Thermal Radiation Effects Research Articles

MHD hybrid nanofluid and slip flow towards an exponentially stretching/shrinking sheet with nonlinear thermal radiation and nonuniform heat source/sink

The analysis of heat transfer of a hybrid nanofluid [Formula: see text] in the MHD stagnation point motion toward an exponentially expanding/shrinking sheet with a nonuniform heat source/sink, multiple slip conditions and nonlinear thermal radiation effects are carried out in this study. By applying the similarity transformation, the governing equations are transformed into Ordinary Differential Equations (ODEs). The Runge–Kutta method using bvp4c in MATLAB software is implemented to explain the ODEs. The results show that the local Nusselt number is decreased while the skin friction coefficient remains unaltered by the accumulation of thermal slip, space, and temperature-dependent parameters.

Chemically reacted blood Cu O nanofluid flow through a non-Darcy porous media with radially varying viscosity

The study investigates the flow of a Newtonian Cu O nanofluid through a non-Darcy porous medium with radially varying viscosity, which is crucial for various industries such as pharmaceuticals, chemicals, nuclear, solar, and solar technologies. The peristaltic motion of the nanofluid is studied with thermal radiation and chemical reaction effects, and the viscosity varies with both radius and axial coordinates. The study assumes low Reynolds and long wavelength assumptions and uses the homotopy perturbation technique to obtain a semi-analytical solution of velocity, temperature, nanoparticle concentration, and skin friction. The results show that axial velocity increases with the increase of slip velocity and viscosity parameters, while wave amplitude and chemical reaction parameters increase while nanoparticle concentration decreases. High viscosity parameters allow fluid nanoparticles to gain more active energy and move more freely, which is the main idea behind crude oil refinement. This physical modeling is essential for physiological flows, such as stomach juice flow during endoscope insertion.

Mixed convection hybrid nanofluid flow over a stationary permeable vertical cone with thermal radiation and convective boundary condition

AbstractMany real‐world devices, such as heat exchangers, geothermal reservoirs, and cooling systems, utilize the concept of boundary layer flow across a cone geometry. The current study presents and analyses the mathematical formulation for the mixed convection flow of a hybrid nanofluid over a permeable stationary cone. The heat transfer analysis considers the effects of thermal radiation and convective boundary condition. Numerical and statistical analyses of this flow problem yield new, physically significant results. The numerical analysis is carried out using the bvp4c solver in Matlab. Similarity transformations are performed to obtain a system of nonlinear ordinary differential equations from the governing partial differential equations and boundary conditions. In both assisting and opposing flows, spherical‐ and platelet‐shaped nanoparticles are observed to produce the lowest and highest local skin friction coefficient, respectively. The spherical‐ and blade‐shaped nanoparticles also offer the highest and lowest local Nusselt number, respectively, with a difference of 6.4% (assisting) and 6.03% (opposing). Meanwhile, the increase in the mixed convection parameter raised the velocity profile but diminished the temperature profile of the hybrid nanofluid. Then, the relationship of the Biot number , suction , and thermal radiation ) parameters with the local Nusselt number is investigated through the response surface methodology (RSM). The local Nusselt number for the current flow problem is estimated to be maximized at 0.814323 (assisting) and 0.814629 (opposing) when these parameters are at the highest range of , , and . Several researchers had presented experimental studies conducted at different temperatures (15, 25, 35°C), mass flow rates (ranging from 0.00076 to 0.041 kg/s), and nanoparticle concentrations (0.387, 0.992, 3.12, 4.71 mass%).

Finite element analysis of cross fluid model over a vertical disk suspended to a tetra hybrid nanoparticles mixture

Nanoparticles have numerous applications and are used frequently in different cooling, heating, treatment of cancer cells and manufacturing processes. The current investigation covers the utilization of tetra hybrid nanofluid (aluminum oxide, iron dioxide, titanium dioxide and copper) for Crossflow model over a vertical disk by considering the shape effects (bricks, cylindrical and platelet) of nanoparticles, electro-magneto-hydrodynamic effect and quadratic thermal radiation. In the current inspection model is first derived given PD-equations and then altered into a system of OD-equations by including similarity variables. The converted ordinary differential equations are solved by using the finite element procedure and the impact of the solution against numerous involved parameters is displayed through tables and graphs. It is observed that tetra-hybrid nanoparticles are recommended better in industrial applications where the highest production of thermal energy. Moreover, an enhancement of thermal production can be achieved utilizing different values of the magnetic parameter, time relaxation number, variable thermal radiation number and magnetic induction number but the opposite trend has been noticed with the effects of radiation number.

Heat and mass transfer characteristics of Al2O3/H2O and (Al2O3+Ag)/H2O nanofluids adjacent to a solid sphere: A theoretical study

A theoretical study is carried out to explore the heat and mass transfer features in the flow of two types nanofluid, i.e., A l 2 O 3 / H 2 O micropolar nanofluid and ( A l 2 O 3 + Ag ) / H 2 O hybrid nanofluid, adjacent to a solid sphere. Furthermore, simultaneous effects of linear thermal radiation and chemical reaction are also explored on the heat and mass transfer characteristics. In mathematical formulation basic conservation laws are utilized along with the Soret and Doufer effects as a coupling agents in the energy and mass concentration equations. The normalized variables are used to transform the governing system of non-linear partial differential equations into the system of dimensionless partial differential equations. Stream function reduces the number of dependent variables and the resulting system is solved numerically by Keller box method. Several plots are presented to explore the impact of involved parameters on the different profiles and engineering interest quantities for both types of fluids. The temperature profile and Nusselt number are large in magnitude for hybrid nanofluid as compared to A l 2 O 3 /water based nanofluid. The heat transfer and mass transfer rates rises with thermal radiation parameter and chemical reaction parameter, respectively.

Evaluation of mixed convection-radiation flow of a viscous fluid restricted to a vertical porous channel: A comparative study

This article examines the steady mixed convection flow in an upstanding porous channel of a hydrodynamic viscous fluid that is electrically conductive due to the thermal radiation effect. The homotopy perturbation method (HPM) is used to generate analytical solutions to the governing differential equations that characterize the velocity and temperature flow properties. For relevant temperature jump and velocity slip situations, the effects of mixed convection parameters, thermal radiation parameters, and magnetic field effects on the velocity field, skin friction coefficient, temperature distribution, and heat transfer rate have been described. This research also analyses and compares the results obtained by Abbas et al. (2020) with this present work when HPM was used for the limiting cases. It is interesting to report that an excellent agreement was established, thereby authenticating and validating the accuracy of HPM as a strong tool for obtaining approximate solutions. According to the results of this study, it is possible to effectively control the velocity and temperature gradients by varying the main relevant parameters such as: the mixed convection parameter for a constant pressure gradient, the thermal radiation parameter, the magnetic field effect, the rarefaction parameter, and the wall ambient temperature difference ratio parameter

Numerical Simulations of Chemically Dissipative MHD Mixed Convective Non-Newtonian Nanofluid Stagnation Point Flow over an Inclined Stretching Sheet with Thermal Radiation Effects

The study of non-Newtonian nanofluid stagnation point flow over an inclined stretching sheet with thermal radiation effects aims to understand how the fluid's non-Newtonian behavior, nanoparticles, the inclined sheet, and thermal radiation affect velocity profiles, temperature distribution, shear stress, and heat transfer rates. It might be used in materials processing, chemical engineering, and energy systems, where understanding fluid behavior in complicated settings is essential for process optimization and system efficiency. The flow problem is reflected in a set of partial differential equations (PDEs) that serve as the governing equations. After appropriate reformatting into Ordinary Differential Equations (ODEs). Mathematica's NDSolve technique is implemented to do a numerical treatment of the dimensionless equations once they have been translated. The upsides of this strategy lie in its ability to automatically track errors and select the best algorithm. Various dimensionless parameters effects on velocity, temperature, and nanoparticle concentration have been studied, and the results are graphically shown. These include the Casson parameter, Brownian motion and thermophoresis, chemical reaction parameter, thermal radiation, viscous dissipation, and mixed convection parameter. The Casson parameter slows down the velocity and speeds up the distributions of temperature and concentration. The skin friction coefficient increases rapidly with increasing tilt and thermophoretic impact amplitudes. The insights were cross-referenced with previous inquiries in order to validate their veracity. All indications are that it complies rigorously and is highly accurate.

Investigating the Impact of Magnetohydrodynamic (MHD) and Radiation on the Casson-Based Nanofluid Flow over a Linear Stretching Sheet in a Porous Medium with Heat Source or Sink

This study delves into the magnetohydrodynamic (MHD) flow of Casson-based nanofluids over a linear stretching sheet, accounting for multiple influencing factors. These findings offer significant real-time applications across a spectrum of fields, including energy generation, environmental engineering, and materials science. The acquired insights into Casson-based nanofluid behaviour within magnetohydrodynamic contexts can foster efficiency improvements, energy conservation, and enhanced overall system and process performance. Furthermore, the current study aims at Casson-based nanofluid's magnetohydrodynamic flow across a linear stretching sheet considering effects of thermal radiation, heat source/sink, and porosity. The governing equations are converted to ordinary differential equations by using similarity transformations. The Runge-Kutta-4 method, along with the shooting technique, is used to solve the reduced equations. The effects of dimensionless parameters, magnetic, Casson, thermophoresis, thermal radiation, and Brownian motion on velocity, thermal, and concentration profiles are considered in the study. As the magnetic and Casson parameters are increased, the findings indicate a reduction in the thickness of the momentum boundary layer. Moreover, the fluid temperature intensifies with the enhancement of thermophoresis and Brownian motion of particles. Finally, for various combinations of applied parameters, the values of skin friction coefficient, Nusselt number, and Sherwood number are obtained and are shown in the tables. The research is unique in a way that incorporates the impacts of heat source/sink and porosity as well as a more precise description of Casson nanofluid flow when compared to earlier findings. The novelty of the investigation lies in the implementation of a heat source/sink and porosity to obtain refined Casson nanofluid flow.

Investigation of Magnetized Casson Nanofluid Flow along Wedge: Gaussian Process Regression

An unsteady two-dimensional magnetized Casson nanofluid flow model is constructed over a wedge under the effect of thermal radiation and chemical reaction. The multiple slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. This study investigates the application of soft computing techniques to address the challenges posed by the complexity of problem modeling and numerical methods. Traditional approaches incorporating various model factors may struggle to provide accurate solutions. To resolve this issue, Gaussian process regression (GPR) is employed to predict the solution of the proposed flow model. With the help of the numerical shooting method together with Runge–Kutta–Fehlberg fourth-fifth-order (RKF-45) reference data, the GPR model is trained. The numerical simulation illustrated that the Casson fluid parameter β and the unsteadiness parameter S strengthen the friction factor, and the heat transfer rate is enhanced as the radiation parameter Rd becomes larger. In addition, the Biot numbers Bi1 & Bi2 lead to strengthen nanoparticle temperature; an opposite behavior is noticed with the skin friction coefficient S˜fxRex0.5, heat transfer rate H˜tx Rex0.5, and nanoparticle transfer rate C˜txRex0.5. The GPR model with the exponential Kernel function provided better performance than other functions on both training and checking datasets to predict S˜fxRex0.5,H˜tx Rex0.5, and C˜txRex0.5. Statistical metrics including RMSE, MAE, MAPE, MSE, R2, and R are employed to check the accuracy and convergences of the predicted and numerical solutions obtained through GPR and RKF-45. It is observed that all three GPR models had an R2 value of higher than 0.9. The proposed study demonstrates the advantages of employing soft computing methods (GPR) to effectively analyse the behavior of complex flow models.

Consequences analysis of a natural gas pipeline: The case of the trans‐Anatolian natural gas pipeline

AbstractIndustrial accidents include fire, explosion, and toxic substance spread involving hazardous substances. They threaten the health of many people, cause permanent or long‐term pollution of the natural environment, cause a high degree of property damage, and require a large‐scale emergency response. Pipelines that transfer hazardous chemicals over a large area are risky for industrial accidents. In this study, we aimed to analyze the consequences of a possible industrial accident at the Edirne Ipsala compressor station in the trans‐Anatolian natural gas pipeline (TANAP). Analyses were carried out with the ALOHA software on two hypothetical scenarios: In Scenario 1, the chemical escapes from the pipe without the gas burning; and in Scenario 2, the chemical escapes from the pipe with the gas burning (jet fire). In the analysis of overpressure effects, TNT EM and TNO MEM were used besides the software. The largest effect distance (≈5000 m) was determined in the flammable area as a result of Scenario 1, and the prominent hazard property of the chemical was supported. The overpressure effects obtained with TNO MEM and the software were compatible with each other, but the values obtained with TNT EM were less severe and quite different. In the analysis of overpressure effects, it is shown that the ALOHA software provided more conservative results and that buildings would collapse and lethal effects might occur at a distance of 1000 m from the source. ALOHA produced outputs integrated with GIS by providing thermal radiation and toxic effect threat zones as well as overpressure effects. ALOHA turns out to be a more convenient and practical tool for risk assessment studies and emergency plans.

Study of an unsteady magnetohydrodynamic‐free convective flow under parabolic ramped temperature and concentration in the presence of Soret and heat sink

AbstractThe purpose of this paper is to investigate the effects of Soret, thermal radiation, and chemical reaction on an unsteady magnetohydrodynamic free convective flow past an impulsively initiated semi‐infinite vertical plate with heat sink under parabolic ramped temperature and parabolic ramped concentration. Using some nondimensional parameters, the flow boundary equations in this case are first converted to dimensionless equations. The closed‐form Laplace transform technique is employed here to solve the partial differential equations and get the solutions for fluid velocity, temperature, and concentration. The velocity, temperature, and concentration of the fluid tend to vary with the effect of various flow factors. These changes are graphically represented and analyzed. Differences in skin friction, Nusselt number, and Sherwood number for the different relevant parameters are also recorded. The Soret number hikes the fluid velocity and concentration. The rate of heat transfer, mass transfer, and momentum transfer improves due to the application of parabolic ramped conditions.

Integrating ISPH simulations with machine learning for thermal radiation and exothermic chemical reaction on heat and mass transfer in spline/triangle star annulus

This work integrates incompressible smoothed particle hydrodynamics (ISPH) with machine learning (ML) to examine the uses of two different domain shapes, spline star-domain, and triangle star-domain, on double diffusion of nano-encapsulated phase change material (NEPCM). The effects of thermal radiation and exothermic chemical reactions are conducted in this work. The hexagonal-shaped is located inside the center of the star-shape carrying (Th&Ch). The left/right walls of the star shape are kept at (Tc&Cc) and the other walls have an adiabatic condition. It is recommended to examine the smoothness of closed curves in the heat and mass transfer by changing the triangle to spline curves. The present investigations of transmission of heat and mass of NEPCM within a complicated star shape can be employed in cooling systems of electronic/battery, heat exchangers, food processing, and chemical engineering. The ISPH simulations are executed for the pertinent parameters, Darcy number, Frank-Kamenetskii number, Rayleigh number, Dufour number, Soret number, and thermal radiation parameter. The performed simulations showed the significance of the spline star domain compared to the triangle star domain in smoothening the nanofluid flow and double-diffusive convection in an annulus. Frank-Kamenetskii number is a promising factor in the enhancement of heat transfer and controlling the phase change zone within an annulus. At a spline-star cavity, the maximum velocity rises by 32.32 % and 54.95 % when the Frank-Kamenetskii number grows from 0 to 5, and thermal radiation increases from 0 to 5. Soret number works effectively in enhancing the distribution of concentration at large temperature differences. Machine learning plays a vital role in many engineering applications. Hence, ML's powerful capabilities to predict the average Nu‾ and Sh‾. In the proposed ML model, the dimensionless time and thermal radiation parameter are used as input to the ML model, while their corresponding numeral estimated values of Nu‾ and Sh‾ are used as output targets for the ML model. The values of Nu‾ and Sh‾ are predicted by the suggested ML model with a comparatively small error less than 1 %.

Peristaltic transport of hybrid nanofluid under the effects of thermal radiation through asymmetric curved geometry: a numerical approach

ABSTRACT Magnetohydrodynamics (MHD) has various applications in the field of medicine, particularly in drug delivery and hyperthermia treatment for cancer therapy to the affected area via peristaltic phenomena. Further elaboration is required to optimize the delivery method of hybrid nanoparticles with aluminum oxide and zinc oxide to the target area via the esophagus to get the best-desired results. Keeping the importance of MHD in mind, the present problem highlights the characteristics of Magnetohydrodynamics (MHD) peristaltic transport by incorporating the properties of nanoparticles of aluminum and zinc oxides when suspended in water through an asymmetric curved conduit. The governing equations are mathematically modeled under consideration of Hall current, viscous dissipation, ohmic heating, thermal radiation, and heat sink/source effects. The influence of magnetic field, velocity, and thermal slips is also considered. Negligible Reynolds number and long-wavelength approximations are used to overcome the complexity of the system. To compute the numerical solutions of the simplified nonlinear system, two different techniques are utilized via MATLAB and Mathematica. The outcomes of the different flow parameters on the hybrid nanofluid’s velocity, trapping phenomena, temperature distribution, heat transfer rates, and pressure gradient are analyzed through tables and graphs.

Impacts of thermophoretic deposition and thermal radiation on heat and mass transfer analysis of ternary nanofluid flow across a wedge

ABSTRACT Ternary nanofluids have attracted significant attention due to their improved thermal characteristics and adaptability for many applications. Nanoparticles interact with one another in complex ways and have a noticeable effect on heat transmission. Due to this, nanofluids have significant promise in several fields. Notably, investigating the behavior of ternary nanofluids via a wedge enables the optimization of heat transfer processes in heat exchangers, cooling mechanisms, and thermal control systems. The current study examines the effects of thermal radiation and thermophoretic particle deposition on the ternary hybrid nanofluid flow across a wedge. The governing equations are precisely modeled and solved numerically using Runge Kutta Fehlberg’s fourth-fifth order (RKF-45) approach and shooting procedure. The governing equations are reduced to ordinary differential equations (ODEs) using similarity transformations. The results are efficiently shown via visual depictions, facilitating a precise understanding of the outcomes. The study outcomes show that increased thermophoretic parameter and solid volume fraction decreases the mass transfer rate. Researchers may incorporate this comprehension to effectively utilize ternary nanofluids to enhance heat transfer in practical situations, as well as the development of technology and energy management.

Contrast enhancement method in aero thermal radiation images based on cyclic multi-scale illumination self-similarity and gradient perception regularization.

In aerospace, the effects of thermal radiation severely affect the imaging quality of infrared (IR) detectors, which blur the scene information. Existing methods can effectively remove the intensity bias caused by the thermal radiation effect, but they have limitations in the ability of enhancing contrast and correcting local dense intensity or global dense intensity. To address the limitations, we propose a contrast enhancement method based on cyclic multi-scale illumination self-similarity and gradient perception regularization solver (CMIS-GPR). First, we conceive to correct for intensity bias by amplifying gradient. Specifically, we propose a gradient perception regularization (GPR) solver to correct intensity bias by directly decomposing degraded image into a pair of high contrast images, which do not contain intensity bias and exhibit inverted intensity directions. However, we find that the GPR fails for dense intensity area due to small gradient of the scene. Second, to cope with the cases of dense intensity, we regard the dense intensity bias as the sum of multiple slight intensity bias. Then, we construct a cyclic multi-scale illumination self-similarity (CMIS) model by using multi-scale Gaussian filters and structural similarity prior to removing the dense intensity layer by layer. The result acts as coarse correction for GPR, which does not need to be overly concerned with whether the result has intensity residuals or not. Finally, the coarse corrected result is input to the GPR module to further correct residual intensity bias by enhancing contrast. Extensive experiments in real and simulated data have demonstrated the superiority of the proposed method.

Effects of nonlinear thermal radiation on the efficiency of building integrated photovoltaic systems with nanofluid cooling.

The nonlinear effects of thermal radiation on the free convection flow of certain nanofluids along a heated wall are studied numerically using an original finite-difference method. Nanofluids are used to improve the performance of flat and curved integrated photovoltaic modules. The partial differential equations governing the flow are difficult to solve due to the strong non-linearity of the radiative term. In contrast to previous studies, the problem is solved directly without linearization by Rosseland's nonlinear approximation. The proposed numerical method is validated with results from the literature. The effects of nonlinearity and various physical parameters such as time, volume fraction and radiation parameter on the velocity, temperature, Nusselt number and skin friction coefficient of the CuO-water nanofluid are analyzed and presented graphically. A comparative study between the solutions given by the linear and non-linear problems reveals that Rosseland's linear approximation is no longer valid when the effect of thermal radiation is significant. On the other hand, the non-linear model better reflects the physical phenomena involved in the cooling process. Finally, a comparison of the performance of five nanofluids (CuO, Ag, Al2O3, Cu and TiO2 in water) shows that the Cu-water nanofluid performs best, with a high heat transfer rate and low shear stresses.

Thermal radiation effects on oscillating frequency of heat transfer of Darcy–Forchheimer nanofluid with chemical reaction and applications in machining operations

The advancement of cutting tool components and design is presently promoting innovative developments in numerous different machining-related industries. The characteristics of nanofluid are important for machining activities such as the drilling process, grinding, rotating, milling, and cutting. Various machining procedures require distinct lubricating oils and nanofluids for cutting-edge innovations. The significant contribution of the current mechanism is to explore the fluctuating heat and mass flux of Darcy–Forchheimer chemically reactive nanofluid along a buoyancy-driven porous plate under solar radiation region. Flow through a Darcy medium has a wide range of applications such as the use of oil in various hydrothermal transfer control, radioactive nuclear disposal systems, water improvement, and filtration of water. The dimensional model is transformed into non-dimension for scaling factors. The primitive-based transformation is applied on steady and oscillatory parts for smooth algorithm in FORTRAN language machine by using an implicit finite difference method. The numerical and graphical results of velocity, temperature, and concentration are executed by the Gaussian elimination method. To enhance the frequency and wavelength, the impact of solar radiations is applied on periodic nanoparticles with Darcy–Forchheimer relation. The novelty of this proposal is to explore the wave oscillations, amplitude, and phase angle of thermal and concentration boundary layer of Darcy–Forchheimer nanofluid flow under chemical reaction and solar radiation region. It is noticed that the prominent wavelength and frequency in thermal and concentration boundary layers is generated under porous and solar radiation region. The significance of temperature variation increases as solar radiation, chemical reaction, Brownian motion, and thermophoresis increase. It is found that minimum oscillation in heat transport is observed as Pr decreases but maximum oscillation in heat transfer is sketched as Pr enhances.

Thermal Radiation Effects on 2D Stagnation Point Flow of a Heated Stretchable Sheet with Variable Viscosity and MHD in a Porous Medium

Thermal Radiation Effects on 2D Stagnation Point Flow of a Heated Stretchable Sheet with Variable Viscosity and MHD in a Porous Medium

DARCY-FORCHHEIMER FLOW OF A CONDUCTING MICROPOLAR FLUID AT A STRETCHING SHEET WITH CONVECTIVE BOUNDARY CONDITIONS

In this paper we study the Darcy-Forchheimer flow of a magnetohydrodynamic (MHD) micropolar fluid over a stretching surface with convective boundary conditions. The effects of viscous dissipation, thermal radiation, activation energy, and chemical reaction, along with Dufour and Soret effects, are considered and analyzed. By using a suitable similarity transformation, the governing partial differential equations (PDEs) are converted into a system of nonlinear coupled ordinary differential equations (ODEs). The non-linear ODEs are solved numerically by a shooting technique with the bvp5c MATLAB package. The effects of the physical parameters on the velocity, the micro-rotation, the temperature, and the concentration fields are analyzed through graphs and tables. The present results are validated with the results in the existing literature for some special cases. It is observed that an increase in the magnetic strength leads to a decrease in the velocity field. However, the thermal radiation parameter and the Eckert number significantly boost the temperature distribution. The concentration field is improved by the activation energy parameter. We believe that this investigation has a definite bearing to industries such as heat exchangers and lubricant refining process.

Finite Element Analysis for NEG coated vacuum chamber based on ANSYS Workbench

The Hefei Advanced Light Facility (HALF) is a diffraction limited storage ring (DLSR) being constructed. As the main component of the storage ring vacuum system, the vacuum chamber transports the beam and withstands the thermal effect of synchrotron radiation simultaneously. The thermal and mechanical condition of the vacuum chamber of HALF were quantitatively analysed by means of ANSYS Workbench in this work. Combining the Computational Fluid Mechanics (CFD) and Finite Elements Analysis (FEA), the temperature and thermal stress maps of the vacuum chamber were calculated. The CFD calculation displays that the heat transfer coefficient between the water and the chamber is 7966-13093 W/(m2·°C). The thermal-mechanical simulation shows that the maximum temperature and thermal stress are 53.5 °C and 42.1 MPa, respectively. The static structural analysis was performed on vacuum chamber under the ultra-high vacuum condition, with the maximum stress of 1.7 MPa and the maximum deformation of 0.0003 mm. These results show that the vacuum chamber meets the design requirements and provide a critical theoretical basis for the design of the vacuum system of HALF.