The Mathematic Model and Method for Solving the Dirichlet Heat-Exchange Problem for Empty Isotropic Rotary Body

2018 ◽  
Vol 277 ◽  
pp. 168-177
Author(s):  
Mykhailo Berdnyk
Keyword(s):  
Temperature Field ◽  
Dirichlet Problem ◽  
Heat Exchange ◽  
Angular Velocity ◽  
Integral Transformation ◽  
Mathematic Model ◽  
Constant Angular Velocity ◽  
Temperature Fields ◽  
Finite Velocity ◽  
Finite Space

It is the first generalized 3D mathematic model, which is created for calculating temperature fields in the empty isotropic rotary body, which is restricted by end surfaces and lateral surface of rotation and rotates with constant angular velocity around the axis OZ, with taking into account finite velocity of the heat conductivity in the form of the Dirichlet problem. In this work, an integral transformation was formulated for the 2D finite space, with the help of which a temperature field in the empty isotropic rotary body was determined in the form of convergence series by the Fourier functions.

Mathematic Model and Method for Solving the Heat-Exchange Problem in Electron-Beam Welding of Arbitrary Areas

2019 ◽  
Vol 291 ◽  
pp. 173-182
Author(s):  
Mykhailo Berdnyk
Keyword(s):  
Electron Beam ◽  
Electron Beam Welding ◽  
Integral Transformation ◽  
Mathematic Model ◽  
Convergent Series ◽  
Dirichlet Boundary Conditions ◽  
Temperature Fields ◽  
The Finite Element Method ◽  
Finite Space ◽  
First Time

For the first time in this article, a mathematical model has been developed for calculating the temperature fields in arbitrary areas in electron-beam welding; this model was created in the form of a boundary value problem of mathematical physics for a parabolic equation of heat conductivity with Dirichlet boundary conditions. A new integral transformation was constructed for a two-dimensional finite space, with the use of which, as well as the finite element method and Galerkin's method, a temperature field has been determined in the form of a convergent series.

scholarly journals MATHEMATIC SIMULATION OF GENERALIZED PROBLEM OF HEAT-EXCHANGE IN THE BODIES WITH HEMISPHERICAL SHAPE

2019 ◽  
Vol 6 (125) ◽  
pp. 55-67
Author(s):  
Mykhailo Berdnyk
Keyword(s):  
Heat Conduction ◽  
Dirichlet Boundary ◽  
Integral Transformation ◽  
Dirichlet Boundary Conditions ◽  
Temperature Fields ◽  
Finite Velocity ◽  
Drilling Operations ◽  
Equation Of Heat Conduction ◽  
Finite Space ◽  
Drilling Bit

The article presents the first mathematical model for calculating temperature fields of hemispherical bodies, which approximately simulates operation of the diamond-drilling bit and takes into account angular velocity of drilling operations and finite velocity of heat conduction, and which was created as a physicomathematical boundary problem for hyperbolic equation of heat conduction with the Dirichlet boundary conditions. Besides, a new integral transformation was formulated for the two-dimensional finite space, with the help of which and with the help of finite element method and Galerkin method a temperature field was found in the form of convergence series.

scholarly journals MATHEMATIC MODEL OF AND METHOD FOR SOLVING THE DIRICHLET HEAT-EXCHANGE PROBLEM FOR ONE-SHEET ROTARY HYPERBOLOID

2020 ◽  
Vol 1 (126) ◽  
pp. 23-36
Author(s):  
Mykhailo Berdnyk
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Boundary Problem ◽  
Heat Conductivity ◽  
Integral Transformation ◽  
Mathematic Model ◽  
The Body ◽  
Initial Moment ◽  
Thin Wall ◽  
Conductivity Equation

It is the first generalized 3D mathematical model developed for calculating temperature fields in the thin-wall one-sheet rotary hyperboloid, which rotates with constant angular velocity around the axis OZ, ; the model was created with the help of known equations of generating lines in cylindrical coordinate system with taking into account finite velocity of heat conductivity and in the form of the Dirichlet boundary problem for the hyperbolic equation of heat conduction under condition that heat-conduction properties of the body were constant, and no internal sources of the heat were available. At initial moment of time, the body temperature was constant; values of temperature on outside surfaces of the body were known and presented continuous function of coordinate.The hyperbolic heat-conductivity equation was derived from the generalized energy transfer equation for the moving element of continuous medium with taking into account finiteness of the heat conductivity velocity.In order to solve the boundary problem, the desired temperature field was represented as a complex Fourier series. The obtained boundary problems for the Fourier coefficients were found with the help of Laplace integral transformations and the new integral transformation for two-dimensional finite space. Intrinsic values and intrinsic functions for the integral transformation kernel were found by method of finite element and the Galerkin methods. Besides, the domain was divided into simplex element.As a result, the temperature field in the thin-wall one-sheet rotary hyperboloid was found in the form of convergent series in Fourier functions.

The Effect of Regulating Elements on Convective Heat Transfer along Shaped Heat Exchange Surfaces

2013 ◽  
Vol 34 (1) ◽  
pp. 5-16 ◽  
Author(s):  
Jozef Cernecky ◽  
Jan Koniar ◽  
Zuzana Brodnianska
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Cfd Simulation ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Temperature Fields ◽  
Transfer Coefficients ◽  
Heat Transfer Intensification ◽  
Heat Transfer Coefficients ◽  
Forced Air

Abstract The paper deals with a study of the effect of regulating elements on local values of heat transfer coefficients along shaped heat exchange surfaces with forced air convection. The use of combined methods of heat transfer intensification, i.e. a combination of regulating elements with appropriately shaped heat exchange areas seems to be highly effective. The study focused on the analysis of local values of heat transfer coefficients in indicated cuts, in distances expressed as a ratio x/s for 0; 0.33; 0.66 and 1. As can be seen from our findings, in given conditions the regulating elements can increase the values of local heat transfer coefficients along shaped heat exchange surfaces. An optical method of holographic interferometry was used for the experimental research into temperature fields in the vicinity of heat exchange surfaces. The obtained values correspond very well with those of local heat transfer coefficients αx, recorded in a CFD simulation.

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

Numerical Analysis of Flow Fields and Temperature Fields in a Regenerative Heating Furnace for Steel Pipes

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Yi Han ◽  
Feng Liu ◽  
Xin Ran
Keyword(s):  
Temperature Field ◽  
Flow Field ◽  
Flow Velocity ◽  
Gas Flow ◽  
Flow Fields ◽  
Heating Furnace ◽  
Temperature Fields ◽  
Turbulent Layer ◽  
Steel Pipes ◽  
Pipe Blanks

In the production process of large-diameter seamless steel pipes, the blank heating quality before roll piercing has an important effect on whether subsequently conforming piping is produced. Obtaining accurate pipe blank heating temperature fields is the basis for establishing and optimizing a seamless pipe heating schedule. In this paper, the thermal process in a regenerative heating furnace was studied using fluent software, and the distribution laws of the flow field in the furnace and of the temperature field around the pipe blanks were obtained and verified experimentally. The heating furnace for pipe blanks was analyzed from multiple perspectives, including overall flow field, flow fields at different cross sections, and overall temperature field. It was found that the changeover process of the regenerative heating furnace caused the temperature in the upper part of the furnace to fluctuate. Under the pipe blanks, the gas flow was relatively thin, and the flow velocity was relatively low, facilitating the formation of a viscous turbulent layer and thereby inhibiting heat exchange around the pipe blanks. The mutual interference between the gas flow from burners and the return gas from the furnace tail flue led to different flow velocity directions at different positions, and such interference was relatively evident in the middle part of the furnace. A temperature “layering” phenomenon occurred between the upper and lower parts of the pipe blanks. The study in this paper has some significant usefulness for in-depth exploration of the characteristics of regenerative heating furnaces for steel pipes.

Method of Lines to Solve 2-D Steady Temperature Field of FGM

2007 ◽  
Vol 353-358 ◽  
pp. 2003-2006 ◽  
Author(s):  
Wei Tan ◽  
Chang Qing Sun ◽  
Chun Fang Xue ◽  
Yao Dai
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Transfer Problem ◽  
Method Of Lines ◽  
Main Idea ◽  
Functionally Graded ◽  
Temperature Fields ◽  
Steady Temperature ◽  
Thermal Transfer ◽  
Steady Temperature Field

Method of Lines (MOLs) is introduced to solve 2-Dimension steady temperature field of functionally graded materials (FGMs). The main idea of the method is to semi–discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs with functions of thermal properties. As numerical examples, six kinds of material thermal conductivity functions, i.e. three kinds of polynomial functions, an exponent function, a logarithmic function, and a sine function are selected to simulate spatial thermal conductivity profile in FGMs respectively. The steady-state temperature fields of 2-D thermal transfer problem are analyzed by the MOLs. Numerical results show that different material thermal conductivity function has obvious different effect on the temperature field.

scholarly journals Heat exchange between non-insulated barn and the ground in experimental research

2013 ◽  
Vol 12 (3) ◽  
pp. 035-038
Author(s):  
Wacław Bieda ◽  
Jan Radoń ◽  
Grzegorz Nawalany
Keyword(s):  
Heat Flux ◽  
Heat Exchange ◽  
Experimental Research ◽  
Operating Conditions ◽  
Temperature Fields ◽  
Final Conclusion

The paper presents the results of two-year studies conducted in real operating conditions of a non-insulated and unheated barn for 120 cows. As a result, it was possible to determine temperature fields in the ground beneath the floor and around the building, as well as to define heat flux directions. It was concluded that there is no analogy between temperature fields and heat flux directions with the heated buildings. In colder periods of the year, the heat accumulated in the ground is emitted to the inside of the building; in the summer, the ground absorbs the excess of heat from the building. The final conclusion was that the foundations should be insulated vertically.

scholarly journals A Method for Reconstruction of Boiler Combustion Temperature Field Based on Acoustic Tomography

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yuhui Wu ◽  
Xinzhi Zhou ◽  
Li Zhao ◽  
Chenlong Dong ◽  
Hailin Wang
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Optimal Parameter ◽  
Interpolation Method ◽  
Least Square Method ◽  
Reconstruction Algorithm ◽  
Least Square ◽  
Temperature Fields ◽  
Acoustic Tomography ◽  
Measured Temperature

Acoustic tomography (AT), as a noninvasive temperature measurement method, can achieve temperature field measurement in harsh environments. In order to achieve the measurement of the temperature distribution in the furnace and improve the accuracy of AT reconstruction, a temperature field reconstruction algorithm based on the radial basis function (RBF) interpolation method optimized by the evaluation function (EF-RBFI for short) is proposed. Based on a small amount of temperature data obtained by the least square method (LSM), the RBF is used for interpolation. And, the functional relationship between the parameter of RBF and the root-mean-square (RMS) error of the reconstruction results is established in this paper, which serves as the objective function for the effect evaluation, so as to determine the optimal parameter of RBF. The detailed temperature description of the entire measured temperature field is finally established. Through the reconstruction of three different types of temperature fields provided by Dongfang Boiler Works, the results and error analysis show that the EF-RBFI algorithm can describe the temperature distribution information of the measured combustion area globally and is able to reconstruct the temperature field with high precision.

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