Differential Equations For Heat Transfer Research Articles

Modeling the effect of processing parameters on temperature history in Directed Energy Deposition: an analytical and finite element approach

PurposeThe purpose of this paper is to assess the feasibility of analytical models, specifically the radial basis function method, Akbari–Ganji method and Gaussian method, in conjunction with the finite element method. The aim is to examine the impact of processing parameters on temperature history.Design/methodology/approachThrough analytical investigation and finite element simulation, this research examines the influence of processing parameters on temperature history. Simufact software with a thermomechanical approach was used for finite element simulation, while radial basis function, Akbari–Ganji and Gaussian methods were used for analytical modeling to solve the heat transfer differential equation.FindingsThe accuracy of both finite element and analytical methods was validated with about 90%. The findings revealed direct relationships between thermal conductivity (from 100 to 200), laser power (from 400 to 800 W), heat source depth (from 0.35 to 0.75) and power absorption coefficient (from 0.4 to 0.8). Increasing the values of these parameters led to higher temperature history. On the other hand, density (from 7,600 to 8,200), emission coefficient (from 0.5 to 0.7) and convective heat transfer (from 35 to 90) exhibited an inverse relationship with temperature history.Originality/valueThe application of analytical modeling, particularly the utilization of the Akbari–Ganji, radial basis functions and Gaussian methods, showcases an innovative approach to studying directed energy deposition. This analytical investigation offers an alternative to relying solely on experimental procedures, potentially saving time and resources in the optimization of DED processes.

Exponential sinusoidal modelling and parameterizing studies for the air temperature waves during underground tunnel ventilation

Air precooling or preheating in underground tunnels is beneficial for reducing air conditioning energy consumption and has been widely used in underground spaces such as hydropower stations and utility tunnels. The fluctuation of the ambient temperature has a significant effect on the precooling and preheating performance of underground tunnels. To explore the fluctuation characteristics of the air temperature in an underground tunnel, field testing was conducted at a hydropower station and an exponential sinusoidal model based on the one-dimensional heat transfer differential equation was established. Comparative analysis has shown that the established model can effectively describe the field air temperature fluctuations in the tunnel. The research results reveal that the air temperature wave propagates along the underground tunnel with a period of 24 h, and the amplitude and average temperature continuously decay from 4.57 °C to 24.87 °C at the tunnel inlet to 0.51 °C and 22.95 °C at the tunnel outlet, respectively, with a delay time of approximately 3 h. Furthermore, the wavelength of the air temperature wave propagating along the underground traffic tunnel is approximately 7912 m, which is longer than the tunnel's actual length of 1000 m. Comparative analysis has verified that the exponential sinusoidal model established in this study has reliable predictive performance, which is beneficial for designing the ventilation and air conditioning system of underground spaces and the utilization strategy of surrounding rock natural energy.

Thermoelastic creep evolution in a variable thickness functionally graded piezoelectric rotating annular plate considering convection and radiation heat transfer

The thermoelastic time-dependent creep progress of a rotating annular plate with nonuniform thickness made of functionally graded piezoelectric material considering convection heat transfer and solar radiation was investigated. The nonlinear differential equation of heat transfer considering conduction, convection, and solar radiation was solved using the differential transformation method. Then, the differential equation of equilibrium for the annular plate containing creep strains was derived. Firstly, the differential equation was solved analytically for the zero time . Then, the stress and strain rates were achieved using Norton’s law with Prandtl–Reuss equations. Finally, the time-dependent creep stresses and deformation redistributions were obtained employing an iterative method.

Investigation of Mhd Non-Newtonian Nanofluid Stagnation-Point Flow with Variable Transport Properties and Multislip Effects: An Application to Solar Radiation

Heat and mass transfer performance of Casson nanofluid for both non-conducting (m=0), electrically conducting (m≠0) fluids with solar radiation effects in stagnation point flow is considered. In this model, entropy, irreversibility, and multi slip impacts over a shrinking, static, and stretching sheet are investigated. To minimize the energy used in the solar system, it is important to monitor the processes of heat and mass transfer in the solar radiation process. The slips boundary conditions acts as a closure of the fluid velocity, mass, and heat transfer differential equations. The equations obtained are solved numerically via Galerkin Weighted Residual Method (GWRM). In the limiting sense, the present results conform with the existing work. The Behaviors of the flow physical quantities, temperature, concentration, and velocity for distinct values of the applicable dimensionless numbers are demonstrated with tables and graphs. The results reveal that, for a theoretical account of thermal boundary layers, Prandtl number serves as a variable. Furthermore, higher values of variable thermal conductivity have a significant influence on the skin friction coefficient than the case of constant variable thermal conductivity even when the fluid viscosity is assumed to be variable. The structure of the new method can be applied to the development of oil production.

МАТЕМАТИЧНІ МОДЕЛІ ВИЗНАЧЕННЯ ТЕМПЕРАТУРНИХ ПОЛІВ У НЕОДНОРІДНИХ ЕЛЕМЕНТАХ ЦИФРОВИХ ПРИСТРОЇВ ІЗ УРАХУВАННЯМ ТЕРМОЧУТЛИВОСТІ Primary tabs View(active tab) Edit Translate

Linear and nonlinear mathematical models for determining the temperature field and subsequently analyzing temperature regimes in isotropic spatial media with semi-through foreign inclusions subjected to internal and external thermal loads are developed. For this purpose, the heat transfer coefficient for such structures is described as a single unit using asymmetric unit functions, which makes it possible to consider boundary value problems of heat transfer with one linear and nonlinear differential equations of heat transfer with discontinuous and singular coefficients and linear and nonlinear boundary conditions on the boundary surfaces of the media. In the case of a nonlinear boundary value problem, the introduced linearizing function is used to linearize the original nonlinear heat conduction equation and nonlinear boundary conditions, and as a result, a partially linearized second-order differential equation with partial derivatives and discontinuous and singular coefficients is obtained relative to the linearizing function with partially linearized boundary conditions. For the final linearization of the partially linearized differential equation and boundary conditions, the temperature is approximated by one of the spatial coordinates on the boundary surfaces of the inclusion by piecewise linear functions, as a result of which both the differential equation and boundary conditions become fully linearized. To solve the resulting linear boundary value problem, the Hankel integral transformation method is used, which results in an analytical solution that determines the introduced linearizing function. As an example, the linear dependence of the thermal conductivity coefficient of structural materials of a structure on temperature, which is often used in many practical problems, is chosen. As a result, analytical relations in the form of quadratic equations were obtained to determine the temperature distribution in a thermally sensitive layer with a foreign semi-through inclusion under external heating in the form of a heat flux. A numerical analysis of the temperature behavior as a function of spatial coordinates for given values of geometric and thermophysical parameters is performed. The influence of a foreign inclusion on the temperature distribution is investigated if the VK94-I ceramic is chosen as the material of the medium and the inclusion is silver. To determine the numerical values of temperature in the above structures, as well as to analyze heat transfer processes inside these structures caused by internal and external thermal loads, software tools have been developed that have been used to perform a geometric image of the temperature distribution depending on spatial coordinates. The obtained numerical temperature values indicate that the developed mathematical models for analyzing heat transfer processes in spatially heterogeneous environments with internal and external heating correspond to a real physical process. The software also makes it possible to analyze such environments subjected to internal and external thermal loads in terms of their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual elements but also the entire structure.

Analiza toplotnih efekata u postupcima frikcionog zavarivanja mešanjem

This paper describes the formation of an analytical model of heat generation and transfer during friction stir welding. By solving differential equations of heat transfer, adapted for friction stir welding, the foundations for the formation of an analytical model were laid. In order to vary the technological parameters of welding that affect the generated heat, certain approximations were performed and the stress state of the material was observed at elevated temperatures. The aim was to simulate heat transfer for thin and thick plates, by obtaining a planar and spatial temperature image for certain welding parameters. The formation of the analytical model was performed in the Python programming language.

THE LATEST TRENDS IN THE CREATION OF IMPACT-VIBRATION EQUIPMENT WITH DIFFERENT TYPES OF DRIVES FOR SOIL PROBING

The study of soils by immersion of a cone under the influence of ultrasonography is one of the express methods of obtaining engineering and geological information about the physical and mechanical properties of the foundation from loose soils of buildings and structures. It makes it possible to detect the degree of homogeneity of probed soils; determine the position of the boundaries (contacts) of various lithological layers and bearing layers for the fuel base; to identify and delineate in plan and in depth the weakened zones on the studied areas for the exact reference of the place of conducting experimental works; choose the optimal options for choosing hammers; evaluate the physical and mechanical properties of sandy soils (density, angle of internal friction, etc.); roughly estimate the modulus of deformation of sandy soils. The main tasks are the development, research and calculation of the main parameters of installations with a hydraulic impulse drive for soil probing. The object of research is the process of soil probing. The subject of the study is the hydropulse drive of the soil probing installation. Experience has shown that the effective use of field methods is possible only under the condition of a methodically correct approach to the preparation and execution of programs of the entire complex of search operations. Various aspects of the problem of comprehensive soil research using field methods were developed and deepened gradually.The main research methods include the analysis of information on existing methods and installations for spraying tungsten powders, mathematical modeling of processes in the spindle unit of the installation for spraying metal powders, taking into account its design features and operating modes based on nonlinear differential equations of heat transfer from solid and liquid bodies using numerical methods of their solution based on the FlowVision program.

Concept, modeling and experimental evaluation of an integrated cooling, heating and thermoelectric generation system

A concept of an integrated system for cooling, heating and electricity generation using thermoelectric effect and water is presented. The concept consists of two 2-L capacity water reservoirs: The first one has been used to store cold water and the second one to store heated water. Both reservoirs are thermally connected by two thermoelectric modules, which can be used to heat and cool the water when supplying electrical energy to the modules or generate electricity when hot and cold water are stored in these two reservoirs. A theoretical model of the system is developed for transient simulation where heat transfer and energy conservation differential equations were numerically solved and a real prototype was built. The model uses the maximum performance parameters available in commercial thermoelectric datasheets to obtain all other relevant thermoelectric variables. The agreement between the developed model and the experiment was close to 95%, and the proposed system was able to cool water near zero degrees Celsius, to heat it near the water boiling point, and generate more than 1.5 W of electrical power when operated as thermoelectric generator using heated water and cold water with 70 °C temperature. The simulations also showed that water reservoirs of 25 L capacity, with initial temperatures of 95 °C for hot water and 25 °C for cold water, can be used to supply peak electrical power of 2.3 W and mean power of 1 W for 12 h, energy equivalent 6 AA alkaline batteries. This system has the potential to be applied for sustainable cooling, heating and electricity generation in isolated communities and in non-urban regions.

IMPROVING THE EFFICIENCY OF SOIL SOUNDING AT HYDROPULSE DRIVE INSTALLATIONS

The study of soils by immersion of the cone under the influence of UVZ is one of the express methods of obtaining engineering and geological information about the physical and mechanical properties of the foundation from loose soils of buildings and structures. It allows to detect the degree of homogeneity of probed soils; determine the position of the boundaries (contacts) of different lithological layers and bearing layers for the fuel base; identify and delineate in plan and depth weakened areas in the study areas to accurately link the location of research work; choose the best choice of hammers; evaluate the physical and mechanical properties of sandy soils (density, angle of internal friction, etc.); to estimate the modulus of deformation of sandy soils. The aim of the work is to increase efficiency, speed and the ability to regulate the process of sounding soils by developing and using installations with a hydropulse drive. The main tasks are the development, research and calculation of the basic parameters of installations with hydropulse drive for soil sounding. The object of research is the process of sounding the soil. The subject of research is the hydropulse drive of the installation for soil sounding. Experience has shown that the effective application of field methods is possible only with a methodically correct approach to the preparation and implementation of programs of the whole complex of exploration work. Various aspects of the problem of integrated soil research by field methods were developed and deepened gradually. The main research methods include the analysis of information on existing methods and installations for spraying tungsten powders, mathematical modeling of processes in the spindle assembly of the installation for spraying metal powders, taking into account itdesign features and modes of operation based on nonlinear differential equations of heat transfer from solid and liquid bodies using numerical methods for solving them based on the program FlowVision.

Transient Pressure and Temperature Analysis of a Deepwater Gas Well during a Blowout Test

On one hand, a blowout test can clean the bottom of the well, and on the other, it can learn the productivity of the well, which is important work before putting the well into production and also the main basis for production allocation of the well. The accurate prediction of the blowout test process provides a theoretical basis for the design of a reasonable blowout test system and the determination of well cleaning time. During deepwater blowout tests, gas and liquid flows are unsteady in pipes, and flow parameters change over time. At present, accurately predicting changes in fluid temperature, pressure, liquid holdup, and other parameters in a wellbore during an actual blowout process using the commonly used steady-state prediction methods is difficult, and determining whether a test scheme is reasonable is impossible. Therefore, based on the conservation of mass, momentum, and energy during the blowout test process, in this study, formation, wellbore, and nozzle flows were coupled for the first time, and a time and space of unsteady pressure drop and a heat transfer differential equation system was established; furthermore, using the Newton–Raphson method, the equations were solved. Finally, the simulation of the transient flow of the blowout test was completed. Considering a measured deepwater gas well A as an example, the blowout test process was simulated, and the variations in the wellbore flow parameters were analyzed. Comparing the simulation result with the test data, we concluded the following. (1) During the blowout process, the wellbore temperature gradually increased; pressure at the bottom of the wellbore decreased; and pressure at the wellhead increased; and (2) the established model agreed well with the actual production data, and the average error of the wellhead pressure and temperature was less than 5%. Considering the high production capacity of deepwater gas wells, the use of large-sized tubing and nozzles to spray is recommended, which can improve the speed of clearing wells and prevent the formation of hydrate.

Experimental study of horizontal ground heat exchangers embedded in the backfilled mine stopes

Abundant geothermal resources are stored in underground mines in China. In order to realize the green cooperative development of deep mineral resources and geothermal resources, the heat storage functional backfill technology can be used to form artificial thermal reservoir, and the geothermal energy can be extracted through the buried pipes, so as to expand the auxiliary value and reduce the cost of backfill mining. It's important to investigate the heat storage/release behavior of the backfill body with buried pipes and its influencing factors for improving the geothermal energy utilization efficiency. In view of the limitations of field experiments, a scale model test platform for backfill coupled heat exchanger of mine was established in this paper. According to the heat transfer differential equations, the similarity criterion number and similarity constant that should be satisfied between the model and the prototype were deduced, and the effects of different pipe arragement, flow rate of heat-carrying fluid, surrounding rock temperature on the heat transfer performance of the backfill coupled heat exchanger were studied. Based on the heat balance, the total energy efficiency of the backfill coupled heat exchanger system was calculated. The experimental results showed that with the increase of the distance between pipes, the pipe length, the flow rate and the surrounding rock temperature, the heat extraction and water outlet temperature of the system all increased. With the increase of the velocity of heat-carrying fluid, the water outlet temperature decreased. The increase in the number of pipes in the backfill body and the decrease in the distance between pipes lead to the increase in thermal interference and thus the decrease in heat extraction, but the decrease value is less than the increase value of heat charging caused by the increase in pipe length (serpentine) and flow rate (double U-type). The total energy efficiency of the system was the highest, which was 47.9%, when the serpentine pipe arrangement was adopted, the working fluid velocity was 0.7 m/s, and the surrounding rock temperature was 35°C. According to the scale model, 1.06 × 109 kJ of heat can be obtained from the mines a year by applying BCHE system in engineering practice.

Thermal stresses in a functionally graded rotating disk: An approximate closed form solution

The purpose of this study is to analyze a circular annulus made of a functionally graded material (FGM) subjected to thermomechanical loading. The governing nonlinear differential equation for heat transfer, comprising of all the modes of heat transfer, such as conduction, convection, radiation, and internal heat generation, was formulated and then solved using the homotopy perturbation method (HPM). The stress field in the circular annulus due to thermomechanical loading was obtained using a HPM based approximate closed-form solution for a steady-state nonhomogeneous temperature field coupled with the solution of the classical theory of elasticity. The present work considered both Dirichlet and Neumann boundary conditions. A rigorous study on the effect of various thermomechanical parameters and grading parameters on temperature as well as the stress field is presented. The present approximate closed-form solution was validated with the finite element method (FEM) based solution. The close agreement between HPM based solutions of this work with the results of the ANSYS based FEM confirms the effectiveness and the viability of the present solution method for a FGM rotating disk with multiple variable nonlinearities. The present closed-form solution is more rational and computationally efficient over FEM and other numerical solutions.

Steady state heat transfer analysis in a rectangular moving porous fin

In this article, the variation of temperature distribution and fin efficiency in a porous moving fin of rectangular profile is studied. This study is performed using Darcy's model to formulate the governing heat transfer differential equation. The approximate analytical solution is generated using the variational iteration method (VIM). The power series solution is validated by benchmarking it against the numerical solution obtained by applying the Runge-Kutta fourth order method. A good agreement between the analytical and numerical results is observed. The effects of porosity parameter, Peclet number and other thermo-physical parameters, such as the power index of heat transfer coefficient, convective-conductive parameter, radiative-conductive parameter, thermal conductivity gradient and non-dimensional ambient temperature on non-dimensional temperature are also studied and explained. The results indicate that the fin rapidly dissipates heat to the ambient temperature with an increase in the Peclet number, convection-radiation parameters and the porosity parameter.

Calculation and Analysis of DC Surge Arrester Temperature Field

Zinc oxide arresters have been widely used in high-voltage, ultra-high-voltage and ultra-high-voltage power transmission systems due to their excellent non-linear characteristics. However, because there is no gap between the arrester itself, there is a slight leakage current when the zinc oxide arrester is subjected to normal line voltage, which causes the aging of the zinc oxide resistance valve. The degree of aging and the rate of temperature rise are related to the temperature distribution, so it is of great significance to study the temperature field distribution of the DC arrester. This paper takes multi-column zinc oxide arrester as an example. According to the differential equation of heat transfer and the auxiliary equation, the simulation of time-varying temperature field is carried out. The simulation results are helpful to optimize the structure of multi-column parallel arrester and analyze the aging characteristics of valve.

Thermotechnical properties of the fire-extinguishing powder for extinguishing materials based on magnesium alloy chips

The article addresses the relevant issue of determining the thermotechnical characteristics of the fire-extinguishing powder for thermal insulation of the fire center of materials based on magnesium alloy chips to prevent fire development and propagation and its effective extinguishing. To solve this problem, laboratory and field experimental studies of the heat-insulating ability of the fire-extinguishing powder of combined effect were conducted. As a result, we obtained the data on the temperature in the center of the fire of materials based on magnesium alloy chips and outside during their suppressing by the fire-extinguishing powder with a combined effect. In this case, the temperature of the non-heated side of the fire-extinguishing powder layer does not exceed 170 °C at the average temperature of the fire center of 740 °C, which indicates high insulation capacity of the powder and, consequently, its high fire-fighting efficiency in extinguishing the fires of materials based on magnesium alloy chips. The obtained temperature data were used to determine the thermophysical parameters of the layer of the fire-fighting powder using the created mathematical model of the heat transfer process in the powder layer at the heat insulation of the fire center. To create a mathematical model of the heat transfer process, the main provisions during consecutive consideration of several experimental situations were stated. The first experimental situation meets the conditions of the stationary thermal process, and other experimental situations meet the conditions of the non-stationary thermal process. These experimental situations were created with the help of changing the thickness of the fire-fighting powder layer at different parameters of its feeding to the fire center. The mathematical model of the process is based on the use of the differential equation of heat transfer at its approximation by the method of finite differences. At the same time, it is believed that the heat transfer conditions at the boundary between the non-heated side of the insulating layer of the fire-extinguishing powder and the environment in each experimental situation are the same. Using the created model, the coefficient of heat transfer between the non-heated side of the insulating layer of the fire-extinguishing powder and the environment was determined. It amounted to 395.7 W(m 2 ×°С). The dependence of the effective thermal conductivity coefficient on the thickness of the insulating layer was explored. It was shown that this dependence can be approximated by linear dependence l(d)=–0.016+93.907×d (d is the thickness of the layer of the fire-extinguishing powder in meters). After conducting the necessary calculations, we obtained the value of the required thickness of the layer of fire-extinguishing powder d=45.2 mm

Study on phase changes of ice and salt in saline soils

The occurrence of different ice and salt phases in saline soils may result in severe failure in engineering practice. Therefore, studying the phase changes of these two components may improve the understanding of saline soils. Through a series of cooling experiments on sulfate saline soils, the internal temperature variation of soils is obtained to study the rule of salt crystallization and the effect of salt on liquid water content. Based on the thermodynamic principle, the heat transfer equation is expressed considering the phase changes of ice and salt, and the control volume approach is applied to discretize the differential equation of heat transfer. Combined with the internal temperature curve of the soils, the discrete equations allow the calculation of ice porosity variation, salt crystal porosity, and unfrozen water content in saline soils. Additionally, the equations provide a useful general criterion for salt crystallization at different temperatures. Experimental and theoretical results confirm that unfrozen water content in saline soils decreases as the salt content increases, and that liquid water content is lower in salt-free soils. In addition, the concentration of salt solution in soils with low salt content increases owing to the phase change between water and ice; salt crystallization can only occur if the concentration reaches 20% at a negative temperature.

Mathematical Modeling of Heat Flux Distribution in Raw Cotton Stored in Bunt

The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some improvements. Therefore, the mathematical modeling of storage conditions of raw cotton in bunts and the physical and mechanical conditions that occur in it is of great importance. In the developed mathematical model, the main factor influencing the physical and mechanical properties of raw cotton is the change in temperature. Due to the temperature, kinetic and biological processes accumulated in the raw cotton in Bunt, it can spread over a large surface, first in a small-local state, over time with a nonlinear law. As a result, small changes in temperature lead to a qualitative change in physical properties. In determining the law of temperature distribution in the raw cotton in Bunt, Laplace’s differential equation of heat transfer was used. The differential equation of heat transfer in Laplace’s law was replaced by a system of ordinary differential equations by approximation. Conditions are solved in MAPLE-17 program by numerical method. As a result, graphs of temperature changes over time in raw cotton were obtained. In addition, the table shows the changes in density, pressure and mass of cotton, the height of the bun. As the density of the cotton raw material increases from the top layer of the bunt to the bottom layer, an increase in the temperature in it has been observed. This leads to overheating of the bottom layer of cotton and is the main reason for the deterioration of the quality of raw materials.

Mixed convective hybrid nanofluid flow in lid-driven undulated cavity: effect of MHD and Joule heating

A numerical analysis has been conducted to show the effects of magnetohydrodynamic (MHD) and Joule heating on heat transfer phenomenon in a lid driven triangular cavity. The heat transfer fluid (HTF) has been considered as water based hybrid nanofluid composed of equal quantities of Cu and TiO2 nanoparticles. The bottom wall of the cavity is undulated in sinusoidal pattern and cooled isothermally. The left vertical wall of the cavity is heated while the inclined side is insulated. The two dimensional governing partial differential equations of heat transfer and fluid flow with appropriate boundary conditions have been solved by using Galerkin's finite element method built in COMSOL Multyphysics. The effects of Hartmann number, Joule heating, number of undulation and Richardson number on the flow structure and heat transfer characteristics have been studied in details. The values of Prandtl number and solid volume fraction of hybrid nanoparticles have been considered as fixed. Also, the code validation has been shown. The numerical results have been presented in terms of streamlines, isotherms and average Nusselt number of the hybrid nanofluid for different values of governing parameters. The comparison of heat transfer rate by using hybrid nanofluid, Cu-water nanofluid, TiO2 -water nanofluid and clear water has been also shown. Increasing wave number from 0 to 3 enhances the heat transfer rate by 16.89%. The enhanced rate of mean Nusselt number for hybrid nanofluid is found as 4.11% compared to base fluid.

Quadratic Convective Heat Transport of Casson Nanoliquid Over a Contract Cylinder: An Unsteady Case

An unsteady MHD flow of nonlinear radiative heat transfer of Casson liquid over a contract cylinder has been modeled. This is a theoretical study that involves mathematical approach to do the investigation. The nonlinear partial differential equations for heat transfer are solved numerically using the RKF-45 method. Effects of embedded kinetic parameters on the velocity and temperature of the system are depicted graphically and discussed accordingly. It is found that the rate of cooling is much faster for higher values of unsteadiness parameter. The higher value of unsteady parameter decreases the profiles of velocity and temperature. Further, thermal boundary layer thickness is decreased when the Prandtl number increases.

Аналитическое исследование теплообмена в термогидроциклоне для промысловой депарафинизации нефти

The article considers modernization of the design of thermohydrocyclone (THC), where cooling, solidification and heating mechanisms are carried out in one continuous process. This reduces the time of the complete cycle of oil removal from paraffin, increases the productivity and efficiency of the plant. The technological scheme of continuous operation THC is presented. The general factors and simplifying allowances for mathematical modeling of phase transition processes (melting and solidification) are considered. Differential equations for heat transfer in the course of paraffin melting and solidification in a conical layer have been solved analytically. Formulas for determining thickness of the conical layer of the new phase, time of formation of a new solid phase, and average density of the heat flow in the conical layer on a THC wall have been derived. The effect of centrifugal inertia forces is taken into account. The formulas for calculating the basic parameters are summarized in the form of power criterion equations linking Fourier criteria (Fo), Kosovich criteria (Ko) and Pomerantsev criteria (Po) under the quasiconductive non-stationary heat exchange in THC.