Mathematical model of heat transfer in opening electrical contacts with tunnel effect

The mathematical model describing the dynamics of heating in opening electrical contacts is presented. It takes into account the imperfect thermal contact between anode and cathode due to tunnel effect. The model is based on the system of spherical heat equations in a domain with moving boundary. The analytical solution is found in the form of series containing the integral error functions.

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Systems Actuated by Shape Memory Alloys: Identification and Modeling

SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL ◽

10.52846/stccj.2021.1.2.20 ◽

2021 ◽

Vol 1 (2) ◽

pp. 12-20

Author(s):

Najmeh Keshtkar ◽

Johannes Mersch ◽

Konrad Katzer ◽

Felix Lohse ◽

Lars Natkowski ◽

...

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Constitutive Model ◽

Shape Memory Alloys ◽

Numerical Simulations ◽

Shape Memory ◽

Transfer Equation ◽

Mechanical Parameters ◽

Heat Transfer Equation ◽

The Mathematical Model

This paper presents the identification of thermal and mechanical parameters of shape memory alloys by using the heat transfer equation and a constitutive model. The identified parameters are then used to describe the mathematical model of a fiber-elastomer composite embedded with shape memory alloys. To verify the validity of the obtained equations, numerical simulations of the SMA temperature and composite bending are carried out and compared with the experimental results.

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Development of condenser mathematical model for research and development of ways to improve its efficiency

Istrazivanja i projektovanja za privredu ◽

10.5937/jaes0-27517 ◽

2020 ◽

Vol 18 (4) ◽

pp. 578-585

Author(s):

Madina Shavdinova ◽

Konstantin Aronson ◽

Nina Borissova

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Water Temperature ◽

Steam Turbine ◽

Cooling Water ◽

Laboratory Research ◽

Thermal Engineering ◽

Linear Regression Method ◽

Cooling Water Temperature ◽

The Mathematical Model

The condensing unit is one of the most important elements of the steam turbine of a combined heat and power plant. Defects in elements of the condensing unit lead to disturbances in the steam turbine operation, its failures and breakdowns, as well as efficiency losses of the plant. Therefore, the operating personnel need to know the cause of the malfunction and to correct it immediately. There are no diagnostic models of condensers in the Republic of Kazakhstan at the moment. In this regard, a mathematical model of a condenser based on the methodology of Kaluga Turbine Plant (KTP) has been developed. The mathematical model makes it possible to change the input parameters, plot dependency diagrams, and calculate the plant efficiency indicators. The mathematical model of the condenser can be used to research ways for the improvement of the condensing unit efficiency, for diagnostic purposes of the equipment condition, for the energy audit conduction of the plant, and in the training when performing virtual laboratory research. Using static data processing by linear regression method we obtain that the KTP methodology of condenser calculation is fair at cooling water temperature from 20 °C to 24 °C, but at cooling water temperature from 20 °C to 28 °C, the methodology of JSC "All-Russia Thermal Engineering Institute" (JSC "VTI") is used. One of the ways to increase the condenser efficiency has been proposed. It is the heat transfer augmentation with riffling annular grooves on tubes. This method increases the heat transfer coefficient by 2%, reduces the water subcooling of the heating steam by 0.9 °C, and decreases the cooling area by 2%.

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A Mathematical Model of Epidemics—A Tutorial for Students

Mathematics ◽

10.3390/math8071174 ◽

2020 ◽

Vol 8 (7) ◽

pp. 1174 ◽

Cited By ~ 2

Author(s):

Yutaka Okabe ◽

Akira Shudo

Keyword(s):

Mathematical Model ◽

Analytical Solution ◽

Analytical Solutions ◽

Sir Model ◽

Exact Analytical Solutions ◽

The Mathematical Model ◽

Epidemic Diseases

This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

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Parametric Study of Temperature Field During the Cooling Stage for Extrusion Blow Molded Part

Heat Transfer, Part B ◽

10.1115/imece2005-80373 ◽

2005 ◽

Author(s):

Zhan-Song Yin ◽

Hon-Xiong Huang

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Internal Heat ◽

Mold Material ◽

Orthogonal Experimental Design ◽

Ann Model ◽

Molded Part ◽

Artificial Neural Network Ann ◽

The Mathematical Model ◽

Part Thickness

A mathematical model of the transient heat transfer during the cooling and solidification of extrusion blow molded part was developed. The temperature profiles were obtained by using finite element (FE) code POLYFLOW to solve the mathematical model. The influences of blow mold material, internal heat transfer coefficient, part thickness, and initial parison temperature on cooling were analyzed. An orthogonal experimental design was applied to determine the significance of four process parameters on the time for opening the mold. The calculated results were estimated by analysis of variance (ANVOA). An artificial neural network (ANN) model based on the numerical simulation data was developed to build for predicting the temperature distribution across thickness. The results showed that ANN approach was an effective method for analyzing the cooling of blow molded part.

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Heat Convection from a Horizontal Cylinder Rotating in a Quiescent Fluid

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1986-0017 ◽

1986 ◽

Vol 10 (3) ◽

pp. 141-152

Author(s):

H.M. Badr ◽

S.M. Ahmed

Keyword(s):

Heat Transfer ◽

Experimental Data ◽

Mathematical Model ◽

Horizontal Cylinder ◽

Heat Transfer Process ◽

Two Dimensional ◽

Two Dimensional Flow ◽

Boussinesq Fluid ◽

The Mathematical Model ◽

Quiescent Fluid

The aim of this work is a theoretical investigation to the problem of heat transfer from an isothermal horizontal cylinder rotating in a quiescent fluid. The study is based on the solution of the conservation equations of mass, momentum and energy for two-dimensional flow of a Boussinesq fluid. The effects of the parameters which influence the heat transfer process namely the Reynolds number and Grashof number are considered while the Prandtl number is held constant. Streamline and isotherm patterns are obtained from the mathematical model and the results are compared with previous experimental data. A satisfactory agreement was found.

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Experimental Research on Performance of Heat Transfer and Pressure Drop for Primary Surface Recuperator With Mini Channels

ASME 2011 Power Conference, Volume 2 ◽

10.1115/power2011-55437 ◽

2011 ◽

Author(s):

Hugen Ma ◽

Hui Gao ◽

Wenjing Tu

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Pressure Drop ◽

Experimental Research ◽

Transfer Factor ◽

Flow And Heat Transfer ◽

Good Consistency ◽

Mini Channels ◽

Performance Of Heat Transfer ◽

The Mathematical Model

Based on the single blow technique, experimental research was conducted for the performance of heat transfer and flow drop for six test cores with cross corrugated (CC) or corrugated undulated (CU) primary surfaces for different geometries. After the mathematical model was established for heat transfer under the condition of single blow, a matching numerical solution was obtained for different NTU. The correlations of hear transfer factor j and friction factor f were obtained for three types of cross corrugated primary surfaces (crossed angle 45∼75°) with a range of Re = 120∼800 and three types of corrugated undulated primary surfaces (crossed angle 52.5∼67.5°) with a range of Re = 200∼1200. Hydraulic diameters of all heat transfer surfaces are from 1.2∼1.48mm. Analysis on the flow and heat transfer for cross corrugated and corrugated undulated primary surfaces was made based on the comprehensive evaluating factor j/f. The experimental results were compared to references with good consistency. The regressive errors of correlations were less than 16%.

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Torus-Like Balloons

Journal of Geometry and Symmetry in Physics ◽

10.7546/jgsp-56-2020-59-65 ◽

2020 ◽

Vol 56 ◽

pp. 59-65

Author(s):

Ivïalo M. Mladenov ◽

Keyword(s):

Mathematical Model ◽

Analytical Solution ◽

Elliptic Integrals ◽

Deployable Structures ◽

The Future ◽

The Mathematical Model

The concepts for inflatable deployable structures have been under development and evaluation for many years. Strangely enough only the Mylar balloon up to now has been described adequately. Here we provide the mathematical model and its analytical solution for the torus-like balloons. Their characteristics and shapes are described explicitly in terms of elliptic integrals. The obtained results are commented shortly and the possible directions for the related studies in the future are outlined.

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Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

Prosiding SNFA (Seminar Nasional Fisika dan Aplikasinya) ◽

10.20961/prosidingsnfa.v1i0.4528 ◽

2017 ◽

Vol 1 ◽

pp. 114

Author(s):

Imam Basuki ◽

C Cari ◽

A Suparmi

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Heat Conduction ◽

Partial Differential Equations ◽

Finite Difference ◽

Finite Difference Method ◽

Numerical Solution ◽

Difference Method ◽

The Finite Difference Method ◽

The Mathematical Model

Abstract: Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β Keywords: heat transfer, triangle coordinates system. Abstrak Persamaan Diferensial Parsial (PDP) Laplace dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut dan Kata kunci : perpindahan panas, sistem koordinat segitiga.

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Modeling of additive height and numerical analysis of cooling parameters for aero blade remanufacturing

Mechanical Sciences ◽

10.5194/ms-12-803-2021 ◽

2021 ◽

Vol 12 (2) ◽

pp. 803-818

Author(s):

Miao Gong ◽

Shijie Dai ◽

Tao Wang ◽

Liwen Wang

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Numerical Analysis ◽

Cooling Effect ◽

Transfer Model ◽

Factors Affecting ◽

Coupled Heat Transfer ◽

Blade Repair ◽

Geometric Morphology ◽

The Mathematical Model

Abstract. Additive remanufacturing height and matching cooling parameters are the key factors affecting blade repair quality. First, the mathematical model of the single additive remanufacturing repair height and wire-feeding speed was established, the solution method was proposed and the numerical solution was obtained, and the validity of the model was verified by experiments. Then, based on the calculation results of a single additive remanufacturing repair, the geometric morphology of the cross section under double additive remanufacturing repair was analyzed, and the mathematical model was established. Second, based on the optimal parameters obtained by numerical analysis and the mathematical model, the fluid structure coupling heat transfer model of “blade fixture” for base channel cooling was established. The cooling effect of the typical section under different initial temperatures and different flow rates was calculated, and the coupled heat transfer in the process of blade remanufacturing was explained by the mechanism. Third, through the comparative analysis of the cooling effect, optimal cooling parameters of double additive remanufacturing repair were obtained, and the model of coupled heat flow was verified by experiment. The results showed that the mathematical model of additive remanufacturing height is effective for studying the thermal cycle and cooling effect of welding, and the cooling parameters obtained by numerical analysis can effectively guarantee the quality of double additive remanufacturing of blade repair.

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Inverse Approach Using Bio-Inspired Algorithm Within Bayesian Framework for the Estimation of Heat Transfer Coefficients During Solidification of Casting

Journal of Heat Transfer ◽

10.1115/1.4045134 ◽

2019 ◽

Vol 142 (1) ◽

Cited By ~ 1

Author(s):

P. S. Vishweshwara ◽

N. Gnanasekaran ◽

M. Arun

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Initial Conditions ◽

Bayesian Framework ◽

Simultaneous Estimation ◽

Unknown Parameters ◽

Single Experiment ◽

Inverse Approach ◽

Solidification Problem ◽

The Mathematical Model

Abstract In any parameter estimation problem, it is desirable to obtain more information in one single experiment. However, it is difficult to achieve multiple objectives in one single experiment. The work presented in this paper is the simultaneous estimation of heat transfer coefficient parameters, latent heat, and modeling error during the solidification of Al–4.5 wt %Cu alloy with the aid of Bayesian framework as an objective function that harmoniously matches the mathematical model and measurements. A 1D transient solidification problem is considered to be the mathematical model/forward model and numerically solved to obtain temperature distribution for the known boundary and initial conditions. Genetic algorithm (GA) and particle swarm optimization (PSO) are used as an inverse approach and the estimation of unknown parameters is accomplished for both pure and noisy temperature data. The use of Bayesian framework for the estimation of unknown parameters not only provides the information about the uncertainties associated with the estimates but also there is an inherent regularization term in which the inverse problem boils down to well-posed problem thereby plethora of information is extracted with less number of measurements. Finally, the results of this work open up new prospects for the solidification problem so as to obtain a feasible solution with the present approach.

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