Fourier Number Research Articles

Investigation of the melting and solidification processes of a phase change material in cylindrical annular enclosures: A parametric study for energy densification in hot water tanks

The present study focuses on the analysis of the effect of the phase change material (PCM) cavity size on the melting and solidification processes for application to thermal energy densification in a hot water tank through latent heat thermal energy storage in cylindrical annular cavities. A 2D axisymmetric composite geometrical pattern is considered, formed by a phase change material surrounded by a conductive and an insulating material. A parametric study is conducted on the phase change material cavity size, and the results are presented using non-dimensional numbers: Fourier number, Rayleigh number, and aspect ratio. Two approaches have been developed based on local and global analyses. The local one showed the predominance of the conductive or convective heat transfer process concerning the influence of the phase change material size, and thus the Rayleigh number, on the evolution of the solid/liquid interface and streamline shapes. The global one allowed correlations for melting and solidification Fourier numbers with respect to the Rayleigh number and aspect ratio to be built from simulation data. Two parameters for each process have been identified and defined from the present study: the critical Fourier number and the aspect ratio constant. The critical Fourier number corresponds to the maximum Fourier number that the phase change material needs to achieve for a melting or solidification process. The aspect ratio constant provides information on the phase change material aspect ratio value where the Rayleigh number no longer influences the process. In the case of the melting process, this parameter is an indication that convection has reached a maximum intensity and no longer influences the process. Finally, this study proposes a suitable aspect ratio for optimizing the melting process: 19.32, and another for optimizing the solidification process: 16.29.

A novel liquid fraction iteration methodology for addressing oscillatory issues in the total enthalpy method

The total enthalpy method (TEM) has been proposed and employed for several decades to address both isothermal and gradual phase change problems. However, recent investigations into isothermal phase changes have revealed that the phase interface predicted by the TEM oscillates with variations in spatial and temporal discretizations, due to the inconsistency between liquid fraction and enthalpy. To address this issue, and drawing inspiration from the liquid fraction iteration methodology used in the widely adopted heat source method (HSM) to ensure consistency between liquid fraction and temperature, this paper introduces a novel liquid fraction iteration methodology specifically tailored for the TEM, referred to as the iterative TEM (ITEM). This approach is validated against an experimental benchmark involving the melting of a pure substance. Grid and time-step dependence studies confirm that the ITEM effectively eliminates oscillations and exhibits convergence with respect to both grid size and time step. Moreover, the ITEM achieves accuracy comparable to that of the HSM. Finally, the computational costs associated with the ITEM are examined, revealing that costs increase rapidly once the grid Fourier number (Fo) exceeds one. Maintaining the grid Fo number below approximately 0.5 and ensuring the ratio of the relaxation factor to the grid Fo number to approach one significantly improve computational efficiency. The relaxation factor is a crucial parameter within the liquid fraction iteration scheme.

Role of two isothermal cylinders towards three-dimensional flow and melting of phase-change materials

Recently, investigators focused on examining the melting of phase change materials (PCM) in regular two-dimensional or three-dimensional flow domains. At the same time, this topic still needs more study to get a better understanding of it. Also, such problems should be reported using the local thermal non-equilibrium (LTNE) model because the latent heat substances and the included porous elements have different temperatures. Therefore, this study examines the three-dimensional flow and melting process of phase change materials (PCM) within cubic enclosures filled with copper foam, using a local thermal non-equilibrium model (LTNE). The system includes two isothermal cylinders with different temperature conditions, varying distances, and radii, placed within the flow domain. The enthalpy-porosity approach is applied to model the PCM behavior, while the Brinkman-extended non-Darcy model accounts for high-velocity flow situations. A magnetic field is introduced to control the flow, with the Lorentz force acting opposite to gravity. The governing equations are solved using a home-developed code based on the finite volume method with the SIMPLE algorithm. Key parameters investigated include cylinder radii, Fourier number, Hartmann number, horizontal and vertical distances between cylinders, and Darcy number. The results are presented through streamlines, temperature distributions for fluid and solid phases, and profiles of the Nusselt number and average liquid fraction.

Discharging Performance Analysis of MXene Nano‐Enhanced Phase Change Material for Double and Triplex Tube Thermal Energy Storage

ABSTRACTThe present study numerically investigates the energy and exergy analysis of solidification of phase change materials within a double tube and triple tube latent heat storage unit using ANSYS Fluent. Double tube and triple tube thermal energy storage system's thermal characteristics are examined using MXene nano‐enhanced phase change material to determine system efficiency, discharged energy, heat transfer rate, exergy destruction, entropy generation number, exergetic efficiency, liquid fraction, solidification temperature contours. The result revealed that the double tube thermal energy storage with pure cetyl alcohol PCM has 14.76% lower discharge exergy than MXene‐based nano‐enhanced phase change material in pure solidification. In a triple tube thermal energy storage system, the solidification time for MXene‐based nano‐enhanced phase change material is impressively reduced by 54.76% compared to a double tube system using pure phase change material. At a Fourier number of 0.00672, MXene nano‐enhanced phase change material exhibits an 11.69% higher Stefan number (St) than cetyl alcohol phase change material in a double tube thermal energy storage system. At 2400 s, pure phase change material and MXene nano‐enhanced phase change material generated 3.14% and 4.88% less entropy than pure cetyl alcohol in the triple tube thermal energy storage system. During the pure solidification process in a double tube thermal energy storage system, pure cetyl alcohol experiences 7.60% higher exergy destruction compared to MXene nano‐enhanced phase change material at a solidification time of 2400 s. In a triple tube thermal energy storage system, the discharging temperature for pure cetyl alcohol phase change material is 2.92% lower than that in a double tube system. Double tube thermal energy storage with pure cetyl alcohol discharged more efficiently over 2400 s. The triple tube thermal energy storage system solidified cetyl alcohol PCM 20.83% faster than pure phase change material due to MXene nanoparticles' better thermophysical properties. Thus, MXene‐based nano‐enhanced cetyl alcohol phase change material solidifies faster per volume in a triple tube thermal energy storage latent heat system.

Correlation between microstructural inhomogeneity and architectural design in additively manufactured NiTi shape memory alloys

ABSTRACT Additively manufactured Nitinol (NiTi) architectured materials, designed with unit cell architectures, hold promise for customisable applications. However, the common assumption of homogeneity in modeling and additive manufacturing of these architectured materials needs further investigation because geometric-dependent melt pool behaviour results in inhomogeneous microstructure and thermomechanical properties. This study shows that property inhomogeneity at the mesoscale is one reason for pseudo-linear response and partial superelasticity of the fabricated NiTi body-centered cubic (BCC) architectured materials. We modeled using a phenomenological constitutive relation and additively manufactured NiTi architectured materials with varying relative densities. These fabricated samples showed distinct microstructural textures and compositions that affected their local recoverability. The edge effects and laser turn regions were identified as the causes underlying the observed microstructural inhomogeneity. The dimensionless Fourier number is used to describe the transition of printing modes. This study provides valuable information on rigorous experimental/computational consistency in future work.

Numerical study on the combined application of multiple phase change materials and gradient metal foam in thermal energy storage device

Latent heat thermal energy storage (LHTES) offers significant energy-saving benefits, but its application is limited due to the low thermal conductivity of phase change material (PCM). To address this issue, this article studied the combined application of metal foam structures with different porosity gradients and multiple PCMs with different melting points through numerical simulation to accelerate the melting of PCM and enhance system efficiency. The results showed that the application of multiple PCMs improved the heat transfer performance of the system, reducing the complete melting time by 9.18% compared to using a single PCM with uniform metal foam. Based on the multi-PCM storage system with an average porosity of 0.90, this article designed metal foam structures with one-dimensional and two-dimensional porosity gradients and explored their impacts. The results indicated that in the structure with a one-dimensional porosity gradient along the heat flow direction, the positive gradient decreased thermal resistance, further reducing the complete melting time by 6.18%, while the negative gradient increased it by 19.78%. However, the temperature non-uniformity was lowest with the negative gradient and highest with the positive gradient. The optimal two-dimensional porosity gradient multi-PCM storage model not only reduced thermal resistance but also effectively solved the issue of uneven melting, reducing the complete melting time by 17.96% and increasing the energy storage efficiency by 20.16% compared to the single PCM system with uniform porosity. Furthermore, the article conducted a dimensionless analysis of the optimal structure and different gradient structures, establishing formulas for the liquid fraction concerning modified Fourier number, modified Stefan number, and modified Rayleigh number.

Melting Behavior Effect of MXene Nanoenhanced Phase Change Material on Energy and Exergy Analysis of Double and Triplex Tube Latent Heat Thermal Energy Storage

Abstract The impacts of melting behavior on the thermal performance of triple tube thermal energy storage (TT-TES) and double tube thermal energy storage (DT-TES) systems employing cetyl alcohol and 3% v/v. MXene nano-enhanced PCM (NEPCM) are compared and numerically evaluated in this work. For both the DT-TES and TT-TES systems, the following were investigated in connection to melting time: system efficiency, discharged energy, heat transfer rate, exergy destruction, entropy generation number, exergetic efficiency, melting fraction, and melting temperature contours. In addition, the effect of Stefan, Rayleigh, and Nusselt numbers on Fourier numbers are compared for the DT-TES and TT-TES systems with MXene NEPCM. MXene-based nano-enhanced PCM melting in TT-TES displayed 6.53% more Stefan number than cetyl alcohol. DT-TES with pure cetyl alcohol phase change material (PCM) consumes 0.4% more energy at 7800 s than MXene NEPCM. Pure melting of MXene-based nano-enhanced PCM in a TT-TES had 4.16% higher storage exergy than cetyl alcohol. The entropy generation number of pure melting of MXene-based nano-enhanced PCM in TT-TES is 7.93% lower than that of cetyl alcohol. Pure melting of MXene-based nano-enhanced PCM in TT-TES reduces storage energy by 1.95% over cetyl alcohol. Pure cetyl alcohol has 76.99% optimal system efficiency at 5400 s melting time and MXene NEPCM 77.04% at 4800 s in DT-TES. The charging temperature for pure cetyl alcohol PCM in TT-TES is 0.7% lower than in DT-TES. Furthermore, pure melting of MXene-based nano-enhanced PCM in a TT-TES has 1.95% lower storage energy than cetyl alcohol. For a given volume of MXene-based nano-enhanced cetyl alcohol PCM, melting occurs more rapidly in a TT-TES system.

Heat charge performance prediction and optimization of locally refined bionic fin heat exchanger with PCM and nanoparticles based on NSGA-II

Phase change energy storage plays an important role in the popularization of renewable energy sources (wind, solar, geothermal, etc.). However, previous studies have paid little attention to the correlation and optimal solution of phase transformation thermal performance prediction. This research combines Response Surface Methodology with the Non-dominated Sorting Genetic Algorithm II to forecast and enhance the performance of tree-shaped biomimetic latent heat storage units, targeting optimal functionality under operational conditions. Initially, the study delves into a mechanistic analysis of the heat transfer in latent heat storage units, focusing on the coupling of conductive and natural convective heat transfer during the melting phase. The synergistic enhancement of heat conduction and convection is realized through locally refined and punched fins. Subsequently, Response Surface Methodology was applied to analyze the interactions between the design variables and the objective functions, leading to the attainment of Pareto-optimal frontiers using the Non-dominated Sorting Genetic Algorithm II. The results demonstrate that the Pareto-optimal solutions substantially improved the Nusselt number of novel biomimetic latent heat storage units by 42.58%–45.58 %, relative to tree-shaped fin latent heat storage units. Concurrently, the Fourier number was reduced by 17.54%–19.22 %. Moreover, the effect of adding nanoparticles (aluminum, copper oxide, and copper) to the phase change material was studied. The results show that the proposed locally refined optimal fin structure is superior to the addition of nanoparticles.

Scale modeling of thermo-structural fire tests of multi-orientation wood laminates

The stacking sequence of laminated wood significantly impacts the composite mechanical behavior of the material, especially when scaling down thermo-mechanical tests on plywood. In previous research, we developed a scaling methodology for thermo-structural tests on samples with similar cross sections, however this paper focused on testing plywood samples with different stacking sequences between the scales. Plywood samples at ½-scale and ¼-scale were subjected to combined bending and thermal loading, with the loading scaled to have the same initial static bending stresses. While the ¼-scale 4-layer [0°/90°]s laminate and the ½-scale 8-layer [0°/90°/90°/0°]s laminate had an equal number of 0° and 90° layers, as the char front progresses, the sections behave differently. Thus, modeling becomes essential to extrapolating the data from the smaller ¼-scale test to predict the behavior of the larger ½-scale test. Reduced cross-sectional area models (RCAM) incorporating classical laminated plate theory were used to predict the mechanical response of the composite samples as the char front increased. Three methods were proposed for calibrating the RCAM models: Fourier number scaling, from detailed kinetics-based pyrolysis GPyro models, and fitting to data from fire exposure thermal response tests. The models calibrated with the experimental char measurements produced the most accurate predictions. The experimental char models validated to predict the behavior of the ¼-scale tests within 2.5%, were then able to predict the ½-scale test behavior within 4.5%.

Corner melting in low Pr metals: A study using lattice Boltzmann method

Evolution of melting boundary in the solid–liquid phase-change problem involves nonplanar geometry due to the presence of Rayleigh–Benard convective cells in the melted region. The transition of flow behavior from steady to oscillatory in the melt zone is particularly an interesting phenomenon to study. In this work, numerical investigation of melting of low Prandtl number materials in a square cavity with two adjacent heated walls has been carried out using total enthalpy-based lattice Boltzmann method. The local thermal and fluid flow behavior within a moving melting front has been investigated. The influence of natural convection in the melt zone has been observed for two different cases: (1) heating from a corner formed by the left and the bottom walls and (2) heating from a corner formed by the top and the right walls. The effect of Rayleigh number in the range of Ra = 102–5 × 107 on the convective flow field is evaluated for a typical parametric value of Stefan number of 0.01 and Prandtl number of 0.025. Results show distinct convection rolls at the melt zone for the cases under investigations. Evolution of flow fields in the melt zone has been described by a set of isotherms and streamlines for both the cases. The interface fronts for both the cases are initially of convex shape, and around Fourier number of 0.5 turn into concave shape, as viewed from the direction of the movement of melting front. At higher Ra, the rates of melting for top-right side and left-bottom side heated cavities are nearly the same above Fourier number of about 1.2. The average heat flux from the walls scales with Ran , where n is a constant which varies between 0.98 and 1.11. In the melt region, the instability pattern of flow and thermal field changes with the change of effective melt area. Transition to periodic flow is observed at Ra of 7.5 × 106 for case 1 and 2.2 × 107 for case 2, respectively.

Analysis of energy and exergy of eutectic phase change material solidification for various configuration-based triplex tube

This study delves into the energy and exergy analysis of eutectic PCM solidification within a triplex tube latent heat storage unit featuring inner tubes of triangular, pentagonal, square, and circular configurations, analyzed numerically. Results encompassing the impacts of mean temperature, solidification temperature, melting fraction, exergetic efficiency, exergy destruction, heat transfer rate, entropy generation number, and system efficiency on solidification time are presented and compared using contour maps and figures. The research also scrutinizes the effects of Fourier numbers on Stefan, Rayleigh, and Nusselt numbers for TES systems based on inner configurations. Past studies primarily concentrated on cylindrical shapes for all three tubes within triplex-tube heat exchangers, disregarding varied internal tube configurations. This investigation introduces novelty by investigating diverse innermost tube geometries (triangular, square, pentagonal, circular) within a triplex tube heat exchanger. The tangible advantages encompass enhanced thermal efficiency relevant to industries such as oil and gas, chemical processing, food and beverage, and power generation. The inner triangular triplex tube thermal energy storage (TES) system exhibits superior performance over pentagonal topologies, boasting stronger Stefan and Rayleigh numbers by 22.52% and 22.86%, respectively, at Fo = 0.0023. Eutectic PCM solidifies 50%, 65%, and 66% faster within triangular configurations than the triplex tube's pentagonal, square, and circular interiors.However, the pentagonal inner tube topology outperforms the triangular one by 13.36 % at a solidification time of 300 seconds. Eutectic PCM solidifies faster in triangular TTTES systems due to their 0.3%, 1.02%, and 1.10% lower heat transfer temperatures than pentagonal, square, and circular systems. Furthermore, in 1800 seconds of solidification, the triangular inner tube discharges 20.16%, 4.92%, and 3.37% more than pentagonal, square, and circular TES systems. Pentagonal, square, and circular inner tube topologies are 13.36%, 3.01%, and 3.84% less efficient than triangular TTTES systems. TES systems with triangular shapes achieve rapid solidification of eutectic PCM at 305.24K, establishing their efficiency over pentagonal, square, and circular configurations.

Interfacial heat transfer and melt-front evolution at a Fractal Cantor structured interface under various PCM melting conditions

With the aim to investigate heat transfer characteristics of PCM on micro-textured hot surface, this study numerically investigates the heat transfer process of PCM at fractal Cantor structured surfaces using the total enthalpy-based lattice Boltzmann method, which is partly validated by experimental testing. The thermal slip length and liquid velocity distribution are assessed as evaluation criteria. Results show that Fractal Cantor structure can significantly stimulate localized thermal convection, thereby reducing the average thermal slip length from 0.3 mm to approximately 0.14 mm. When the Fourier number exceeds 0.1, both thermal conduction and convection should be considered within the melted layer. With the fractal level increasing, a more uniform melt-front evolution can be observed, consequently, minimizing the total melting time by 500 s with the fractal level of 3. Elevating Ste and gravity can significantly increase the flow rate of liquid PCM by augmenting superheat degree and buoyancy effect, thereby enhancing convective heat transfer strength and reducing thermal slip length. According to the orthogonal design, though the fractal level demonstrates minimal range values for both maximum velocity and Rayleigh number, it elevates the sensitivity to the variation of boundary conditions. Ste yields the most significant enhancement in heat transfer performance.

Freezing and Thawing of Enclosing Structures and Foundation Soils Taking into Account the Effects of Solar Energy: Part 2. Problem Statement

Part 1 provides general information about some of the physical properties of water, ice, and snow necessary to understand the non-stationary processes of freezing and thawing of enclosing structures of wet foundation soils. Part 2 presents the physical and mathematical formulation of the problem of freezing of wet soil, the solution of Lyame and Clapeyron, the solution of Stefan, the physical and mathematical formulation of the problem of freezing of the ribbon foundation. The following are considered: description of the process of freezing of a single-layer enclosing structure considering the phase transformations of moisture in the material of the structure according to V.N. Bogoslovsky and the process of freezing of an unlimited plate considering the phase transformations of moisture in the material of the structure according to A.V. Lykov. Mathematical model of non-stationary heat transfer process in wet layered media. Based on the method of small-time intervals, solutions of boundary value problems for frozen and thawed zones in the region of large and small Fourier numbers are given. Prospects for the application of the proposed mathematical models to describe the processes of freezing and enclosing structures and foundation soils are outlined.

Effect of partial cooling-heating configurations on the enhanced latent thermal energy storage performance

A low rate of ice melting can be addressed by adding nanoscale particles of high thermal conductivity; however, other simple and effective techniques are also possible for further enhancement of the thermal characteristics and melting process of ice as well as other phase storage materials for thermal energy storage. In the present numerical study, two techniques combining partial heating and inversion of the active cavity walls in addition to adding hybrid nanoparticles (Cu and Al2O3) are investigated for the sake of enhancing the phase change in the cavity. Modeling is based on Lattice-Boltzmann techniques; numerical predictions are successfully compared with experimental and theoretical published data. The thermal behavior of the enhanced phase change material is analyzed for various Rayleigh and Fourier numbers and nanoparticle concentrations. The isotherms, streamlines, interface position, liquid fraction evolution, and full melting duration are analyzed. The outcomes show that for each concentration investigated, there is a different best configuration for reducing the ice melting time. 76% reduction in the melting time was achieved with a nanoparticle concentration of 6% (hybrid copper and alumina) and proper simultaneous heating and cooling configuration. These findings can guide designing efficient ice-based systems.

The Mutual Influence of Thermal Contact Conductivity and Convective Cooling on the Temperature Field in a Tribosystem with a Functionally Graded Strip.

An analytical model to find the temperature field that has been developed for friction systems consists of a strip and semi-space. The strip is made of a two-component functionally graded material (FGM) with an exponentially changing coefficient of thermal conductivity. In contrast, the material of the semi-space is homogeneous. An appropriate boundary-value problem of heat conduction with constant specific friction power was formulated and solved using the Laplace integral transform method. The model takes into consideration the imperfect thermal friction contact between the strip and the semi-space, and also the convective cooling on the exposed surface of the strip. The appropriate asymptotic solutions to this problem for low and high values of Fourier number were obtained. It is shown how the determined exact solution can be generalized using Duhamel's formula for the case of a linearly reduction in time-specific friction power (a braking process with constant deceleration). Numerical analysis for selected materials of the friction pair was carried out in terms of examining the mutual impact on the temperature of the two Biot numbers, characterizing the intensity of the thermal contact conductivity and convective heat exchange on the exposed surface of the strip. The obtained results can be used to predict the temperature of friction systems containing elements made of FGM. In particular, such systems include modern disc braking systems.

Novel experimental technique to evaluate soil thermal conductivity in a transient state

novel experimental technique to evaluate soil thermal conductivity in a transient state

Asymmetric PCM melting and thermal convection in a rectangular enclosure with straight and wavy heat transfer passages

Experimental and numerical investigations of thermal convection in the vicinity of a straight and wavy horizontal heat transfer fluid passage (HTF)s placed in a rectangular enclosure filled with phase change material (PCM) are presented. The enthalpy-porosity-based finite volume solver is used to simulate the spatiotemporal evolution of the thermal convection, which is well-complemented by experimental visualization and thermocouple measurements. Heat transfer from the horizontal HTF exhibits asymmetrical melting. Heat diffusion is the dominating energy transfer mechanism on the bottom part of the HTF passage and is compared with the Stefan problem. The temporal evolution of thermal convection on the top part of HTF passage involves three distinct phases of melting, viz. initial conduction phase, Rayleigh–Bénard (R-B) convection with linear convection, and vortex coalescence effects. The final stage of the melting process is influenced by the topography of a peninsula of unmelt PCM, which is influenced by specific top-boundary conditions. Thermal convection in PCM above the wavy HTF passage exhibits restricted plume development leading to an improved melting rate and a higher average melt height. Augmentation of internal convection characteristics of HTF with the evolution of melting is also explored. A systematic investigation of the convection plume development and heat transfer characteristics in PCM by varying the HTF Reynolds (1700<Re<2750) and Stefan numbers (0.4<Ste<0.6) has been carried out, and analyzed the nature of thermal plumes, melt fraction, and average penetration length with the Fourier number. Additionally, novel correlations are proposed between Nusselt and Rayleigh numbers for straight and wavy tubes in the intermediate melting stage (1.3×104<Ra<4.7×107).

Assessing the Impact of Thick Electrode Structure on the Fast Charge Performance of Lithium-Ion Batteries

The lithium-ion battery (LIB) is a key technology for inexpensive, renewable, and safe energy storage system, but there are a few challenges that need to be addressed to make LIB more efficient. One critical challenge is increasing both energy density and fast charging capability. Increasing electrode thickness can increase the energy density of lithium-ion batteries. However, increasing electrode thickness increases transport limitations and the risk of lithium plating, which limit safe fast charging capability. This work analyzes prospective improvements to the conventional lithium-ion cell electrode structure that may facilitate high energy density and fast charging capabilities. A 2D lithium-ion battery model is applied to five different cell designs to understand the impact of thick electrode structure on performance at different charge and discharge rates for a single cell. These five different cell designs consist of one conventional cell and four cells with electrodes modified by varied electrolyte channel arrangements. The simulated electrodes were taken as Li(Ni1/3Mn1/3Co1/3)O2 (NMC) for the cathode and graphite for the anode. The simulated electrolyte was 1 M lithium hexafluorophosphate (LiPF6) in 1:1 ethylene carbonate (EC) and diethylene carbonate (DEC). All five cells were simulated under discharge at C/10, C/2 and 1C followed by charge at 1C, 3C, and 5C with no rest time prior to charge. Adding electrolyte channels on the anode side was found to facilitate lithium ion transport and reduce the risk of lithium plating. Modification of both electrodes did not present any benefit compared to the conventional cell. Analysis of cell behavior based on mass transport Fourier number and a dimensionless mass flux parameter was performed to compare different electrodes at different charge and discharge conditions. These dimensionless parameters provide a means for the general assessment of prospective electrode structure modifications.

Scale modeling of thermo-structural fire tests of wood members

Standard fire resistance testing is essential to qualifying wood-based materials to be approved for use in building assemblies. In a previous study, we developed a theoretically based, experimentally validated scaling methodology for reducing the size of the test article while maintaining the same thermal and structural response exhibited in the large-scale test. This paper is focused on demonstrating these scaling laws for wood with combined thermo-structural loading. Due to load capacity limits, dimensional lumber boards at ½-scale and ¼-scale were subjected to combined bending and thermal loading. Samples were placed in static three-point bending with the loading scaled to have structural similitude, while simultaneously, the bottom surface was exposed to a scaled fire exposure. Analytical modeling of wood pyrolysis demonstrated that, due to char kinetics as the heating rate is increased in the tests, equivalently less char is formed in the reduced-scale tests. Therefore, we developed a char timescale correction factor, calculated from both model predictions and measured charring rates, which modified the previous Fourier number time scaling laws. Scaling exposure time by our updated thermo-structural test scaling laws, the smaller ¼-scale test deflection results predict the behavior of the equivalent larger ½-scale tests by between 11.0% to 16.1%.

Effect of Convective Cooling on the Temperature in a Friction System with Functionally Graded Strip.

An exact solution of the boundary-value problem of heat conduction was obtained with consideration of heat generation due to friction and convective cooling for the strip/semi-space system. Analytical solutions to this problem are known for the case with both friction elements made of homogeneous materials or a composite layer with a micro-periodic structure. However, in this study, the strip is made of a two-component functionally gradient material (FGM). In addition, the exact, asymptotic solutions were also determined at small and large values of the Fourier number. By means of Duhamel's theorem, it was shown that the developed solution for a constant friction power allows to obtain appropriate solutions with a changing time profile of this value during heating. Numerical analysis in dimensionless form was carried out for the FGM (ZrO2-Ti-6Al-4V) strip in combination with the cast iron semi-space. The influence of the convective cooling intensity (Biot number) on the temperature field in the considered friction system was investigated. The developed mathematical model allows for a quick estimation of the maximum temperature of systems, in which one of the elements (FGM strip) is heated on the friction surface and cooled by convection on the free surface.