Mathematical Model for Temperature Distribution of Thermally Processed Shrimp

1991 ◽  
Vol 31 (2) ◽  
pp. 0608-0612 ◽  
Author(s):  
Khe V. Chau ◽  
Gary V. Snyder
Keyword(s):  
Mathematical Model ◽  
Temperature Distribution ◽  
Thermally Processed

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.

scholarly journals Mathematical model of heat transfer in roll caliber

2019 ◽  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Rolling Mill ◽  
Thermal Process ◽  
Stationary Heat

A physical model of the thermal process in the roll caliber during the rolling of the tape on a two-roll rolling mill was constructed. A mathematical model of the temperature field of a rolling hollow roll of a rolling state of a cylindrical shape rotating about its axis with constant angular velocity is proposed. The mathematical model takes into account different conditions of heat exchange of the inner and outer surfaces of the roll with the belt and its surrounding environment. The temperature field of a hollow roll of a rolling mill is considered as an initial boundary-value problem for a homogeneous non-stationary heat equation with inhomogeneous, nonlinear boundary conditions, which also depend on the angle of rotation of the roll around its axis. The equation describes the temperature field of the rolls during uncontrolled heat transfer during rolling. It significantly depends on the time and number of revolutions around its axis. With a large number of revolutions of the roll around its axis, a quasi-stationary temperature distribution occurs. Therefore, the simplified problem of determining a quasistationary temperature field, which is associated with a thermal process that is time-independent, is considered further in the work. In this case, the temperature field is described using the boundary value problem in a ring for a homogeneous stationary heat equation with inhomogeneous boundary conditions and heat transfer conditions outside the ring, which lie from the angular coordinate. After the averaging operation, the solution of this problem is reduced to solving the equivalent integral equation of Hammerstein type with a kernel in the form of the Green's function. The Mathcad computer mathematical system builds the temperature distribution of the roll surface. An algorithm for solving a inhomogeneous problem was developed and the temperature distribution of the roll was constructed.

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