Medical Ice Pack Cooling Duration Simulation Testing Optimization Exploration

Medical ice packs can be divided into two types: single-use and reusable; they are widely used in many places and in first aid in the home. The basic therapeutic principle is to use conductive heat exchange to apply a cold source to the local area and take away heat from the surrounding tissues. This process can reduce the temperature of the local tissues directly, constrict the blood vessels, and decrease the metabolic rate; it is one of the main reasons for reducing swelling after trauma, reducing the damage to the surrounding tissues, and safely lowering a high fever. No matter whether it is used in an emergency department for acute trauma management or at home for immediate injury control, the operation is generally to activate the pack and place it on the affected part of the body for a certain period of time.

But there is a practical problem now: there is no standard, high-efficiency test method for the duration of cooling. The cooling period is the time when the ice pack can still maintain an effective temperature gradient for treatment. Currently, the various testing plans of manufacturers are different; they mostly use static environmental conditions and do not take into account changes in the body or external heat. Therefore, the performance of the product label is not uniform. Therefore, there may be problems in the clinical application; for example, medical personnel or patients may remove the pack too early, reducing the effectiveness of treatment, or leave it on for too long during the cooling process, which could cause injury to the affected area. Also, there will be some errors in the data that lead to waste of medical resources; thus, the doctor will use too many ice packs in a row to compensate for the lack of performance indicators for the ice packs.

At the same time, with the rapid development of portable pre-hospital care and community medical services, the number of places where medical resources are used has also increased. It is natural that the resources at our disposal are limited here, and the conditions of the surrounding environment are also relatively harsh. Medical thermal management products need to be more accurate in predicting performance due to the demands of emergency personnel and community health workers; they will need to make important decisions quickly based only on the expected service life of their equipment. Without reliable simulation tests and improved performance prediction, the distribution of medical ice packs in these dispersed areas will still not be satisfactory. A strict, standardised way to determine and predict the length of time that cooling will last is required; thus, a relatively practical and urgent basis for conducting research on simulation test optimisation is laid.

Based on the above, the purpose and main contents of this paper are to construct a high-precision simulation model for medical ice packs and explore how it can meet the practical needs of clinical use. First of all, this paper intends to create a high-precision simulation model that can accurately predict the effective cooling duration of medical ice packs. By defining the basic heat transfer modes (conduction, convection, etc.) and the latent heat absorption in the phase change of the material, and combining the properties of the material and the boundary conditions, a thermal decay curve will be obtained. A set of standard operating rules can thus be used to forecast the cooling effect without repeatedly conducting physical tests. Second, the aim of the study is to improve the old simulation test system to reduce the difference between the test results in the laboratory and those in actual clinical practice. A fixed ambient temperature and a unified contact surface are used in the laboratory to make these results better reflect the actual conditions of the vascular perfusion and irregular tissues in clinical practice. By adjusting the simulation boundary conditions and applying correction algorithms based on clinical experience, the path of the test operation will be adjusted to obtain data that more closely reflects the actual effect of treatment. Thirdly, this paper will develop some general, low-cost testing plans that are suitable for all types of medical ice packs. Manufacturers can use modular simulation parameters and simplified calculation requirements to run standardised tests on ordinary equipment; thus, they will be able to obtain high-fidelity performance evaluations for different configurations of products. It has practical implications to achieve these goals. For the manufacturers of medical devices, after optimisation of the simulation model and low-cost testing programme, product performance test time will be reduced, R&D costs will decrease, the time to market will be shortened, and all regulations will be met. Accurate cooling time predictions are necessary for a good medical cooling plan; therefore, clinical staff need to be able to know how long the pack should last. It avoids premature replacement of the ice packs that would disrupt treatment and does not expose the affected area to the cold for too long to prevent frostbite due to medical causes; this way, the safety and efficacy of local physical cooling are improved. Finally, to provide a reliable forecasting tool, this study can help to use medical ice packs in the best therapeutic period and improve the results of patients with fever and other diseases in clinical practice.

At present, there have been many studies on the simulation of heat transfer for medical cold products in China and abroad. Early research mostly used experimental methods to determine the heat transfer law, but it was not sufficient to describe the change in temperature over time during the solid-liquid phase transition. With the development of Computational Fluid Dynamics and the enthalpy-porosity method, numerical simulation has become the main method to predict the cooling time of medical ice packs. Now researchers are employing these numerical methods to solve the Stefan problem, map the moving solid-liquid interface and predict the latent heat absorption process. At the same time, some human body thermal environment simulation platforms have been constructed. These systems are relatively simple constant-temperature flat plates, and there are also high-end thermal manikins with distributed heating circuits and controllable sweating systems to simulate the complex heat transfer between the ice pack and the human skin.

In the performance test of medical ice packs, the industry generally adopts the cooling time test to verify whether the temperature of the ice pack surface can meet the specified temperature threshold in a specific environment. Although these evaluation rules offer a general basis for comparison, they cannot meet the need for dynamic changes in actual cases in clinical practice.

A review of the literature shows many problems in practice at present. First of all, the fit between the simulation boundary conditions and the actual thermal characteristics of human skin is not good. Most of the simulations simply use simple constant heat flux or convective boundary conditions and do not consider the active thermoregulation mechanism of living bodies, the change in blood flow rate and the non-uniformity of heat transfer in space. Second, there is no integrated optimisation plan for testing procedures with many factors. Most of the experimental design only considers one factor, such as ambient temperature or initial pack temperature, and does not take into account how compression force, the conductivity of the packaging material and the curvature of local anatomy affect thermal resistance and cooling. Third, there is no consistency check between the simulation results and the actual clinical data. A lot of the numerical models are based on the data of insulated calorimeters and cannot be applied in real-life clinical situations where patients move and their metabolism changes.

Accordingly, this study aims to fill these gaps by setting up biofidelic boundary conditions, applying a multi-parameter optimisation algorithm in the testing plan, and addressing the problem of inconsistency between simulation data and clinical data; thus, it will aim to build a new model of thermal management for medical ice packs that is reliable and standardised for use in the clinic.

This section will outline the main research objects and structure of the thesis in a logical order, so that one can clearly know what will be studied theoretically and practically in the following part. Five areas will be studied in the main research. First, the theoretical model of phase change heat transfer of medical ice packs is studied. A mathematical model based on the enthalpy-porosity method is built to accurately describe the process of latent heat release and transient temperature variation at the solid-liquid interface, thereby determining the basic physical boundary conditions. Second, build a simulation testing platform according to the Gazebo framework and calibrate its parameters. Customise a thermal plug-in and add it to the physics engine; then, use the customised thermal plug-in to adjust the position and movement of the parts in the scene; and after adjusting the position and movement of the parts, calibrate them based on the actual data of the model. Third, screen the main influencing factors of the effective cooling time. Through orthogonal experimental design and variance analysis, the study is to extract the main variables, such as ambient temperature, initial phase fraction, and contact thermal resistance, from other noises; thus, the subsequent optimisation space is reduced. Fourth, to address the problem of low test efficiency, a multi-objective optimisation algorithm is developed. A non-dominated sorting genetic algorithm is used to search for the Pareto-optimal frontier of the test parameters in order to increase the effective cooling time and reduce the computation cost of simulation iterations. Fifth, compare the simulation results with the actual test data to verify the predictive accuracy and engineering reliability of the model, and ensure that the optimised parameters meet the requirements of medical practice.

According to the above contents, the structure of the full-text will be arranged in a logical order. The first chapter is the research background and purpose. The second chapter is the phase change heat transfer theory model. The third chapter is about the construction of the Gazebo platform and its calibration. The fourth chapter is Factor Screening and Multi-objective Optimization Algorithm Implementation. The fifth chapter will analyse the results of comparative verification and discuss the reasons for the deviation in practice. The last chapter will draw conclusions and discuss the prospects for engineering application. The above structure is to be an orderly, iterative process of abstract theory, virtual simulation, algorithm improvement and experiment confirmation, so that the reader can know more clearly the general background of the research and the specific technical paths used in the research.

Based on the basic energy conservation principle and enthalpy method, a numerical calculation model for the unsteady heat conduction of the medical ice pack is obtained; it can better deal with the moving boundary problem of phase change heat transfer. The medical ice pack is in a state of unsteady heat conduction throughout the entire melting and heat release period, so we need to build a suitable mathematical model to describe the variation in temperature over time. In order to obtain accurate results for the model, various kinds of ice pack media must have their thermophysical parameters entered correctly. For ordinary water-based ice packs, the parameters are the density, specific heat capacity and thermal conductivity of solid ice and liquid water, as well as the latent heat of fusion. The inputs of the phase change ice pack with sodium carboxymethylcellulose as the main body are apparent specific heat capacity and effective thermal conductivity; it is the thickening of the gel matrix that hinders natural convection in the solid-liquid phase transition.

To solve the strong nonlinearity of the phase change process, the finite difference method will be used to discretise the heat conduction control equation. A one-dimensional grid is built along the thickness direction of the ice pack to divide the space into several discrete nodes. The implicit finite difference scheme is used to ensure the numerical stability of the solution at any time step size. At each time step, the relationship between enthalpy and temperature is used to update the node temperatures, implicitly tracking the movement of the phase boundary without using an explicit front-tracking algorithm. After discretising it, the continuous partial differential equation has become a system of algebraic equations, and we will solve it iteratively to find the temperature distribution at different times during melting.

In addition, the calculation rule of the threshold for the effective cooling time has been explicitly stated. The cooling time is based on the temperature at the contact surface between the ice pack and the human body. The effective threshold is the moment when the contact surface temperature rises to the upper limit of the clinically safe and effective cooling temperature range. It is now possible to directly relate the theoretical heat production to the actual demands of clinical medicine and obtain clinically relevant data through simulation.

Finally, the reasonableness of the numerical model is checked by solving the basic analytical solution for one-dimensional unsteady heat conduction. Remove the phase change term first and compare the numerical results of single-phase transient heat conduction under the same boundary conditions and initial conditions with the exact Neumann solution to verify the discretisation accuracy and the logic of the algorithm. In order to ensure the reliability of the model, first verify and then add the nonlinearity of the phase change term for full simulation.

The boundary condition setting standard for the simulation of a thermal environment on the surface of human skin is a necessary condition for ensuring that the cooling time of a medical ice pack is accurately predicted. It mainly refers to converting the complex life and physical phenomena of soft tissue injury into calculable constraints, thus connecting the theoretical phase-change heat transfer with real-world clinical practice. The basic idea is that the simulated boundary should be in line with the actual thermal characteristics of the human body's skin when it is still after being injured; thus, the simulation results are scientifically reliable.

To determine the standard, the operational procedure will sequentially determine four necessary parameters. First, the range of the constant heat flux from the basal metabolism of local skin will be established; that is to say, a continuous internal thermal driving force of 40 to 80 Watts per square metre for the resting soft tissue will be used. Second, the thermal resistance value of common medical dressings or isolation layers between the ice pack and the skin should be included. Therefore, the heat transfer rate and the temperature difference at the interface will be different, so empirical data based on the material's thickness and thermal conductivity must be obtained. Third, a rule for how the skin temperature changes when in contact with a low-temperature ice pack will be constructed. This will determine a transient dynamic boundary that can quickly decrease first and then level off when the skin absorbs the latent heat of phase change material. Fourthly, set the heat transfer coefficient of the non-contact surface of the ice pack to the surrounding air; thus, the external convective and radiative heat loss of the ice pack will be determined, and then the total cooling time of the ice pack will be determined.

The actual effect of this standardised boundary is very significant. If the boundary conditions are not correct, simulation errors will be large and could be applied in clinical practice; thus, the predicted cooling time is not accurate. For the sake of consistency with the actual operating environment, specific rules for adjusting parameters will be set according to different simulation scenarios. The parameters of various parts of the human body will be changed based on their own blood supply and fat; for example, the extremities have less metabolic activity and thinner soft tissue, so their base heat flux is lower than that of the trunk. For different metabolic states of patients, such as when children have fever or adults are in a resting state, the boundary of basal heat flux should be adjusted proportionally to account for changes in body temperature. Based on the above rules of adjustment, the simulated thermal environment can be made in line with the actual situation; thus, the medical ice pack test system is designed to be optimised and obtain practical engineering results.

The first section is about the physical parameter calibration module, which will help the Gazebo-based simulation test platform be more accurate. The basic idea is that there should be a precise mathematical and physical correspondence between the physical world and its digital twin representation to eliminate the systematic errors caused by manufacturing tolerances, sensor drift and hardware performance differences in the test. The principle of this module is to use a standard reference source to quantify the static and dynamic errors of each parameter acquisition channel and then calculate a compensation coefficient for the accurate mapping of parameters in the Gazebo environment.

The first operation steps of calibrating the key parts are as follows. First, a standard blackbody radiation source is used to calibrate the surface emissivity and thermal conductivity of a constant-temperature simulation skin panel. The actual temperature of the panel surface is compared with the standard source, and a polynomial fitting algorithm is used to obtain a correction matrix for the temperature distribution. Second, a high-precision temperature sensor array is calibrated at multiple points in a standard thermostatic bath. Based on the deviations of the output at the set temperature values, zero-point drift and sensitivity errors for each node are calculated to meet the requirement that the acquisition error is within the range of allowable errors. Third, a standard reference thermometer and hygrometer are used to calibrate the ambient temperature and humidity control box. The operating path compares the internal gradient reading of the control box with the reference instrument, adjusts the PID control parameters and compensates for the dynamic response lag to make the ambient conditions stable. Finally, the data real-time acquisition unit will be calibrated for timing synchronization and electrical signal transmission to ensure that there are no transmission delays or analog-to-digital conversion errors.

In addition, there will be stricter error correction rules for each parameter acquisition channel. For the temperature channel, the standard requires that the absolute measurement error after calibration does not exceed a certain threshold. For the heat flux channel, a standard heat flow meter is used to calibrate it and verify that the linearity and transient response time of the measurement are correct. A localised pressure film system is used in the contact pressure channel to display the distribution of the actual contact pressure and correct the point-load error caused by sensor installation.

Through all the above calibration processes, a good relationship has been built between the module's physical objects and the Gazebo digital twin model. The above precise mapping can make the thermal boundary conditions and material properties in the simulation more accurate. Calibration is particularly important in practice as it can ensure that the data from the cooling time test of medical ice packs in the simulation is reliable and repeatable, thus providing a scientific basis for improving the product and its application in clinics.

The field thermal environment coupling test module for portable medical scenario simulation is a necessary construction to fill the gap between the ideal conditions in the laboratory and the harsh environment in pre-hospital first aid and outdoor rescue. It can be seen as a multi-physics field coupling simulation logic that dynamically combines the ambient temperature, wind speed and local heat dissipation of the human body. In a non-laboratory portable medical environment, the cooling time of a medical ice bag is affected by various types of heat transfer, such as convection, radiation and evaporation. Therefore, this module is necessary to examine the performance of the ice pack under real boundary conditions and obtain practical data for testing based on the standard.

At the bottom of the module, there are thermal boundary conditions. Based on a parameterized algorithm, the total heat flux at the surface of the ice pack and the surrounding environment will be calculated. Using adjustable variables for ambient temperature and forced convection from wind speed, along with the heat dissipation of the simulated human body's local metabolism, a comprehensive thermal load map is generated. The multi-physics coupling can accurately simulate the combined effects of environmental exposure and patient physiology under the conditions of emergency medical deployment.

Operationally, the implementation path is to synchronously link the physical simulation platform in the Gazebo environment with the digital simulation model. The physical platform will have an environmental chamber equipped with variable-speed fans and localised thermal heaters to simulate wind and body heat, respectively. A collection of sensors will be used to measure the temperature gradient and flow rate of the environment at various places. The aforementioned empirical data is constantly sent to the Gazebo digital twin through a powerful communication interface. The digital simulation model in Gazebo continuously updates the thermal boundary parameters to keep up with the changes in the physical test module's virtual thermal field. Through bidirectional data transfer, a closed-loop verification system will be constructed to faithfully reproduce and predict the thermal behaviour of the physical platform by the Gazebo model.

The use of this test module can dynamically simulate the changes in the thermal environment of portable medical devices in real life and at the same time meet the requirements of repeated tests. The traditional outdoor field test has many uncontrollable factors due to the weather, so it cannot be standardised for verification. By decomposing the complex outdoor environment into adjustable and controllable parts, this coupling module can carry out controlled repetition of extreme thermal conditions by researchers. Thus, it can serve as a uniform, repeatable and high-accuracy method for optimising the cooling time of medical ice packs and improve the reliability of thermal therapy in emergency medicine.

The selection of the influencing factors that affect the effective cooling time is an important step in the optimisation of the simulation test process. The effective cooling time is the continuous time when the medical ice pack is used to simulate and maintain a stable skin temperature in line with the required range of treatment safety. The length of time is determined by the intricate thermodynamic characteristics; therefore, the main methods of heat transfer are conduction heat transfer, convection heat transfer and latent heat absorption of phase change. In actual application, we should find the main influencing factors among many interactive ones accurately. It can not only determine the main physical limits of the simulation system, but also reduce computational error due to secondary variables and thus improve the reliability and clinical usefulness of the test results.

In order to systematically evaluate the seven possible variables of the initial freezing temperature of the ice pack, the thickness of the ice pack medium, the contact pressure between the ice pack and the simulated skin, the ambient temperature, the relative humidity, the thermal resistance of the isolation layer, and the phase change latent heat of the cooling medium, the Plackett-Burman experimental design method is used. This method is a very effective way to screen many variables with few experiments. The first part of the operation is to set the high and low levels of each of the seven factors as high and low according to the preliminary engineering threshold. Then the simulation tests will be carried out in strict accordance with the structure of the Plackett-Burman matrix. Collect the data of the effective cooling time and then conduct an analysis of variance to obtain the main effects and significance levels of each factor.

Based on the above process, the main variables that have a significant impact on the effective cooling time will be identified, and those that do not meet the significance level will be removed from the first model. Therefore, it is necessary to conduct the above screening in practice. By removing the redundant variables, the dimension of the parameter space can be significantly reduced. This provides a direct basis for building a concise and accurate multi-objective optimisation algorithm. From the perspective of operation, removing non-significant factors can reduce the number of non-essential test links and computational iterations in the simulation process, improve testing efficiency, reduce resource consumption and not affect the accuracy of cooling duration evaluation. Finally, the simulation testing system will be operated with the highest level of technical rigour and the best operational economy.

A multi-objective optimisation algorithm is built to improve the efficiency of simulation testing for the medical ice pack cooling duration. Essentially, this is to balance two conflicting indicators at the same time, i.e., reduce the error between the simulation test results and the actual cooling time, and shorten the time of one single simulation test. A two-objective approach is necessary because accuracy cannot be guaranteed due to denser meshing and more iterations, and therefore it will take more time to compute. By addressing this problem, the algorithm can reduce the time consumed by the simulation test and still maintain a high level of accuracy.

The basic idea is to use a Genetic Algorithm (GA) in combination with the Response Surface Method (RSM). RSM is first used to build a mathematical surrogate model based on the screening results of the key influencing factors, and the relationship between the control variables (number of simulation iterations, frequency of adjustment of boundary conditions, etc.) and the optimisation objectives is established. The surrogate model can replace the computationally expensive finite element simulation and provide quick evaluation. Then, GA will conduct a global multi-objective search on this RSM model. The operational steps are as follows: First, a central composite design will be used to obtain the sample points and fit the response surface for the error and time objectives. Second, a non-dominated sorting genetic algorithm will be used to initialise a population of variable sets. Third, by repeatedly performing selection, crossover and mutation operations on successive generations, the algorithm will gradually find the Pareto front, which is the best set of solutions.

The weight distribution of the optimization goals is a critical technical problem in this implementation. Because of the high requirement for thermal fidelity in medical ice pack testing, the weight for reducing simulation error is set to 0.7 and the weight for shortening the single test time is set to 0.3. Based on these weights, the fitness of the GA selection phase can be determined; that is to say, solutions with low accuracy will be penalized. The number of simulation iterations and the frequency of adjusting the boundary conditions can be optimised dynamically based on the change in the weighted fitness.

In order to ensure the reliability of the algorithm, there is a specific convergence condition. Stop the iteration when the change in the hypervolume indicator of the Pareto front is less than a certain value (e.g., less than 0.01% for 50 consecutive generations) or when the maximum number of generations is reached. To avoid premature convergence, a too tight condition will be set, and at the same time, too little calculation will not be carried out. The constructed algorithm can be used directly to find the best configuration of the control variables, and then engineers can run simulation tests to achieve a relatively good prediction of the cooling time in a short time and thus improve the operation of thermal management verification.

The consistency test of the cooling time in different ambient temperatures is an important part of verifying the reliability of the improved simulation test system. Ice packs have been used in a variety of climates for many years in the medical field, so the simulation system should reflect changes in the surrounding environment's temperature to simulate thermal flow and be safe and effective for clinical practice. In this test, various types of medical ice packs from different batches were selected and subjected to three typical ambient temperature conditions of 10℃, 25℃ and 35℃. These particular gradient conditions are for mild, normal and serious situations in storage or transportation; they also cover most of the operation range of industry standards.

The operation process is to observe all the ice packs chosen and measure how long they take to cool down. At the same time, according to the optimized simulation test system, the theoretical cooling time for the same ice pack under the same ambient conditions of 10℃, 25℃ and 35℃ can be calculated. To establish a good empirical reference value, parallel tests were conducted in a traditional constant temperature laboratory. The resulting data sets are the simulation output and the empirical data obtained in the laboratory, and based on these, a comparative statistical analysis can be performed.

To determine whether the two test methods are consistent, we will first compute the linearity of the optimized simulation results and the actual laboratory data in three different environments using Pearson's Correlation Coefficient. A correlation coefficient close to positive one means a strong proportional relationship; thus, the simulation system can accurately follow changes in cooling time with changes in ambient temperature.

Additionally, a Bland-Altman diagram is used to check the agreement and systematic bias between the two sets of data. By plotting the difference between the actual cooling time of a simulation and that of reality against their mean value, this method can identify the boundaries of agreement. If the differences in the Bland-Altman analysis are within the clinically acceptable range and there is no proportional bias in the temperature range, it can be concluded that there is no large-scale deviation systematically.

Based on dual statistics, it can be confirmed that the modified simulation testing system can not only reflect isolated data points but also show the pattern of change in ice pack cooling time at different ambient temperatures. The validation is to replace the resource-intensive physical lab experiments with a standard and highly reproducible simulation protocol to enhance the practical value of medical thermal preservation engineering.

Error analysis of the simulation results and clinical practice data will be conducted to determine whether the optimized medical ice pack cooling time simulation testing system is reliable. The above is the data of the first year of the project, and the below are the data of the second year of the project. At the heart of it is the difference between the length of time in the simulation and the actual time of the data, and thus the boundary conditions and systemic errors that the mathematical model cannot capture. Therefore, it is very important to choose a good cooling time; otherwise, there will be no therapeutic hypothermia or tissue frostbite, and thus it will affect the patient's health and treatment effect.

In the comparison verification experiment, 200 groups of clinical application records were collected from the emergency department and orthopaedic department of a local general hospital. These records show how long medical ice packs can be kept at a suitable temperature in real life, and they take into account various factors such as the type of injury, the constitution of different patients, etc., as well as the conditions of different wards. Based on these 200 empirical data sets and the output results of the optimised simulation test system under the same input parameters, an error distribution map was constructed. The specific values of these clinical variables are fed into the simulation system, and then the predicted cooling time and its absolute and relative errors relative to the actual clinical situation are calculated.

An analysis has been carried out to identify the main reasons for the remaining errors. First, there are some inherent differences in the local blood flow and subcutaneous fat thickness of different patients; therefore, they are not uniform in the simulation. Second, the fluctuation of the convection heat transfer coefficient due to some factors in the hospital environment (such as random wind changes or sudden increases in humidity due to air conditioners) is not considered by the simulation. Finally, due to different people's habits in preparing the initial ice packs, there will be some slight differences in the actual temperature of the initial interior.

To improve the practicality of the simulation results, some suggestions for improvement are presented. A dynamic physiological correction factor should be added to the simulation algorithm to adjust for local tissue metabolic rates in various injury parts. A clinical operation compensation coefficient should be built with the environmental residual error statistics to adjust the output duration. Finally, standardize the pre-cooling and storage steps according to the operating instructions to reduce the initial state variance. After these corrections, the simulation system will change from a theoretically perfect model to one that is applicable in clinical practice and can be used to predict how well medical ice packs work reliably and based on evidence.

Medical ice packs were tested to extend their cooling time in order to improve the quality of life for patients suffering from heatstroke, and this is the intersection of theory and practice in the field of medicine. In essence, cooling time is the length of time that the ice pack should be kept in contact with the body to maintain a surface temperature of no higher than eight degrees Celsius; this is the range required for local tissue vasoconstriction and the reduction of inflammation. The basic reason for this time is the equation of the transient state of heat conduction; the rate of change in heat energy of a phase-change material is determined by the thermal resistance of the enclosure and the convective boundary at the skin surface. To improve the predictive accuracy of the model, one can adjust the simulation parameters according to the actual physical boundary conditions and make the model more precise for clinical use ^[3].

At this time, to better optimize things, a certain path was chosen. First, baseline empirical data was gathered from a standard bench-top experiment to calibrate the initial simulation conditions. Then, according to the above ideas, we built a finite element analysis model, and this model should also consider the latent heat absorption of the gel and the anisotropic thermal conductivity of the flexible outer film. According to the above ideas, adjust the key parameters in the optimization path, that is, the initial mass of the phase-change material, ambient application temperature, and convective heat transfer coefficient, to reduce the difference between the simulated cooling curve and the experimentally observed decay curve. The above-mentioned iterative calibration method has addressed the problem of systematic computation deviation and thus improved the accuracy of the thermal gradient in the simulation.

The above results have high practical application value in the development of mechanical engineering and medical device standards. In clinical work, using an optimised simulation plan can help manufacturers estimate the cooling performance of the equipment more accurately without making many physical prototypes; therefore, it will be easier to meet regulatory requirements and speed up the development of new products ^[6]. Accurate time model is helpful for healthcare workers to carry out evidence-based application plans and reduce the problem of too long cryotherapy or premature warming causing tissue necrosis due to poor treatment effect. Finally, this study will provide a method for the foundation of thermal management simulation of disposable medical devices in the future, and the analysis is based on verified and standardised operating systems, so that it can meet the requirements of the thermal system and be safe for patients.

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