Mathematical modelling of temperature profile of volcanic soils affected by an external thermal impact

Soil Research ◽  
2006 ◽  
Vol 44 (1) ◽  
pp. 57 ◽  
Author(s):  
Mónica Antilén ◽  
Olivier Fudym ◽  
Alvaro Vidal ◽  
Juan E. Foerster ◽  
Nelson Moraga ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Soil Temperature ◽  
Temperature Profile ◽  
Soil Surface ◽  
Heat Diffusion ◽  
Volcanic Soils ◽  
Heat Diffusion Equation ◽  
Transient Heat Diffusion ◽  
Relative Errors ◽  
The Mathematical Model

In this work, the soil temperature at depth was measured in the laboratory, and a mathematical model to fit the temperature profile in volcanic soils classified as Ultisols and Andisols was used. The mathematical model considered the transient heat diffusion equation, and a numerical discrete method was used to solve the equations system. The soil surface was heated for 2500 s and the temperature rose close to 700°C; the soil temperature decreased with depth; the temperature v. time curves showed a constant value when the temperature reached around 100°C, associated with water phase change and related to the water content of soils. The model was corrected by including the heat volumetric formulation. The observed relative errors are close to 10% in all fitted curves with respect to experimental data, showing the quality of the parametrisation chosen in the mathematical model. The fitting curve deviations were reduced when the actual position of thermocouples was considered, showing the sensitivity of the mathematical model. The simplified mathematical transient diffusion model proposed, which considers 2 ranges of thermal conductivity of soils and the surface temperature, was able to describe the experimental temperature profile in volcanic soils with wide differences in mineralogy, organic matter, and moisture contents.

scholarly journals Computational and Mathematical Model with Phase Change and Metal Addition Applied to GMAW

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Alfredo dos Santos Maia Neto ◽  
Marcelo Gonçalves de Souza ◽  
Edson Alves Figueira Júnior ◽  
Valério Luiz Borges ◽  
Solidônio Rodrigues de Carvalho
Keyword(s):  
Mathematical Model ◽  
Phase Change ◽  
Thermal Model ◽  
Complex Geometry ◽  
Golden Section ◽  
Simulated Data ◽  
Heat Diffusion ◽  
Data Logger ◽  
Heat Diffusion Equation ◽  
Metal Addition

This work presents a 3D computational/mathematical model to solve the heat diffusion equation with phase change, considering metal addition, complex geometry, and thermal properties varying with temperature. The finite volume method was used and the computational code was implemented in C++, using a Borland compiler. Experimental tests considering workpieces of stainless steel AISI 304 were carried out for validation of the thermal model. Inverse techniques based on Golden Section method were used to estimate the heat transfer rate to the workpieces. Experimental temperatures were measured using thermocouples type J—in a total of 07 (seven)—all connected to the welded workpiece and the Agilent 34970A data logger. The workpieces were chamfered in a 45° V-groove in which liquid metal was added on only one weld pass. An innovation presented in this work when compared to other works in scientific literature was the geometry of the weld pool. The good relation between experimental and simulated data confirmed the quality and robustness of the thermal model proposed in this work.

Transfer Heat Mechanism of Oil-Gas-Water Three-Phase Flow in Pipeline

2011 ◽  
Vol 199-200 ◽  
pp. 1609-1612
Author(s):  
Qian Jun Mao
Keyword(s):  
Mathematical Model ◽  
Soil Temperature ◽  
Phase Flow ◽  
Fundamental Theory ◽  
Three Phase ◽  
Three Phase Flow ◽  
The Mathematical Model ◽  
Oil Gas ◽  
Flow Transfer ◽  
Heat Mechanism

It is well known that the oil-gas-water three-phase flow belongs to the field of multiphase flow,transfer heat mechanism of which is very complicated.Transfer heat mechanism is affected not only by different buries in oil gathering pipeline, but also by soil temperature periodicity change. Both domestic and oversea scholars have already studied on the transfer heat mechanisms of oil-gas-water three phase,but they are still in the level of fundamental theory and laboratory.This paper establishes transfer heat models of the oil-gas-water three-phase flow in buried oil gathering pipeline, including the physical model and the mathematical model,and testing in experiment .The purpose of this paper is to analyze value between the calculation and the testing . The results show that the mathematical model of this paper is accurate , and the relative error is ≤ 10%.

A Control System on Soil Temperature

2014 ◽  
Vol 599-601 ◽  
pp. 673-679
Author(s):  
Shi Guo Chen ◽  
Li Hua Hu ◽  
Dong Sheng Wu ◽  
Xue Yong Chen
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Soil Temperature ◽  
Control Algorithm ◽  
Soil Ecology ◽  
Control Soil ◽  
Pid Algorithm ◽  
And Control ◽  
The Mathematical Model

The soil’s temperature plays an important role of soil ecology research. In order to gain and control soil’ temperature. A control system is proposed for soil’s temperature. And a new control algorithm which is based on the PID algorithm is designed in the control system to handle the complex change of the soil’s temperature. It does not need to know the mathematical model of soil’s temperature. At last, the control result is analyzed in this paper. The result shows that the soil’s temperature is controlled ideal by this control system which is accurate to 0.5°C.

scholarly journals Mathematical model of coal self-heating in a stack

2021 ◽  
Vol 318 (3) ◽  
pp. 90-96
Author(s):  
K.M. Akhmetov ◽  
◽  
G.S. Shaikhova ◽  
V.V. Zhurov ◽  
E.N. Khmyrova ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Diffusion Coefficient ◽  
Differential Equations ◽  
Specific Heat ◽  
Heat Release ◽  
Temperature Profile ◽  
Exponential Growth ◽  
Self Heating ◽  
The Mathematical Model

The article presents a mathematical model of coal self-heating in the stack in which the heat exchange and gas exchange processes are described by a system of two non-linear differential equations of the second order with respect to the temperature t of coal self-heating and the volume fraction C of oxygen in the voids of the stack with boundary and initial conditions. The differential equations took into account that self-heating of coal in the stack and appearance of spontaneous combustion are observed in a relatively small layer adjacent to the surface of its contact with the air and called the zone of oxygen influence. In the mathematical model, the influence on the process of coal self-heating of parameter F- specific heat release power was taken into account, which in addition characterises the stability of coal during storage. When compiling the differential equations, such physical parameters as thermal conductivity, diffusion coefficient, specific heat capacity of coal in the stack, bulk density, thermal effect of oxidation, stack voidness, temperature coefficient of exponential growth of heat release power were also used. For numerical implementation of the mathematical model, dimensionless variables and criteria were introduced, which allowed us to apply the net method. Analysis of the obtained results allowed to get: change in the stack temperature profiles with time; change in the stack oxygen concentration profiles with time; influence on the stack temperature profile of the specific heat release power; influence on the stack temperature profile of the parameter characterizing exponential growth of heat release intensity with temperature increase. It has been determined that the dynamics of coal self-heating in the stack is mostly influenced by the Lykov criterion, proportional to the diffusion coefficient, and the Nusselt criterion related to the effective thermal conductivity and to the effective thermal diffusivity of coal. The obtained results suggest that self-heating in the stack is due on the one hand to intensive penetration of air oxygen and on the other hand to a weakened heat transfer. Self-heating and the transition of self-heating into ignition are associated with the occurrence of turbulent diffusion in the stack, arising from increased thermal blowing, whose impact can be enhanced by directing it perpendicular to the surface of the stack.

Cellular and humoral immunity of carp at the action of biologically active additives

2017 ◽  
Vol 4 (1) ◽  
pp. 70-73
Author(s):  
N. Ohorodnyk ◽  
K. Smolianinov ◽  
M. Ratsky
Keyword(s):  
Mathematical Model ◽  
Sugar Beet ◽  
Vertical Plane ◽  
Soil Surface ◽  
Biologically Active ◽  
Advanced Mathematics ◽  
Root Crop ◽  
Cleaning Machine ◽  
Linear Differential ◽  
The Mathematical Model

The work of a tractor-towed machine for cleaning beet top residues from root crop heads, when used with supporting pneumatic wheels, is accompanied with its oscillations in the vertical plane, which has consider- able impact on the quality of implementing the technological process. Therefore, the determination of opti- mal parameters for the cleaning machine, ensuring more stable movement of its cleaning working tool, in the longitudinal-vertical plane fi rst and foremost, is an important task of the mechanization of sugar beet grow- ing industry. Aim. To enhance the effi ciency of cleaning sugar beet top residues from root crop heads via the elaboration of the mathematical model of the oscillating movement of the towed machine for cleaning beet top residues from root crop heads in the longitudinal-vertical plane. Methods. The methods of building computational mathematical models for the functioning of agricultural machines and equipment, based on theoretical mechanics and advanced mathematics, were used. Results. The elaborated equivalent scheme of the movement of the towed cleaning machine was used to obtain the system of two non-linear differential equations for detailed study of the oscillations of the root crop head cleaner in the longitudinal-vertical plane while its supporting pneumatic wheels are moving along uneven soil surface. The mathematical model for the movement of the cleaner with horizontal cleaning roller, elaborated on the basis of initial dynamics equa- tions in the Lagrangian form of the second kind, allowed determining the connection between constructive and kinematic parameters of the vehicle and its oscillating characteristics. The established dependencies formed the prerequisites for further mathematical digital modelling of the parameters of the towed machine for cleaning of root crop heads with a horizontal cleaning roller. Conclusions. The established computation- al model allows optimizing the values of several parameters, characterizing the oscillations of the machine in the longitudinal-vertical plane.

Volumetric Heat Capacity Enhancement in Thin Films of Amorphous Fluorocarbon Polymers

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Hongxiang Tian ◽  
Marc G. Ghossoub ◽  
Oksen T. Baris ◽  
Jun Ma ◽  
Murli Tirumala ◽  
...  
Keyword(s):  
Heat Capacity ◽  
Film Thickness ◽  
Heat Diffusion ◽  
Volumetric Heat Capacity ◽  
Dimensional Solution ◽  
Heat Diffusion Equation ◽  
Adhesion Promoters ◽  
Capacity Enhancement ◽  
Ultrathin Layers ◽  
Transient Heat Diffusion

Plasma deposited amorphous fluorocarbon polymers find use in biopassivation, and as low-friction coatings, adhesion promoters, and interlayer dielectrics. Here, we exploit their ease of deposition into ultrathin layers (<50 nm thick) to explore their potential as thermal storage elements. We design and fabricate a microcalorimeter for measuring the heat capacity of thin fluorocarbons. Conventional thin film calorimetry assumes adiabatic conditions that lead to large errors as film thickness decreases. We propose a new data analysis procedure that incorporates a one-dimensional solution of the transient heat diffusion equation to account for conduction losses. The data for films with thicknesses in the range 12–27 nm reveal a lowering of the melting point and an increase in the volumetric heat capacity with decreasing thickness. We attribute this to change in the carbon to fluorine ratio in the films’ composition. The volumetric heat capacity approximately doubles at room temperature as the film thickness decreases from 27 nm to 12 nm.

Convergence and error analysis of an automatically differentiated finite volume based heat conduction code

2019 ◽  
Vol 29 (7) ◽  
pp. 2389-2406
Author(s):  
Christopher DeGroot
Keyword(s):  
Heat Conduction ◽  
Finite Volume ◽  
Automatic Differentiation ◽  
Heat Diffusion ◽  
Reconstruction Method ◽  
Heat Diffusion Equation ◽  
Content Type ◽  
Discretization Schemes ◽  
Transient Heat Diffusion ◽  
Volume Method

Purpose This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate derivatives of solutions outputs with respect to arbitrary solution input(s). A problem involving conduction in a plane wall with convection at its surfaces is used as a test problem, as it has an analytical solution, and the error can be evaluated directly. Design/methodology/approach The finite volume method is used to discretize the transient heat diffusion equation with constant thermophysical properties. The discretized problem is then linearized, which results in two linear systems; one for the primary solution field and one for the secondary field, representing the derivative of the primary field with respect to the selected input(s). Derivatives required in the formation of the secondary linear system are obtained by automatic differentiation using an operator overloading and templating approach in C++. Findings The temporal and spatial discretization error for the derivative solution follows the same order of accuracy as the primary solution. Second-order accuracy of the spatial and temporal discretization schemes is confirmed for both primary and secondary problems using both orthogonal and non-orthogonal grids. However, it has been found that for non-orthogonal cases, there is a limit to the error reduction, which is concluded to be a result of errors in the Gauss-based gradient reconstruction method. Originality/value The convergence and error properties of derivative solutions obtained by forward mode automatic differentiation of finite volume-based codes have not been previously investigated.

Vibration Analysis Based on the Mathematical Model of the Air-Suction Device Tillage Seeder Seeding

2014 ◽  
Vol 1061-1062 ◽  
pp. 794-798
Author(s):  
Xu Zhang ◽  
Man Quan Zhao ◽  
Fei Liu ◽  
Shuai Dong ◽  
Yue Qin Liu
Keyword(s):  
Mathematical Model ◽  
Working Condition ◽  
Seed Quality ◽  
Surface Soil ◽  
Soil Surface ◽  
Vibration Characteristics ◽  
Forward Speed ◽  
Suction Device ◽  
The Mathematical Model ◽  
Gas Suction

In order to study air-suction when tillage planter in the field farming, Vibration due to the surface roughness of the resulting excitation tillage effects on seed planter of the device, Derivation of the air-suction device tillage planter seeder vibration characteristics of the mathematical model, Vibration characteristics of the mathematical model derived gas suction device tillage seeder seed planter primarily by structural properties, Forward speed when operating, Seed row distance between the soil surface, Soil roughness and soil sticky decision. Can predict and analyze working condition tillage planter seed quality through the establishment of the vibration characteristics of the mathematical model.

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