods that do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasi‐stationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A. Ziqmound continuity modules have been received.

HEAT TRANSFER INVESTIGATION FOR A MULTILAYER INSULATION SYSTEM VIA RADIATIVE-CONDUCTIVE APPROACH UNDER LOW TEMPERATURE CONDITIONS IN SPACE

2020 ◽  
Vol 19 (2) ◽  
pp. 70
Author(s):  
G. N. Lacerda ◽  
M. F. Curi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Temperature Field ◽  
Insulation System ◽  
Final Temperature ◽  
Space Applications ◽  
Conduction Heat Transfer ◽  
Stationary Temperature Field ◽  
Layer Density ◽  
Multilayer Insulation

Thermal insulation is an important area, not restricted to mechanical engineering, but widely studied in environmentalissues, such as global warming and, above all, energy-saving, since controlling the heat flux on microprocessorsthrough temperature control on components in space applications. This work focuses on controlling the temperature incomponents that could not lose or gain so much heat in space, especiallywhen the overall safety of sending satellites onspecific missions is required. To ensure that, Multilayer Insulation (MLI) is used. With fluid mechanics and radiation-conductionheat transfer theory, it was possible to calculate the transient and stationary temperature field and heat flux inMLI. The boundary temperatures are specified at 300K and 4K. The results, from solving the resulting discretized ODE,simulated with fsolve and odeintScipy subroutines in Python, able to solve the equations numerically, were shown. Thedata given by the simulation was able to indicate the impacts of varying the layer density, emissivity of screen, the distancebetween screens and the perforation coefficient in stationary and transient approaches. A way to simulate the performanceof MLI numerically was presented. Modifying emissivity (e) showed variations higher than in the perforation coefficient(ξ). Layer density controls the distance between layers (d ), changing the conduction heat transfer. In the transient casesimulation, it was possible to notice that varying parameters impact in time to reach steady-state and final temperature.

scholarly journals DETERMINATION OF THE NON-STATIONARY TEMPERATURE FIELD IN THE SYSTEM OF TWO CYLINDRICAL SHELL UNDER THE FIRE CONDITIONS

Fire Safety ◽  
2019 ◽  
pp. 84-90
Author(s):  
R. M. Tatsii ◽  
O. Y. Pazen ◽  
L. S. Shypot
Keyword(s):  
Boundary Condition ◽  
Cylindrical Shell ◽  
Temperature Field ◽  
Original Problem ◽  
Auxiliary Problem ◽  
Technical Problem ◽  
Small Radius ◽  
Steel Shell ◽  
Solid Cylinder ◽  
Stationary Temperature Field

The proposed work is devoted to the application of the direct method to the study of heat transfer processes in the system "solid cylinder inside a cylindrical shell". It is assumed that there is an ideal thermal contact between them, and the law of changing the ambient temperature, which rinses the surface of the structure, is an arbitrary function of time, and evenly distributed over the surface. Consequently, isotherms inside this construction are concentric circles, that is, the problem is symmetric and is solved for the first time in such a statement. To solve such a problem, the auxiliary problem of determining the distribution of a non-stationary temperature field in a two-layer hollow cylindrical structure with a "withdrawn" cylinder of sufficiently small radius is raised in parallel. In this case the symmetry condition of the original problem is replaced by the condition of the second kind on the inner surface of this construction. The implementation of the solution of the auxiliary problem is carried out by applying a reduction method using the concept of quasi-derivatives. In the future, the Fourier scheme is used with the use of the modified eigenfunctions method. To find the solution of the original problem, the idea of the boundary transition is used by passing the radius of the withdrawn cylinder to zero. It is established that in this approach all the eigenfunctions of the corresponding problem on the eigenvalues have no singularities at zero, which means that the solutions of the original problem are constrained throughout the design. In order to illustrate the proposed method, a model example of finding the temperature field distribution in a column of a circular cross-section (concrete in a steel shell) is solved under the influence of the standard temperature regime of the fire. The results of the calculations are presented in a bulk schedule of temperature changes, depending on time and spatial coordinates. The generalization of the results obtained in the case of any finite number of cylindrical shells is a purely technical problem, and not a fundamental one. Note that while changing the boundary condition of the third kind to any other boundary condition (for example, the first kind) does not affect the scheme of solving similar tasks. Since the general scheme of studying the distribution of temperature fields in multi-layered structures with an arbitrary number of layers in the presence of internal sources of heat is studied in detail, the setting and solving of such problems for the system of "solid cylinder inside a cylindrical shell" is not without difficulty.

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