Mathematical model and calculation of heating regime of a tunnel furnace to produce a given temperature distribution in the firing zone

Refractories ◽  
1981 ◽  
Vol 22 (1-2) ◽  
pp. 77-83
Author(s):  
V. G. Abbakumov ◽  
E. F. Mosin
Keyword(s):  
Mathematical Model ◽  
Temperature Distribution ◽  
Firing Zone ◽  
Heating Regime ◽  
Tunnel Furnace

scholarly journals Heat Localization in the Medium in Blow-Up Regime

2020 ◽  
Keyword(s):  
Temperature Distribution ◽  
Blow Up ◽  
Maximum Temperature ◽  
Heating Regime ◽  
Heating And Cooling ◽  
Localized Heating ◽  
Finite Period ◽  
Equation Of Heat Conduction ◽  
The Given ◽  
Heat Front

The existence of the effect of heat metastable localization in the medium in the blow-up heating regime was experimentally proved. This is the regime in which the heating energy for a finite period of time tends to infinity. Previous theoretical studies have shown that in this case some regions, inside of which the temperature increases, may arise, while their size remains constant or decreases with time (heat localization regions). These regions exist as long as there is some energy input from the outside. An installation for the experimental study of the thermal blow-up regimes in a solid was developed. The object of research was an aluminum rod with a heater at its end. The temperature distribution along the rod was measured with thermocouples. The temperature of the rod end could vary according to the given law. Calibration of the installation was performed. The sensitivity of thermocouples was determined. The inertia of the heating and cooling process was estimated. The mathematical description of the thermal processes, occurring during the experiment, was made. The nonlinear equation of heat conduction for the rod was solved, with the heat exchange with the environment by convection and radiation taken into account. The thermal regime at the boundary, which is necessary to create the thermal structures, was determined. The temperature distribution in the rod in the blow-up regime and non-blow-up regime was measured. In the blow-up regime the heat front (the coordinate of the point with the temperature equal to half the maximum temperature) initially shifts from the heat source, and then in the opposite direction, and the size of the area under heating decreases. In the non-blow-up regime the size of the heated region increases all the time. The predicted effect was supposed to be used in installations for thermonuclear fusion where the target was heated by laser radiation pulses of a special shape. This effect can also be used for localized heating in cutting and welding, when the adjacent regions are not to get very hot, and in other similar situations.

Temperature Distribution in a Turbulent Flow in the Heat Pollution Phenomena

2020 ◽  
Author(s):  
Victorita Radulescu
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Fluid Flow ◽  
Temperature Distribution ◽  
Prandtl Number ◽  
Experimental Results ◽  
Turbulent Heat ◽  
Fluid Viscosity ◽  
Solid Walls ◽  
Good Agreement

Abstract The thermal pollution, with major effects on the water quality degradation by any process involving the temperature transfer, represents nowadays a major concern for the entire scientific world. The turbulent heat and the mass transfer have an essential role in the processes of thermal pollution, mainly in problems associated with the transport of hot fluids in long heating pipes, thermal flows associated with big thermo-electric power plants, etc. In the last decades, the problems of the turbulent heat and mass transfer were analyzed for different dedicated applications. The present paper, in the first part, estimates the universal law of the velocity distribution near a solid wall, with a specific interpretation of the fluid viscosity, valid for all types of flows. Most of the scientific researches associate nowadays both the turbulent heat and the mass transfer with the Prandtl number. In the turbulent fluid flow near a solid and rigid surface, there are three flowing domains, laminar, transient, and fully turbulent, each one with its characteristics. In this paper, it is assumed that the friction effort at the wall remains valid at any distance from the wall, but with different forms associated with the dynamic viscosity. By using the superposition of the molecular and turbulent viscosity and by creating the interdependence between the molecular and turbulent transfer coefficients is estimated the mathematical model of the velocity profile for the fluid flow and temperature distribution. Three supplementary hypotheses have been assumed to estimate the dependence between the laminar and thermal sub-layer and the hydrodynamic sub-layer. The theoretical obtained distribution was compared with some experimental results from the literature and it was observed there is a good agreement between them; the differences are smaller than 3%. In the second part of the paper is determined the temperature field for a fluid flowing also in presence of the solid surfaces with different temperatures, associated not only with the Prandtl number but also with the fluid viscosity and its dependence with the temperature, correlated with the Grashoff number. In the next paragraph is used the concept of the laminar substrate with different thicknesses for the hydrodynamic flows with thermal transfer to the solid walls, and also the inverse transfer from the solid walls affecting the fluid flow and the mass transfer. The obtained mathematical model is correlated with the semi-empirical data from the literature. By numerical modeling, the obtained results were compared with the experimental measurements and it was determined the dependence between the Stanton number and the Prandtl number. The numerical results demonstrate a good agreement with the experimental results in a wide range of the Prandtl numbers from 0.5 to 3000. Finally, are mentioned some conclusions and references.

Computational analysis of temperature distribution in microwave-heated potatoes

2020 ◽  
Vol 26 (6) ◽  
pp. 465-474
Author(s):  
Deepak Singh ◽  
Dhananjay Singh ◽  
Sattar Husain
Keyword(s):  
Mathematical Model ◽  
Temperature Distribution ◽  
Computational Analysis ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Maximum Temperature ◽  
Bacterial Inactivation ◽  
Food Material ◽  
Drying Time ◽  
Temperature Ranges

This research article reports the computational analysis of temperature distribution in microwave-heated convenience food such as potato. The detailed study of temperature (because temperature is a function of bacterial inactivation) and microwave powers along with drying time for the preservation of food material has been presented. Therefore, a mathematical model for potato sample is developed to predict the behavior of temperature distribution at each possible point and different shapes (slab, cylindrical, and spherical) of food material. The developed mathematical model is programmed by MATLAB software. Another parameter, microwave power is also a function of temperature. The ranging values of various microwave powers (125 W, 375 W, 625 W, 875 W, and 1250 W) along with different values of drying time (0 to 10 minutes) have been used for computation. The obtained results show the uniformity of temperature distribution throughout the whole product in the form of a three-dimensional structure. The model provides the minimum and maximum temperature ranges in specimens without performing an experiment which depicts the condition of bacterial inactivation.

Study on a New Mathematical Model for Aggregate Air Cooling or Heating

2011 ◽  
Vol 374-377 ◽  
pp. 1882-1886
Author(s):  
Li Juan Wang ◽  
Yan Feng Liu ◽  
Jia Ping Liu ◽  
Fei Lu
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Transfer Coefficient ◽  
Temperature Distribution ◽  
Hydraulic Structure ◽  
Surface Heat ◽  
Air Cooling ◽  
Foundation Engineering ◽  
Heating Capacity ◽  
Surface Heat Transfer Coefficient

Before the construction of hydraulic structure, aggregate must be cooled or heated by air (we call it aggregate air cooling or heating in this paper) or other technologies to the required temperature. Previous model of aggregate air cooling or heating cannot provide the center temperature of each aggregate. So a more accurate mathematical model is developed to determine the thermal performance of aggregate, and the surface heat transfer coefficient of wet aggregate is revised. This model can predict the center temperature of an aggregate and can accurately calculate the cold down time or temperature distribution of aggregate, so that the refrigeration or heating capacity can be reasonably supplied. It’s significant for foundation engineering of hydraulic structure.

Mathematical Model for Heat Transfer Simulation of Rotary Alumina Kiln

2013 ◽  
Vol 423-426 ◽  
pp. 881-884
Author(s):  
Xiao Yan Yang ◽  
You Gang Xiao ◽  
Xian Ming Lei
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Temperature Distribution ◽  
Phase Change ◽  
Heat Loss ◽  
Chemical Reactions ◽  
Outer Shell ◽  
Test Results ◽  
Distribution Rule ◽  
Heat Transfer Simulation

According to kiln structure and material movement features, considering convective, radioactivity, conductivity and various phase change and chemical reactions, a series of comprehensive models are built for quantifying the thermal fluxes from the gas to the material bed and the heat loss from outer shell to the atmosphere in the rotary alumina kiln. The results show that the temperatures of outer shell accord with test results; the temperature distribution rule of gas is the same with that of materials, but the gas temperatures are higher; it is feasible to use the model to improve alumina kiln performance.

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