Mathematical Model Of Heat Transfer Research Articles

Mathematical model for heat transfer during underground coal gasification process

Purpose. To develop a mathematical model of the “coal-gas” medium heat transfer during underground coal gasification to predict the combustion face advance velocity and the duration of gasification column mining. Methodology. To detect the temperature fields in the coal seam and gas, depending on the displacement length of the phase transition boundary, a boundary-value problem of mathematical physics has been developed. To solve this boundary-value problem, Boltzmann transformations, as well as methods for solving ordinary differential equations, are used. Newton-Raphson method, which has quadratic convergence, is used to find the roots of the transcendental equation. Findings. Tendencies in the formation of mathematical models when studying temperature fields around an underground gasifier have been analyzed, with highlighting their disadvantages. A mathematical model of heat transfer during underground gasification has been developed, taking into account the phase transition boundaries of the “coal-gas” medium. A computational experiment was conducted to determine the temperature of the phase transition boundary based on the length of the gasification column and the duration of the process. Originality. A mathematical model for heat transfer during coal gasification in the form of a boundary-value problem of mathematical physics, which consists of parabolic heat-transfer equations, the Stefan condition at the phase transition boundary, and the Dirichlet boundary conditions, has been constructed. As a result of solving the boundary-value problem, a self-similar solution has been obtained for the distribution of the coal seam and gas temperature fields, as well as the position of the phase transition boundary depending on the gasification duration and on the medium density, thermal conductivity coefficients, specific heat capacity of gas and coal, specific calorific value and temperature of coal combustion, initial coal temperature and constant temperature of the gasification process. The conducted analysis of numerical calculations provides a deeper understanding of the dynamics of underground coal gasification process and makes necessary corrections to achieve the maximum process efficiency. Practical value. A methodology for determining the displacement length of the phase transition boundary of the “coal-gas” medium has been developed, taking into account the change in the combustion face temperature along the gasification zone length depending on the duration of this process. Application of the methodology makes it possible to predict the time of mining the gasified coal column for drawing up a calendar plan for mining operations.

Thermal analysis of mathematical model of heat and mass transfer through bioconvective Carreau nanofluid flow over an inclined stretchable cylinder

In this proceeding the main focus to scrutinize the heat and mass transfer rate increment due to the involvement of motile microorganisms in the Carreau nanofluid flow through an inclined stretchable cylinder under the consequences of activation energy and thermal radiation. This phenomenon has many physical applications in the field of civil, mechanical and seismographic engineering. The research focuses on creating and analyzing new nanocomposites with applications in energy storage, showcasing the transformative impact of nanotechnology on the advancement of high-performance materials. First of all, for the numerical treatment of the above physical model mathematical model is developed in the form of partial differential equations (PDE's) by considering all involving quantities. The resultant model is highly nonlinear and of higher order. Appropriate similarity variables are defined to transform this system of PDE's into first order ordinary differential equations (ODE's). For numerical results we develop a numerical algorithm from nonlinear ODE's and use ‘bvp4c’ built in package of MATLAB. Numerical results are acquired from software in the form of graphical visuals and tabular data as narrated in the results and discussion section. Using this tabular data streamlines are constructed for the better understanding of heat and mass transfer through this phenomenon under the defined constraints. From results, velocity profile increased by the augmentation of values of curvature parameter. Thermal profile is stronger when values of thermophoresis parameter is boosted, Concentration of nanoparticle profile get smoother when temperature coefficient increased, and motile microorganism's density profile is enlarged upon inclining the values of bioconvection lewis number.

Fractional-Order Modeling of Heat and Moisture Transfer in Anisotropic Materials Using a Physics-Informed Neural Network.

Mathematical models of heat and moisture transfer for anisotropic materials, based on the use of the fractional calculus of integro-differentiation, are considered because such two-factor fractal models have not been proposed in the literature so far. The numerical implementation of mathematical models for determining changes in heat exchange and moisture exchange is based on the adaptation of the fractal neural network method, grounded in the physics of processes. A fractal physics-informed neural network architecture with a decoupled structure is proposed, based on loss functions informed by the physical process under study. Fractional differential formulas are applied to the expressions of non-integer operators, and finite difference schemes are developed for all components of the loss functions. A step-by-step method for network training is proposed. An algorithm for the implementation of the fractal physics-informed neural network is developed. The efficiency of the new method is substantiated by comparing the obtained numerical results with numerical approximation by finite differences and experimental data for particular cases.

Геометрическая модель главного корпуса Ивановской ТЭЦ-2 в ПВК Ansys

Modeling of the heat-air regime in the main body of the TPP in the scientific and technical literature is given insufficient attention. To simulate the heat-air regime in the main building of a thermal power plant, it is necessary to develop a geometric model of the boiler-turbine shop. A mathematical model of the heat-air regime in the main building of the TPP will allow us to develop energy-saving measures and improve the microclimate in the premises of the plant. The study has been carried out using mathematical modeling methods based on the DesignModeler graphic editor in ANSYS software. A geometric model of the boiler-turbine shop of Ivanovo combined heat and power plant-2 (CHPP-2) has been developed. It allows us to develop a mathematical model of heat and mass transfer in the air space of the main building of the plant. The three-dimensional geometric model of Ivanovo CHPP-2 is the first stage of the development of an integrated mathematical model of the heat-air regime of the main building. Its aim is to evaluate measures that reduce consumption of thermal and electrical energy for the in-house needs.

The Problem of Heat and Mass Transfer of a Half-Space with an Air Flow with Periodic Changes in Air Temperature

A system of differential equations, boundary and initial conditions for calculating temperature and moisture content fields in a homogeneous halfspace, the boundary of which is blown by an air flow, is formulated. The heat exchange of the boundary with the air medium occurs according to the Newtonian law, and mass transfer — according to the Dalton evaporation law. In the initial state, the air and the material have the same temperature, and water vapor, both near the surface of the material and outside the boundary layer, is in a saturation state, so there is no exchange of heat and moisture between the air and the material. At some point, the air temperature begins to produce small harmonic fluctuations near its initial value. For a mathematical model of heat and mass transfer, in which the movement of moisture to the surface is considered to be caused only by a drop in moisture content, i.e. the phenomenon of thermal diffusion is neglected, an asymptotic time view of the temperature and moisture content fields is obtained. The moisture content field has the form of a damped harmonic wave, and the temperature field is represented by the superposition of two waves of the same type, which have the same frequency, but different attenuation coefficients and phase velocities. The calculation of the basic wave parameters for a material with clay characteristics is carried out, and the results obtained are compared with experimental data. The constructed solution is a generalization of the Fourier formulas known in the literature, which are valid only in a situation when the material does not contain moisture, and according to the harmonic law, not the air temperature changes, but the surface temperature. The results obtained in the article will be used in geocryology as a theoretical tool in the study of seasonal fluctuations in the thermal and physical state of the soil, which is an important task in planning economic activities in the field of the distribution of frozen rocks.

Numerical Study on the Heat Dissipation Performance of Diamond Microchannels under High Heat Flux Density

Heat dissipation significantly limits semiconductor component performance improvement. Thermal management devices are pivotal for electronic chip heat dissipation, with the enhanced thermal conductivity of materials being crucial for their effectiveness. This study focuses on single-crystal diamond, renowned for its exceptional natural thermal conductivity, investigating diamond microchannels using finite element simulations. Initially, a validated mathematical model for microchannel flow heat transfer was established. Subsequently, the heat dissipation performance of typical microchannel materials was analyzed, highlighting the diamond’s impact. This study also explores diamond microchannel topologies under high-power conditions, revealing unmatched advantages in ultra-high heat flux density dissipation. At 800 W/cm2 and inlet flow rates of 0.4–1 m/s, diamond microchannels exhibit lower maximum temperatures compared to pure copper microchannels by 7.0, 7.2, 7.4, and 7.5 °C, respectively. Rectangular cross-section microchannels demonstrate superior heat dissipation, considering diamond processing costs. The exploration of angular structures with varying parameters shows significant temperature reductions with increasing complexity, such as a 2.4 °C drop at i = 4. The analysis of shape parameter ki indicates optimal heat dissipation performance at ki = 1.1. This research offers crucial insights for developing and optimizing diamond microchannel devices under ultra-high-heat-flux-density conditions, guiding future advancements in thermal management technology.

Experimental and Numerical Study of Air Flow Reversal Induced by Fire in an Inclined Mine Working

Effective fire prevention in mine workings and tunnels requires a thorough theoretical analysis of the heat and mass transfer processes within these structures. This involves using established models to calculate non-isothermal air flow dynamics in long tunnels and mine workings. While the ventilation of tunnels has been extensively studied, significant challenges persist regarding mine ventilation systems, particularly due to their complex and branched topology. This study aimed to address these challenges and gaps in mine ventilation. We designed a laboratory bench to simulate an inclined mine working with a heat source (fire) and validated a mathematical model of heat and mass transfer in such settings. Using experimental measurements, we verified the model’s accuracy. It is important to note that our experimental and theoretical analyses focused solely on the thermal effects of a fire, without considering the release of harmful impurities. Using the validated model, we conducted multiparameter simulations to identify the conditions leading to the formation of a thermal slug in an inclined mine working and the subsequent reversal of air flow. The simulation data enabled us to determine the dependency of the critical heat release rate on the aerodynamic parameters of the mine working. Additionally, we evaluated the changes in average air density within a mine working at the critical heat release rate. These findings are crucial for the further development of a network-based method to analyze air flow stability in mine ventilation networks during fires.

Исследование процессов тепломассопереноса в нефтяной скважине с~призабойным нагревателем различной длины

This paper considers a three-dimensional mathematical model of heat and mass transfer in an oil well with a bottom-hole heater. The vertical section of an oil well with an electric bottom-hole heater device for wells with highly viscous and paraffinic oil was investigated. The bottomhole heater is a monolithic cylinder located in the lower part of the tubing. The tubing contains perforations through which the oil fluid enters the tubing. The use of a local heater in the near-wellbore area makes it possible to increase the temperature of the fluid flowing through it, thereby reducing the viscosity of the oil and the load on the electric centrifugal pump, for which the critical value of the viscosity of the pumped medium is determined. The implementation of this model was carried out by the finite volume method using the ANSYS engineering simulation software. The geometry of finite elements and the finite volume mesh generated, an analogue of a continuous computational domain, were constructed by the MESH preprocessor. The finite volume mesh consists of polyhedral elements. Using the model, the fields of temperature, velocity and viscosity were obtained throughout the entire volume of the area under study. The curves showing the dependence of the average temperature of the cross section on the longitudinal coordinate of the tubing and the dependence of the average temperature at the inlet to an electric centrifugal pump on the heater power are presented. The viscosity value at the maximum permissible temperature of the heater, as well as the value of sufficient heater power to ensure uninterrupted pumping of petroleum liquid, were determined. The results obtained can be used to significantly improve the operating efficiency of an electric centrifugal pump, to increase the turnaround time and to reduce material costs during field development.

Enhanced water permeability and antifouling properties of cross-linked graphene oxide composite membranes with tunable d-spacings

Low flux and membrane fouling are major challenges in membrane distillation (MD) for treating concentrated wastewater. This study compared the performance of GO composite membranes with different interlayer distances, by covalently bonding the terminal amine groups of ethylenediamine (EDA) and 1,12-diaminododecane (DADD) with the carboxyl groups present on the GO sheets. The results indicated that the GO-DADD/PTFE membrane, with longer carbon chain cross-linking, achieved the highest flux and antifouling properties. At 70 °C, the pure water flux reached 68.5 kg/m2·h, and the fluxes for treating NaCl, HA containing NaCl, and BSA containing NaCl were 29.8 %, 37.1 %, and 38.5 % higher than the uncrosslinked GO/PTFE, and 95.7 %, 121.2 %, and 146.9 % higher than the PTFE membrane, respectively. Through mathematical models for mass and heat transfer, the study identified the key to this enhancement as the increased d-spacing within the GO layer due to cross-linking, which weakened the Kelvin effect and enhanced the vapor partial pressure on the hot side. The unique surface structure and electrostatic interactions induced by long-chain cross-linking further boosted the antifouling effect. These modifications not only overcome the typical trade-off between retention rates and flux but also offer a scalable and efficient solution for advanced membrane distillation applications.

Mathematical modeling of heat exchange for efficient automated control systems

The article deals with the problem of mathematical modeling of heat transfer processes, taking into account a large number of factors affecting these processes and a variety of mathematical modeling methods. The article discusses the idea of developing a universal and flexible model that could quickly adapt to different initial modeling conditions and take into account various parameters for further use of the mathematical model in the synthesis of automatic control systems. The paper discusses the main aspects of mathematical modeling of heat transfer and the creation of a mathematical model in distributed heat exchanger parameters with the possibility of changing the properties and parameters of the equipment. The paper analyzes previous studies and identifies the problems of existing methods of mathematical modeling of heat transfer, such as lack of versatility, complexity, and insufficient accuracy. The paper goes on to review different approaches to mathematical modeling of heat transfer, such as models with a group of parameters, models in distributed parameters, and models based on artificial intelligence. The article provides an overview of model implementation methods and their advantages and disadvantages. Based on this analysis, the authors propose a new mathematical model of heat transfer in distributed parameters, which should be universal, easy to use, and accurate in accordance with the requirements of synthesizing automated control systems. The authors also outline the methodology for achieving this goal, which includes the implementation of the geometry of the heat exchanger, the implementation of conditions and mathematical modeling, as well as the study of the influence of parameters and the formation of transients. The general conclusion of the article is that the developed mathematical model of heat transfer can be used to synthesize automatic control systems for heat exchange processes in various industries.

Numerical simulation of melt flow and heat transfer in casting filling process based on SPH

There is a great influence of the melt filling process on the quality of castings. Smoothed particle hydrodynamics (SPH) that materials are approximated by free particles rather than by fixed grids is applied to accurately predict fluid flows involving complex free surfaces. In this paper we present a mathematical model of melt flow and heat transfer by using SPH method. A novel approach is used in the governing equations to ensure stable numerical schemes and homogeneous particle distributions. The SPH heat equation takes into account the thermal release during phase transition and is more suitable for alloy solidification. The solid wall boundary conditions are slightly modified to satisfy the filling simulations. Several case studies are carried out to predict significant details about the filling order and flow structures in the mold cavity. The velocity and temperature distributions during different stages of melt filling are also given. The results show that this proposed model allows us to understand the predisposition of defects such as gas porosity and weld lines in the castings. These predictions can be used as inputs for improving process parameters, venting and cooling systems design.

Improved heat transfer mathematical model forpyramid shaped seasonal heat storage water pit and the influence of boundary conditions

Seasonal heat storage can make use of urban waste heat for low-carbon heating throughout the year. Previous models for pyramid shaped water pit have limited adaptability and ignore the impact of soil temperature in the early stages of operation on the performance of water pits. This article combines two classic mathematical models to establish a mathematical model that can adapt to various sizes of inverted pyramid shaped water pits. The validation of this model was conducted using experimental data from 60000 m3 water pit of Dronninglund, and the influence of boundary conditions for this module were calculated and discussed. The results showed that the root mean square errors of the simulated top, bottom, and average temperature of the water pit were 3.07 °C, 2.39 °C, and 1.37 °C, with relative deviation ratios of 4.25 %, 2.27 %, and 6.62 %, respectively. Furthermore, it was found that for every 5 °C increase in the set average soil temperature, the storage efficiency of the water pits increases by 0.4 %∼0.5 %. In the case of common top insulation of the water pit, the total heat loss at the top, side walls, and bottom are 66.83 %, 31.8 %, 1.37 %. While considering comprehensive insulation in all directions, the heat loss rate for the top, side walls, and bottom are similar with the former, being 67.84 %, 30.79 %, and 1.37 %, respectively. The proposal and findings of this article provide a basis for simplified optimization planning and design of large-scale seasonal heat storage systems.

Applying a heat transfer mathematical model for the cryopreservation of rainbow trout (Oncorhynchus mykiss) sperm: How straw location over liquid nitrogen level affects freezing rate and fertilization yield

Cryopreservation of rainbow trout semen under field conditions was analyzed. Straw location over liquid nitrogen level is a crucial variable that affects freezing rate and fertilization yield due to changes in nitrogen vapor external temperature. The objectives were: to analyze cryopreservation protocols by experimentally measuring the cooling rates and fertilization yield of 0.5 ml plastic straws located in nitrogen vapor at different heights corresponding to different external temperatures; to numerically simulate the freezing process, by solving the heat transfer partial differential equations with the corresponding thermo-physical properties of the biological system and the plastic straw; to evaluate and analyze the surface heat transfer coefficient (h) during the freezing process of the straws; to introduce a new variable, the characteristic freezing time (tc), that enables comparison between protocols; this variable was defined as the elapsed period between the initial freezing temperature and a final reference temperature of −40 °C (temperature in which more than 80 % of the water is in a frozen state). The mathematical model predicted the temperature distribution inside the straw, showing a low effect of straw plastic materials (polyethylene-terephthalate glycol, polyvinyl-chloride, and polypropylene) on freezing rates. The average h value obtained from numerical simulations was 25.5 W/m2 K, close to that obtained from the analytical Nusselt correlation for natural convection. An improvement on fertilization trials was observed when the average external nitrogen temperature was −129.6 °C (temperature range: −94 to −171 °C) with an average tc of 56.8 s (ranging between 47 and 72 s). These results corresponded to a height above the level of liquid nitrogen of 2 cm. Comparison with literature reported data showed satisfactory results. Applying mathematical models in the cryobiology field achieved results that are relevant for cryopreservation activities.

Thermal decomposition and combustion of interior design materials

Research findings on the patterns of thermal decomposition and combustion are reported for widely used interior design materials. The experiments were conducted using a hardware and software system including a thermogravimetric analyzer (to record the characteristics of thermal decomposition), a gas analyzer (with H2, CH4, H2S, SO2, CO and CO2 sensors) and a high-speed camera (to record the characteristics of ignition and combustion). The temperature of the oxidizing medium ranged from 500 to 900°C to investigate the conditions of thermal decomposition initiation and sustained combustion. It was established that the highest concentrations of toxic emissions were typical of the combustion of polypropylene at a maximum temperature of the oxidizing medium (900°C). Wood showed the shortest ignition delay time and the longest duration of combustion. The experimental data were used for a physical problem statement and mathematical model of heat and mass transfer to explore the thermal decomposition and combustion of interior design materials in different rooms. A comparison of the experimental findings with the mathematical modeling results validates the developed model. The growth rates of carbon monoxide and carbon dioxide concentrations were determined for construction (wooden) and interior design (polymer) materials. The maximum concentrations of CO and CO2, and the minimum times taken to reach their threshold values corresponded to wood and polyvinyl chloride panels. This research provides a deeper insight into the thermal decomposition of a wide range of fuels and the formation of gaseous pyrolysis products of these fuels. The results obtained can be used to evaluate the toxicity of construction and interior design materials during compartment fires as well as to estimate the safe egress time and risks involved in the process. They can also serve as a database for the development and testing of mathematical models describing fire outbreaks and propagation in confined spaces.

Contribution to the use of palm kernel oil methyl esters as liquid bio-insulators in distribution transformers: Experimentation and simulation of heat transfer

This work examines the potential use of palm kernel oil methyl esters (PKOME) as liquid bio-insulators in distribution transformers. A mathematical model of heat transfer inside a transformer is developed and solved using COMSOL Multiphysics software. The results of the model are validated by experimental data, showing a temperature variation of 31–81.8 °C in the measurements and 31–82.5 °C in the simulation. This validation confirms the accuracy of the model in predicting the temperature distribution inside the PKOME-filled transformer, paving the way for their use in distribution transformers.

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy.

The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods.

Study on heat transfer law of moving temperature variable gas in thermoacoustic plate stack

Taking gas and the heat transfer process between gas and plate as the research object, the mathematical model of heat transfer in one working cycle by moving variable temperature air mass under the action of sound field is established, which provides a new idea for understanding thermoacoustic effect. The influence factors in the model are analyzed and it is found that the amplitude of the air mass has a significant influence on the heat transfer, and the heat transfer of the air mass in one working cycle is proportional to the square of the amplitude. In a certain working environment, the thermoacoustic refrigerator has a critical operating frequency, and only when the operating frequency is greater than the critical frequency can refrigeration be realized. The critical operating frequency is independent of the amplitude and increases with the increase of the stack temperature gradient. With the pressure belly point as the reference position, the greater the distance from the reference position, the greater the critical operating frequency. On this basis, the idea of short plate overlapping is put forward and the formation mechanism of temperature difference between two ends of plate overlapping is explained.

Перспективные конструкторские решения для сушки жидких пищевых систем

An assessment of promising alternative design solutions for drying liquid food systems is given. Drying technology and techniques for removing moisture from liquid materials in a dispersed state have found widespread use in the food industry. The almost instantaneous drying of the sprayed particles in the coolant flow causes the formation of a developed phase interaction surface and acceleration of heat and mass transfer procedures, as well as the exclusion of overheating of the material due to intensive volumetric evaporation of moisture. A number of dryer designs have been developed to eliminate disadvantages (such as the large size of the dryers and their relatively high energy consumption and complexity of structural elements) or to reduce their impact on the course of the dehydration operation. The design specifics of devices for dewatering in the atomized state are due to the methods of supplying thermal energy, technological conditions and limitations, parameters of the dried product and the final powder substance, as well as its specific yield, peculiarities of the spraying operation, etc. The justification of the method of spray drying of liquid food material and the constructive use of the apparatus should be based on the study of a set of parameters and characteristics of the dehydration object, as well as on the construction and solution of a mathematical model of heat and mass transfer and exchange processes at the boundary of the phase section, as well as their mechanism in the development of a rational method of moisture removal to ensure the quality of finished products and energy- and resource saving. The proposed plant designs are recommended for organizing the drying process of liquid products, in particular for drying broths in fish production technologies.

Formation of subaerial taliks in Larsemann hills, princess Elizabeth land, East Antarctica

This study presents a mathematical model of heat and mass transfer for modelling the formation and evolution of taliks in the upper subsurface of the Larsemann Hills in East Antarctica. Four simulation scenarios were considered. The first one showed that thawed areas cannot form under snowfields. The second and third scenarios demonstrated the taliks did not form if the snow melted immediately after set the positive air temperatures and covered the surface 20 days before the set of negative air temperatures or immediately after that. According to the last scenario, talik forms when snow cover persists even with positive air temperature, and snow falls before the air temperature becomes negative. Modelling demonstrates that taliks in the Larsemann Hills exist, but they are mostly in an unstable state.

Design and Optimization of a Mixed-Flow Drying Chamber for Tiger Nuts Based on CFD-DEM Heat and Mass Transfer Model

In order to solve the problem of inconsistent moisture content in particles during the drying process of tiger nuts (Cyperus esculentus) due to uneven air flow and temperature distribution in the drying chamber, an open-hole corner box was designed based on the principle of negative pressure micro-perforated air supply. Using computational fluid dynamics (CFD) and discrete element method (DEM) simulation, coupled with the basic theory of interphase heat and mass transfer, a mathematical model for interphase heat and moisture coupling transfer was established. The effects of different aperture rates of corner boxes in the drying chamber, spatial location arrangement, and other related variables on the airfield distribution, temperature field distribution, tiger nut temperature, and moisture content changes were investigated. The results show that the average air velocity below the air inlet gradually increases as the opening ratio increases. When the opening rate is 0.33%, the wind field uniformity is better, and the inhomogeneity of the drying chamber wind field is improved. As the lateral distance increases, the consistency of the moisture content distribution increases and then decreases, and the flow rate of the tiger nuts gradually increases when the grain is discharged. The rate of decrease in water content decreases gradually with the increase in longitudinal distance. When the wind speed reaches 4 m/s, the drying chamber wind field is more uniform, and the water vapor diffusion efficiency at the outlet is basically the same. Therefore, the appropriate corner box has a horizontal distance of 320 mm and a longitudinal distance of 420 mm, providing a basis for the design of tiger nut drying equipment.