Thermal Diffusion Coefficient Research Articles

Pressureless Welding of Temperature-Invariant Multifunctionality Body Based on Hydroxyl-Functionalized Boron Nitride Nanosheets and Bifunctional Monoethanolamine Cross-linker.

Bulk hexagonal boron nitride (h-BN) ceramics with structural integrity, high-temperature resistance and low expansion rate are expected for multifunctional applications in extreme conditions. However, due to its sluggish self-diffusion and intrinsic inertness, it remains a great challenge to overcome high-energy barrier for h-BN powder sintering. Herein, a cross-linking and pressureless-welding strategy is reported to produce bulk boron nitride nanosheets (BNNSs) ceramics with well-crystalized and dense B-N covalent-welding frameworks. The essence of this synthesis strategy lies in the construction of >B─O─H2C─H2C─H2N:→B< bond bridge connection structure among hydroxyl functionalized BNNSs (BNNSs-OH) using bifunctional monoethanolamine (MEA) as cross-linker through esterification and intermolecular-coordination reactions. The prepared BNNSs-interlaced ceramics have densities not less than 1.2gcm-3, and exhibit exceptional mechanical robustness and resiliency, excellent thermomechanical stability, ultra-low linear thermal expansion coefficient of 0.06ppm°C-1, and high thermal diffusion coefficient of 4.76mm2s-1 at 25°C and 3.72mm2s-1 at 450°C. This research not only reduces the free energy barrier from h-BN particles to bulk ceramics through facile multi-step physicochemical reaction, but also stimulates further exploration of multifunctional applications for bulk h-BN ceramics over a wide temperature range.

Enhancing Building Energy Efficiency: Leaf Transpiration Inspired Construction of Lignin-Based Wood Plastic Composites for Building Energy Conservation

Incorporating phase change materials (PCMs) into buildings represents a strategic method for reducing reliance on air conditioning systems and decreasing energy usage consequently. Inspired by leaf veins providing channels for transpiration, lignin porous carbon (LPC) was synthesized by chemical activation, showing a vein pore structure. The capillary network system of the LPC provided more channel to adsorb PCM through surface tension and capillary force, achieving an impressive loading capacity of LPC for polyethylene glycol (PEG) (75%), which demonstrated exceptional heat storage capability (133.21 J/g). The lignin-derived wood-plastic composite (L-WPC) was further prepared. With the gradual increase of LPC/PEG, the latent heat of L-WPC increased gradually. The ΔHm, ΔHc and energy storage efficiency of L-WPC-50 (incorporated 50 wt% LPC/PEG-75) reached 39.99 J/g, 42.65 J/g and 90.26%, respectively. The vein pore structure of LPC also provided a thermal conductivity link for L-WPC. L-WPC-50 demonstrated an increased thermal conductivity (0.66 W/(m·K)) and a reduced thermal diffusion coefficient (0.24 mm2/s), optimizing the effectiveness of the phase transition. Additionally, L-WPC-50 displayed satisfactory mechanical properties and dimensional stability, with tensile strength, bending modulus and water absorption thickness swelling rate measuring 14.40 MPa, 1043.72 MPa, and 1.61% respectively. It introduced a feasible approach for utilizing biomass in enhancing building energy efficiency, marking a significant stride towards reducing building energy consumption and advocating sustainable energy practices.

A Novel Numerical Model Considering Unsaturated Soil Properties and Computational Study on Heat and Moisture Transfer Characteristics of Helix Ground Heat Exchanger

Abstract A novel three-dimensional numerical simulation model for the helix ground heat exchanger was proposed in this paper, which takes into account unsaturated soil properties. This model is more suitable for real working conditions. To validate its accuracy, a miniature model heat transfer experimental platform was constructed. Additionally, the study conducted simulation research using three types of soil with significantly different thermal and moisture characteristics. Moreover, the comprehensive thermal conductivity and water diffusion coefficient of these three soil types were determined by relevant literature and experimental tests. The aim was to comprehensively explore the impact of different soil types on the heat and mass transfer of the helix ground heat exchanger. The results indicate that the numerical model developed in this paper accurately captures the heat and mass transfer characteristics of the helix ground heat exchanger to a certain extent. Increasing the comprehensive thermal conductivity and water diffusion coefficient of the soil can significantly enhance the heat exchange capacity of the exchanger. For instance, under sandy loam conditions, the heat exchange capacity is approximately 20.73% higher compared to clay loam conditions. The study also identifies two distinct areas around the helix ground heat exchanger: the severe change region and the soft change region. In the severe change region, there is a notable decrease in soil water content near the exchanger, which inevitably weakens the thermal conductivity of the soil. It is advised to minimize this effect through measures like active water spraying.

A waste hemp‐based biomass carbon aerogel with high fire‐resistance

AbstractTo enhance the efficient utilization of waste hemp rods, a kind of three‐dimensional (3D), mesh‐like lamellar structured hemp‐based biomass carbon aerogel (CA) was developed by freeze‐drying and subsequent high‐temperature carbonization method. The microstructure, flame resistance, thermal stability, and thermal conductivity of CA were investigated using several analytical techniques, including scanning electron microscopy (SEM), Fourier‐transform infrared spectroscopy (FTIR), X‐ray diffraction (XRD), simulated combustion tests, and thermogravimetric analysis (TG). Optimum formulation yielded at an alkali treatment concentration of 20% and a carbonization temperature of 700°C, CA with a 3D network of reticulated lamellae was obtained. CA exhibited minimal values for thermal conductivity (0.06 W/m K) and thermal diffusion coefficient (0.41 mm2/s), which are indicative of superior insulative properties. Moreover, the material demonstrated remarkable thermal endurance and flame resistance, achieving a char yield of 70.03% when subjected to a temperature of 700°C in an oxidative environment.

Microstructural, thermal characterization and CMAS corrosion resistance of novel quaternary (Y0,25Er0,25Tm0,25Yb0,25)2Si2O7 high entropy disilicate material

A novel (Y0,25Er0,25Tm0,25Yb0,25)2Si2O7 high entropy disilicate quaternary composition was synthesized from commercial oxide powders using ball milling and sintering processes as a candidate material for environmental barrier coatings (EBC). As-synthesized high entropy disilicate powders were sintered at different durations (12, 18, 24h) at 1600 °C in muffle furnace before characterization. The XRD and SEM analyses revealed the single-phase monoclinic structure (β-type) with homogeneous elemental distribution for the sintered samples. The (Y0,25Er0,25Tm0,25Yb0,25)2Si2O7 samples exhibited low thermal diffusivity coefficient, low thermal conductivity, a close coefficient of thermal expansion (CTE) to SiC and a high temperature stability. The (Y0,25Er0,25Tm0,25Yb0,25)2Si2O7 samples were subjected to CMAS corrosion tests at 1300°C with different durations (2, 12 and 24h) to evaluate CMAS corrosion resistance. Additionally, Yb2Si2O7 samples were prepared and subjected to molten CMAS in the same way for comparison. Based on the results, the CMAS corrosion resistance was improved with (Y0,25Er0,25Tm0,25Yb0,25)2Si2O7 composition.

Universal thermal profiles with polynomial thermal diffusivity in a channel flow

Fluids used in heat transfer applications range in a wide spectrum of Prandtl numbers. An aspect that is commonly neglected is the influence of variable thermal diffusivity in turbulent heat transfer. A mathematical model was developed in the past few years [1, 2] to address the influence of the variable thermal diffusivity on the turbulent heat transfer. In this work we explore the influence of the friction Reynolds number Reτ, the molecular Prandtl number Pr and the coefficients λi+ of the temperature dependent thermal diffusivity, up to the fourth-order, to the Universal Profiles in a channel flow. This choice minimizes the influence of the boundary and initial conditions. The numerical simulations in the limit of constant thermal diffusivity are validated against literature DNS data. The results show that the influence of the friction Reynolds number is limited, while high molecular Prandtl numbers increase the fluctuating thermal diffusivity heat flux. The factor that influences the solution the most is the thermal diffusivity coefficients, showing that, in certain conditions, the fluctuating thermal diffusivity heat flux is non-negligible even for low Prandtl numbers. The results show that the terms introduced by the model proposed in [1, 2] are non-negligible when the thermal diffusivity in the boundary layer doubles compared to its bulk value. It is suggested that the model presented in [1, 2] could be particularly suitable in cryogenic applications.

The influence of thermal diffusion on water migration through a porous insulation material

Excess water on pipes and equipment under porous insulation materials can lead to undesired corrosion. This work aims to clarify to what extent thermal diffusion affects the migration of water inside insulation materials subject to large temperature gradients. Since no experimental data is available on the thermal diffusion coefficients of humid air, revised Enskog theory for Mie fluids is used to estimate transport properties. Comparison to experimental data from literature shows that the theory reproduces the diffusion coefficient, viscosity and thermal conductivity of humid air within 8.7%, 5.0% and 3.5% respectively. The small discrepancies suggest that the theory can also provide reliable estimates of the thermal diffusion coefficients. In the investigated composition and temperature range, the theory predicts the Soret coefficient of water to be approximately ▪, while the Soret coefficient of oxygen varies from ▪ to +▪. A case study with heating of glass wool insulation containing humid air, encapsulating a cylindrical pipe is investigated. Non-equilibrium thermodynamics is used to consistently incorporate the Soret coefficients into the flux equations in a dynamic, non-isothermal model that includes diffusion, convection, thermal conduction and water sorption in the porous medium. With 50 K temperature difference across 5 cm of insulation, we find that at steady-state, thermal diffusion leads to a mole fraction of water in the gas phase that is about 1.5% higher at the hot location than if thermal diffusion is neglected.

Combined refractance window and far infrared radiation drying of Spirulina platensis biomass: Drying behavior, moisture and thermal diffusivity, and biochemical characterization

A 2 mm thin layer of wet Spirulina platensis biomass was dried using two methods: refractance window drying (RW) and combined RW and FIR drying (RWF). The effect of drying temperature (40–60 °C) and proximity to FIR heaters (5 and 10 cm) was evaluated on falling rate drying characteristics. The moisture (Deff) and thermal (α) diffusivity coefficients were obtained in the range 1.728 × 10−8 to 5.289 × 10−9 and 1.322 × 10−8 to 4.169 × 10−9 m2 s−1, respectively (R 2, 0.921–0.984). RW drying at ≥50 °C caused loss of color, phytopigments, and lipid peroxidation. At 40 °C, RW drying led to a long drying period (300.50 ± 3.53 min), poor drying rate (0.039 ± 0.002 g-H2O/min), lowest Deff and α (5.289 × 10−9 and 4.169 × 10−9 m2 s−1), and chlorophyll loss (32.2%). Combined RW and FIR drying at 40 °C and 5 cm proximity (RWF40-5cm) reduced drying time (15.1%), increased drying rate (27.8%), improved α (15%), and Deff (14.9%). RWF40-5cm dried biomass showed excellent retention of color (ΔE = 4.64 ± 1.32), protein (93.8%), γ-linolenic acid (90.1%), chlorophyll (87.9%), and phycocyanin (86.7%) from freeze-dried biomass (FD). Low-temperature RWF40-5cm drying could be a potential alternative to freeze-drying for effective and safe drying of heat-sensitive Spirulina platensis biomass.

Effects and mechanism of thermal insulation materials on thermal runaway propagation in large-format pouch lithium-ion batteries

The large heat transfer area of large-format lithium-ion batteries primarily facilitates conduction heat, which is responsible for triggering the thermal runaway of adjacent cells. Therefore, the primary consideration is to utilize thermal insulation materials between cells in order to slow down or prevent the process of thermal runaway propagation. In this study, three varieties of thermal insulation materials were employed to insulate individual cells within a module comprising three large-format pouch cells. These materials include pre-oxygenated wire aerogel (AG-ST-POF), polymer-coated pre-oxygenated wire aerogel (PC-AG-ST-POF), and silicone (SI). The study experimentally examined the thermal runaway propagation (TRP) behavior of the battery module under conditions without insulation materials and with various types of insulation materials. The impact of thermal insulation materials on the TRP among cells was analyzed. The study revealed that none of the three materials completely suppressed the propagation of thermal runaway, although they did impede its progress. The overall impact of AG-ST-POF surpassed that of SI and PC-AG-ST-POF. Furthermore, the mechanism by which thermal insulation materials influence TRP was explored. The results of the thermophysical properties testing suggest that evaluating the impact of materials on TRP solely through thermal conductivity is not a reliable approach. Alternatively, the maximum service temperature and thermal diffusion coefficient are critical parameters for the selection of thermal insulation materials. This study can provide a valuable reference for process engineering design and application in the context of lithium-ion batteries, with the aim of mitigating the risk of TRP.

Thermal diffusity in copper benzene-1,3,5-tricarboxylate–reduced graphite oxide mechanical composites

AbstractMetal organic frameworks (MOFs) and particularly copper benzene-1,3,5-tricarboxylate (HKUST-1) are excellent materials for gas storage (e.g., CH4, N2, H2 adsorption) and gas separation. In this work, reduced graphene oxide (RGO)–HKUST-1 mechanical mixtures were studied in order to reveal the effect of RGO content on the pressure tolerance of the texture and heat conductivity. HKUST-1 was obtained by two different synthesis routes. Air-dried MOF and RGO were thoroughly mixed prior to the compression. Powder XRD and Raman spectroscopy were used to characterize the response of the crystal structure, while low-temperature nitrogen adsorption was used the follow the adsorption properties of the pellets. Finally, the "flash" heat pulse method was used to assess the thermal properties. The gas adsorption isotherms revealed that the adsorption capacity decreases when RGO is added. Based on Raman and XRD results, we found that the synthesis route has an effect on multiple scales. We experimentally confirmed that evaluation of the thermal diffusivity requires a model more complex than the simple Fourier equation, due to the inherent heterogeneous structure of the material. A good approximation of the Fourier coefficient of thermal diffusivity was obtained using the parameters of the Guyer–Krumhansl equation. The heat pulse experiments also revealed possible size-dependent behavior.

Experimental study on evaluation of density, P-wave velocity, thermal conductivity, and thermal diffusion coefficient of granite after thermal treatments by using PCA

Temperature significantly influences the physical parameters of granite, resulting in variations in the rock's thermal conductivity. In order to examine the impact of changes in multiple physical parameters of granite at different temperatures on the thermal conductivity of rocks, Principal Component Analysis (PCA) was employed to determine the correlation between granite at different temperatures and various physical parameters, including density (ρ), P-wave velocity (P), thermal conductivity (KT), and thermal diffusion coefficient (KD). Utilizing the linear contribution rate, a single indicator 'y' was derived to comprehensively represent the thermal conductivity of rocks. Research findings indicate that within the temperature range of 150–450 °C, the 'y'-value is relatively high, signifying favorable thermal conductivity of the rock. Notably, longitudinal wave velocity demonstrates higher sensitivity to temperature changes compared to other physical parameters.

Influence of doping elements on thermo-physical properties of co-doped strontium zirconate for potential thermal barrier coatings

Strontium zirconate is a promising material for thermal barrier coatings due to some excellent properties. New four co-doped strontium zirconate with lower thermal conductivity and higher thermal expansion coefficient were synthesized in this study. Sr(Zr0.9Y0.05Yb0.05)O2.95 (SZYYb) with the smallest difference in ionic radius and mass has lowest thermal diffusion coefficients mainly due to the effect of extrinsic phonon scattering mechanisms, including lattice distortion and grain size. The electronic structures of four co-doped SrZrO3 were analyzed by first-principles calculations. The findings suggested that the difference in bond strength caused by different doping affected the differences in the lattice constant, which led to the highest thermal expansion coefficient of SZYYb.

Design, measurement, and demonstrating of a metamaterials with broadband and high transmittance for measuring the thermal conductivity of clothing fabrics samples

An all dielectric metamaterial sensor with smooth spectral lines resonance characteristics over a large frequency range is demonstrated and verified. The average transmittance and reflectance of the metamaterial sample are 0.734 and 0.201 in the frequency range of 4–30 THz. The effects of three important factors on the thermal conductivity of the outdoor clothing fabric samples are measured by using this metamaterial sensor: thickness, ambient temperature, and fabric type. The thermal diffusion coefficient of the fabric samples is decreased with the thickness increasing, which is enhanced by increasing the temperature. In addition, due to differences in preparation processes and materials, the type of fabric sample can also directly affect the thermal conductivity performance. The measurement results verify the feasibility of the metamaterial sensor to measure the thermal conductivity of outdoor clothing fabric samples.

Crystal growth, structure, spectral and thermal properties of ScxY1-xCOB single crystals

Yttrium calcium oxyborate (YCOB) crystals are excellent nonlinear optical crystals. To enhance the thermal properties of YCOB crystal, Sc-doped YCOB crystals, denoted as ScxY1-xCa4O(BO3)3 (x = 0.1 and 0.2) were grown using the Czochralski method along the b-direction. Various measurements, including X-ray powder diffraction, rocking curve analysis, inductively coupled plasma-optical emission spectroscopy (ICP-OES), transmission spectroscopy, density measurements, and thermal property assessments, were conducted to evaluate the characteristics of the ScxY1-xCOB crystals. The results indicated that ScxY1-xCOB crystals have an isostructural arrangement like YCOB, with segregation coefficients of approximately 0.2. The full width at half maximum (FWHM) values of the rocking curves of the ScxY1-xCOB (x = 0.1 and 0.2) crystals are 33.9″ and 29.3″, respectively. Furthermore, the specific heat, thermal diffusion coefficients and thermal conductivity of the ScxY1-xCOB crystals were examined in the temperature range of 298–573 K, which were found to be higher than those of pure YCOB. These high-quality ScxY1-xCOB crystals are expected to serve as suitable nonlinear optical crystals media for optical parametric chirped pulse amplification (OPCPA) applications.

Study of mass and heat transfer for peristaltic transport of cross nanofluid through a curved channel

AbstractNanoparticles have significant applications in drug delivery systems, heat exchanges, treatment of several diseases and chemical reactions. The Cross non‐Newtonian nanofluid model for heat and mass transfer inspection with diethylene glycol‐based fluid is highlighted in this study. The magnesium aluminate nanoparticles are used to evaluate nanofluid characteristics. The current investigation explores the numerical results for magnetohydrodynamics (MHD) peristaltic movement of Cross‐nanofluid via a curved channel under the influences of thermal radiation, heat sink/source and Joule heating. The effects of viscous dissipation, thermophoretic, variable thermal conductivity and Brownian diffusion coefficients in the presence of mass and thermal convection are also taken into consideration. Flow problem is modeled using fundamental conservation laws, and the resulting nonlinear partial differential equations (PDEs) are reduced to a system of nonlinear ordinary differential equations (ODEs) by employing long wavelength and a small Reynolds number approximations. Simplified systems of ODEs are addressed by adopting numerical technique via the NDSolve built‐in command in Mathematica. Furthermore, graphical presentations explain the behavior of relevant flow parameters. Results indicate that better values of the magnetic number and the thermophoresis parameter increase the rate of mass transfer. Results indicate that the nanofluid's temperature increases by improving values of the Brinkman number and falls with the thermal radiation parameter. It is also stated that the nanofluid's velocity reduces near the lower wall for greater values of Hartman number. Moreover, heat transfer rate improves for larger values of the heat generation parameter and curvature parameter.

Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration

We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation (PDE) constraints under uncertainty: the state in our setting is the solution of a parabolic PDE with a random thermal diffusion coefficient, steered by a control function. To account for the presence of uncertainty in the optimal control problem, the objective function is composed with a risk measure. We focus on two risk measures, both involving high-dimensional integrals over the stochastic variables: the expected value and the (nonlinear) entropic risk measure. The high-dimensional integrals are computed numerically using specially designed QMC methods and, under moderate assumptions on the input random field, the error rate is shown to be essentially linear, independently of the stochastic dimension of the problem—and thereby superior to ordinary Monte Carlo methods. Numerical results demonstrate the effectiveness of our method.

Natural convective and Cattaneo–Christov model for couple stress nanofluid at the middle of the squeezed channel with sensor surface

The aim of this work is to present a natural convective and squeezing flow model of two-dimensional couple stress nanofluid which is flowing on the sensory surface with variable fluid viscosity. The fluid flowing on a microcantilever sensory surface and squeezing is happening at free stream. The sensor is also useful to detect the movement of fluid and the variations in thermal and solutal rates. The Cattaneo–Christov model is adopted along with nanoparticle and chemical reaction to explore the transmission of heat and mass rates. The analysis of heat transmission in non-Newtonian couple stress fluid flowing on squeezed sensory surface by using the Cattaneo–Christov heat conduction model has various industrial and scientific applications including the polymer processing, wastewater treatment, chemical reactors, biomedical flows, cooling and heating processes in industries, heat exchangers, microfluidics, oil and gas industries. All the assumptions are applied in the basic governing laws laws and then we get the model of the partial differential equations. The governing model of equations is transmuted into ordinary differential equations form via the transformations and then the numerical results of these ODE’s are examined with a well-defined numerical technique “Shooting Method”. For higher inputs of couple stress, squeezing index and permeability velocity, the fluid’s internal velocity decreases. Because of the Prandtl number and thermal relaxation coefficient, the heat transfer mechanism slows down. Mass transfer increases for greater inputs of the thermal diffusivity coefficient and decreases due to concentration relaxation. Further, the numerical dependency of emerging parameters on the skin friction is illustrated in tabular form. The parametric effects on the model (velocity, temperature and concentration) are introduced using numerical values shown in the table.

Utilization of variable thermal conductivity and diffusion coefficient on non-Newtonian Prandtl model with modified heat and mass fluxes

PurposeThis study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.Design/methodology/approachThe governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.FindingsGraphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.Originality/valueThe reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

Aspects of chemical reaction and mixed convection in ternary hybrid nanofluid with Marangoni convection and heat source

The proposed study examines the effect of inclined magnetic field on a ternary hybrid nanofluid flow that is axisymmetric thermo-solutal Marangoni convective over an infinite disc. Some well-known uses of Marangoni convection include semiconductor production, atomic reactors, crystal growth, fine art mechanisms, melting, thin-film stretching and welding processes. The non-uniform heat generation and viscous dissipation are taken into account. The thermal conductivity and diffusivity coefficient are presumed to vary inversely with linear function of temperature and concentration. The ternary hybrid nanofluid, which consists of silicon dioxide ([Formula: see text]), iron oxide ([Formula: see text]), molybdenum disulfide ([Formula: see text]) and ethylene glycol as base liquid, undergoes an energy transition to improve heat transfer. The system of PDEs is transformed into nonlinear ordinary differential equations (ODEs) by using the appropriate transformations. Using the BVP4C method, this problem is numerically solved. The heat and mass phenomena rates on flow behavior are investigated using tables and graphs to address the impact of several physical and flow parameters on velocity, concentration, and thermal profiles. By increasing the Marangoni convection parameter, the surface tension gradient gets stronger, leading to more efficient heat and mass transfer inside the liquid as well as stronger induced flows. As the temperature and concentration profiles decrease, the outcome is a more consistent dispersion of these properties throughout the liquid.

A computational approach to heat transfer and ablation in space capsule insulation

In this article, the heat transfers and ablation phenomena of thermal insulations utilized in manned space capsules are investigated. In this regard, by collecting and solving the equations related to ablation insulations, a computer program has been developed that is able to predict the thermal response of these insulations under various operating conditions. This approach considers mass and heat transfer equations in two-dimensional solid bodies. To solve these equations, finite volume method and implicit formulation for time dependence have been used. The reaction equation, written in the form of Arrhenius, is solved using the Runge-Kutta method, and the density and the flux of the gas produced at each step are obtained. Furthermore, a practical model with low computational requirements and execution time and execution time is presented to consider the regression rate based on determining the identifier for destroyed cells, charred cells, and virgin material. The research results demonstrate that increasing the thickness of the layers, the heat of decomposition and ablation, the intensity of the reaction, and reducing the thermal diffusion coefficient, density of char, and temperature of ablation enhance the efficiency of thermal insulation. Validation of the model with experimental results in silica-phenolic insulation reveals a good agreement between simulation and experimental observations. Additionally, it was shown that for a carbon-phenolic insulation with a thickness of 5 mm in the specified space capsule under the given conditions, the maximum recession rate is 1.9 mm at a maximum temperature of 1000 K and 4.9 mm at a maximum temperature of 1300 K.