# Tag Archives: mathematical modelling

xxx B. Kulishov, D. Minkin, A. Fedorov and A. Novoselov
Development of the mathematical model of the electric resistance baking process
Abstract |

# Development of the mathematical model of the electric resistance baking process

B. Kulishov¹*, D. Minkin², A. Fedorov¹ and A. Novoselov¹

¹ITMO University, Saint Petersburg, Faculty of Food Biotechnologies and Engineering, School of Biotechnology and Cryogenic Systems, Kronverkskiy ave.49, RU197101 St. Petersburg, Russia
²Saint Petersburg University of State Fire Service of Emercom of Russia, Department of Physical and Technical Fundamentals of Fire Safety, Moskovskiy ave.149, RU 196105 St. Petersburg, Russia
*Correspondence: kulishov.b@list.ru

### Abstract:

The work is dedicated to the development of the mathematical model of the electric resistance baking process for the purpose of predicting temperature changes during baking of dough pieces of arbitrary sizes. The equation for the non-stationary thermal regime of a body with an internal heat source was used with a number of assumptions. The dynamics of the dough temperature changes was determined by numerical solution of the equation in Comsol Multiphysics.
Due to the complexity of the dough baking process and the impossibility of solving the equation by analytical method only, a number of values included in the energy balance of ER baking were determined experimentally. A dough piece with dimensions of 100×50×80 mm was baked during the experiment. After the adjustment, the adequacy of the model was checked by comparing the data on the dough temperature changes during baking dough pieces of the same recipe, but of different sizes (150×49×80, 80×62×80, and 65×75×80). Statistical analysis using Fisher’s criterion confirmed the adequacy of the model.

### Key words:

1227–1234 I. Tipans, J. Viba, M. Irbe and S.K. Vutukuru
Analysis of non-stationary flow interaction with simple form objects
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# Analysis of non-stationary flow interaction with simple form objects

I. Tipans, J. Viba, M. Irbe and S.K. Vutukuru*

Riga Technical University, Faculty of Mechanical Engineering, Transport and Aeronautics, Department of Theoretical Mechanics and Strength of Materials, Viskalu Street 36A, LV – 1006, Riga, Latvia
*Correspondence: vshravankoundinya1989@gmail.com

### Abstract:

The paper is devoted to the analysis of a non-stationary rigid body interaction in a fluid flow. Initially, an approximate method for determining the forces due to fluid interaction with the rigid body is offered. For this purpose, the plane movement of a mechanical system with an infinite DOF (degrees of freedom) is reduced to 5 DOF motion: 3 DOF for the body and 2 DOF for the areas of compression and vacuum in fluid flow. Differential equations of non-stationary motion are formed by the laws of classical mechanics. The use of an approximate method has been quantified by computer modelling. The average difference in results was found to be small (< 5%). The analysis of the fluid (air) interaction is carried out for a rigid body of two simple geometries – flat plate and diamond. The results obtained are used to refine the parameters of the proposed approximate method that is addressed in the present study for fluid interaction with the non-stationary rigid body. Theoretical results obtained in the final section are used in the analysis of the movement of prismatic bodies in order to obtain energy from the fluid flow.

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1127–1140 D. Novák,, P. Kvasnová, J. Volf and V. Novák
Measurement of weld joint parameters and their mathematical modelling
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# Measurement of weld joint parameters and their mathematical modelling

D. Novák¹,*, P. Kvasnová¹, J. Volf² and V. Novák²

¹ Matej Bel University, Faculty of Natural Sciences, Department of Technology, Tajovského 40, SK974 01 Banská Bystrica, Slovakia
² Czech University of Life Sciences Prague, Faculty of Engineering, Kamýcká 129, CZ165 21 Prague, Czech Republic
*Correspondence: daniel.novak@umb.sk

### Abstract:

The article deals with verifying of weld quality of weld joints created by laser beam welding technology, primarily in agricultural components such as reel screws. We presents both metallographic check of the weld structure using electron microscopy, RTG-microanalysis and micro hardness measurement as well as used mathematical models of the welding process and respective weld joints geometry.
First the laser beam welding technology and concerned agricultural components are introduced. Further we specify individual steel types as well as laser types and we define specific welding parameters used in our measurements. We selected several samples of weld joints, which are further examined them in detail using optical microscopy, micro hardness measurements and RTG microanalysis. We further determined the weld shape, measured dimensions of individual weld joints as well as we checked the weld joints structure.
We further introduced a mathematical model based on the program ANSYS. The model can simulate temperatures, speed field and tensions within the weld joint, basing on known thermal conductivity of the base material and specified welding conditions. Using the model, we can predict the shape of the weld and the temperatures within the material. Finally, individual welding parameters and obtained weld joint samples are briefly discussed and the applicability of the model is evaluated.