Fourier Number Research Articles

Thermal Efficiency in Laser-Assisted Joining of Polymer-Metal Composites.

Heat conduction joining is mainly used in laser-based joining of metals with polymers but results in a large amount of dissipated heat. The consideration of thermal efficiency allows the determination of power actually used for creating the joint, which is highly relevant for technical and economic reasons, e.g., for calculating the carbon footprint. In order to describe the thermal efficiency universally, process parameters (focal diameter, joining speed, energy per unit length), metallic materials (AA 6082, AISI 304), geometric parameters (overlap width, material thickness) and various polymers (polypropylene, polyamide 6, polyamide 6.6) were examined experimentally. The discussion of the results is supplemented by numerical simulations of the temperature field. For a general description of the physical relationships, some dimensionless numbers based on the Buckingham π theorem were developed, applied to the experimental data. One of these numbers shows similarity to the Fourier number and provides further information on thermal efficiency and its general understanding in the context of polymer–metal joints, enabling the physical background dissipated to stored heat.

Buoyancy-driven melting and solidification heat transfer analysis in encapsulated phase change materials

Controlled melting and solidification in encapsulated phase change materials (PCMs) is of practical interest, for example, in latent heat storage applications. The choice of PCMs and the dynamic heat transfer characteristics during phase change - affecting the transient charging/discharging rates - are decisive for the energy and power density of the heat storage option. For example, highly conductive, high melting point (above 700 K) metal alloys have a potential advantage as a high energy and power density latent heat storage, compared to the widely used low conducting molten salt and paraffin wax. This advantage depends on the relative dominance of heat transfer modes that vary depending on the thermal properties of the PCM, shape of the encapsulation, and the load conditions, and must be quantified to warrant a fair comparison. We developed a 2D transient phase change model of encapsulated PCMs, accounting for phase change over a temperature range, volumetric expansion and contraction, and multi-mode heat transfer within the encapsulated PCM. The enthalpy-porosity method was used to model the phase change in a fixed grid. Validation was performed with literature data of low and high-conductivity PCM experiments (RT27 and lead). Two types of PCMs were subsequently investigated in detail: a high-conducting binary-eutectic alloy Al-12.6Si and a low-conducting commercially available RT27 paraffin wax (Rubitherm GmbH). The model was used to compare the phase change process and the strength of the various modes of heat transfer in the PCM filled cylindrical stainless-steel encapsulations in horizontal and vertical orientation with constant temperature walls. A full parameter study and non-dimensional analysis are presented for different PCMs. The results quantified the influence of boundary conditions, thermophysical properties and geometrical parameters on the phase change process and the contribution of the natural convection within the encapsulation. The non-dimensional analysis linked the melt fraction and heat transfer rates to a combination of the Fourier, Stefan, Rayleigh and Nusselt numbers. Fitting of the exponents of non-dimensional number groups to the heat transfer calculations allowed to provide general correlations for melting time, melt fraction, heat transfer rates, and characteristics of melting. Such correlations provide general understanding of the transient heat transfer in phase change media and provide engineering tools for designing, for example, a latent heat storage unit.

Mathematical modeling of the diffusion process of liquid additives into extruded pellets of feed stuff for prime fish species

A mathematical model of the diffusion process of liquid components into extruded pellets of feed stuff for prime fish species under vacuum spraying is considered. This will increase the fat content up to 40% and improve the digestibility and nutritive properties of the feed stuff. It is suggested to use the differential equation of molecular diffusion with boundary conditions of the third kind to describe the process of diffusion of liquid in porous pellets. For a mathematical description, the solution of the equation of unsteady molecular diffusion for bodies with the geometric shape of an unbounded cylinder (extruded pellets can be considered such bodies) was used. The studies carried out with values of the Bio criterion over 100 showed that the concentration of liquid additives inside the extruded pellets becomes equal to the concentration of liquid additives on their surface. Given a constant concentration of liquid additives on the surface of extruded pellets, this solution takes place in the form of a rapidly converging series. Considering that for Fourier numbers greater than 0.3 the series converges quickly, then all the members of the series can be discarded except the first one. Thus, the obtained solution of the equation of unsteady molecular diffusion at a constant concentration of liquid additives on the surface of pellets had the form of a rapidly converging series. Taking the logarithm of the obtained equation and solving its Fourier criterion, we attained the expression for determining the duration of the diffusion process. Comparison of the calculated curves and experimental data showed that the root mean square deviation did not exceed 14.3%. The use of vacuum spraying of liquid additives on the surface of pellets made it possible to increase the diffusion coefficient from 4.78?10e-4 to 6.112?10e-4 м2/с in comparison with the traditional technology of pelleting in a drum apparatus.

Microstructural Characterization and Mathematical Modeling for Determination of Volume Fraction of Eutectoid Mixture of the Cu-8.5wt% Sn Alloy Obtained by Unidirectional Upward Solidification

The Cu-8.5wt % Sn alloy presents an extensive microsegregation during its solidification. That microsegregation results in the formation of a eutectoid mixture, which is detrimental to subsequent forming processes. This study deals with the influence of solidification time and cooling rate on the microstructure of that alloy. The unidirectional solidification technique allowed the acquisition of thermal data. The optical microscopy enabled the microstructural characterization of the material, the measurement of dendrite arm spacings and the quantification of the volume fraction of the eutectoid mixture. A semi-analytical mathematical model was proposed to estimate the volume fraction of the eutectoid mixture. The model expresses the volume fraction as an implicit function of the Fourier number. The results showed that the microstructure is dendritic and that the characteristic spacings increase with the solidification time between theliquidusand the peritectic temperatures. The data also showed that for higher cooling rates the dendrite arm spacings are smaller and that there is a tendency for the volume fraction of eutectoid mixture in the columnar zone to increase with the Fourier number and to decrease with the cooling rate. The proposed model allowed obtaining values of volume fraction with the same order of magnitude of the experimental data, but with behavior tendency opposite to that observed.

Compact Algebraic Asymptotes for Small and Large Time Surface Temperatures for Regular Solid Bodies Heated With Uniform Heat Flux: Scrutiny of New Critical Fourier Numbers

Abstract The alternate infinite series at “small time” have been used to analyze the time variation of surface temperatures (ϕs) in regular solid bodies heated with uniform heat flux. In this way, compact algebraic asymptotes are successfully retrieved for ϕs in a plate, cylinder, and sphere in the “small time” sub-domain extending from 0 to the critical dimensionless time or critical Fourier number. For the “large time” sub-domain, the exact solution is approximated in two ways: with the “one-term” series and with the simple asymptotes corresponding to extreme “large time” conditions. Maximum relative errors of 1.23%, 6.24%, and 0.96% in ϕs for the plate, cylinder, and sphere are τcr obtained, respectively, with the “small time”—“large time” approximation using a traditional approach to fix the τcr value. An alternative approach to set the τcr is proposed to minimize the maximum relative error of the approximated solutions so that values of 1.19%, 3.93%, and 0.16% are then obtained for the plate, cylinder, and sphere, respectively, with the “small time”—“large time” approximation. For the “small time”—“one-term” approximation maximum relative errors of 0.024%, 1.33%, and 0.004% for the plate, cylinder, and sphere are obtained, respectively, with this approach.

Coaxial Thermocouples for Heat Transfer Measurements in Long-Duration High Enthalpy Flows.

Coaxial thermocouples have the advantages of fast response and good durability. They are widely used for heat transfer measurements in transient facilities, and researchers have also considered their use for long-duration heat transfer measurements. However, the model thickness, transverse heat transfer, and changes in the physical parameters of the materials with increasing temperature influence the accuracy of heat transfer measurements. A numerical analysis of coaxial thermocouples is conducted to determine the above influences on the measurement deviation. The minimum deviation is obtained if the thermal effusivity of chromel that changes with the surface temperature is used to derive the heat flux from the surface temperature. The deviation of the heat flux is less than 5.5% when the Fourier number is smaller than 0.255 and 10% when the Fourier number is smaller than 0.520. The results provide guidance for the design of test models and coaxial thermocouples in long-duration heat transfer measurements. The numerical calculation results are verified by a laser radiation heating experiment, and heat transfer measurements using coaxial thermocouples in an arc tunnel with a test time of several seconds are performed.

Thermal performance analysis of MWCNT-based capric acid PCM thermal energy storage system

Effect of natural convection during the melting process of capric acid-based multi-walled carbon nanotube (MWCNT/CA) thermal energy storage system has been investigated experimentally. The temperature variations of phase change material were measured during the charging process. Effects of Stefan number and Fourier number on Nusselt number, as well as energy and exergy of the storage medium for different vol. fractions of MWCNT/CA-based phase change material, have been analysed and compared during charging process. Furthermore, the present work also extends to evaluate the thermophysical properties, i.e. thermal conductivity and specific heat capacity in liquid and solid phase of MWCNT/CA-based PCM by T-history method. Results revealed that the melting time for 0.02% vol. fraction of MWCNT/CA-based PCM is 66.66% lower compared to pure capric acid PCM. The thermal conductivity and specific heat capacity of 0.02% MWCNT/CA-based PCM obtained higher value than other samples in liquid and solid phases. Rayleigh number justified that natural convection heating process occurred within the TES system. Furthermore, the energy and exergy of 0.02% vol. fraction-based MWCNT/CA storage medium achieved 61.9% and 70.92% maximum values than pure CA phase change material, respectively. Therefore, 0.02% vol. fraction of MWCNT/CA could be suitable nanoenhanced phase change material for thermal energy storage systems.

New correlations for investigating the melting of phase change material loading green synthesized CuO nanosheets in a spherical container: Experimental study

Abstract In this experimental study, the unconstrained melting process of nano-enhanced phase change material (NePCM) in a spherical container is investigated. For this purpose, the green synthesized copper oxide nanosheets (CuO NSs) as nanomaterial and paraffin wax as phase change material (PCM) is used. The density, thermal conductivity, and viscosity of the samples were measured. The factors of interest were melt fraction (f), Grashof number (Gr), Stefan number (Ste), Nusselt number (Nu), Fourier number (Fo), wall temperature (T, 65, 75 and 85 °C) and nanomaterial mass fraction (wt., 0.00, 0.05, 0.10 and 0.20%). Melt fraction was calculated and validated with a maximum deviation below 16% by using volume shrinkage and image processing methods. Results show that, at the wall temperature of 65 °C, the melting rate of the samples are the same; also, the total melting time for all samples at 65 °C are approximately 40 min, which is 15 and 20 min more extended than the wall temperatures of 75 °C and 85 °C cases. Nu number curves clarify that in the first 5 min of the melting, pure PCM graph is upper than other curves and becomes smoother as the CuO NSs loadings increase. Finally, the melt fraction and Nusselt number correlations are developed with a combination of f, T, Fo, Ste, and Gr. These proposed correlations are valid for the range of 0.002 ≤ FoSte ≤ 0.147 and 12400 ≤ Gr ≤ 169000. Based on the general suggested correlation, the squared correlation coefficient (R2) and mean absolute error (M.A.E.) values for the melt fraction, are 0.912 and 16.4%. Also, these values for the Nu number correlation, are 0.920 and 21%, respectively.

Exergy analysis of a pilot-scale reactor using wood chips

A pilot size reactor has been tested to examine the suitability of the design for effective gas generation. The qualitative assessment of a reactor is considered to be one of the selection criteria for the thermochemical conversion. The pyrolysis reactor is subjected to operate for the temperature histories of 32–400 °C and 33–600 °C, respectively. The chemical exergy and the thermal efficiency are calculated for both operating ranges. The thermal efficiency of the reactor is found to be 46.32%; whereas the chemical exergy of the raw gas is 75.77% while pyrolysing at 600 °C, which is relatively 17% higher than that obtained at 400 °C. The additional burden on the thermal system due to the moisture has reduced the thermal efficiency of the reactor by 5.85% at 600 °C, whereas it is 6.22% for carrying out thermal decomposition at 400 °C. The gas yield for the given reactor is decreased by 0.77% while operating at 400 °C, whereas the char yield is increased by 6.73%. The proposed design is more efficient for higher temperature regimes and for dried biomass. The lumped system analysis is adopted to determine the loss for the transient condition. The heat transfer in the transient condition is measured for the fixed bed of biomass by the Biot and the Fourier numbers. The external heat transfer controls the overall rate of reaction. The intraparticle temperature is homogenous throughout the process though it may depend on the external heat condition. Furthermore, the various losses encountered during pyrolysis make the system energy-intensive. The objective of this work is to provide a clean generation of energy, which can be attained by improving exergetic content of the reactor.

Identification of modes of welding using parametric studies during ytterbium fiber laser welding

Abstract Titanium-based Ti6Al4V alloy and SS 316L are most widely used materials in the manufacturing industry. Also, recent developments in fiber lasers offer remarkable benefits for welding of titanium and stainless steel alloys on account of high processing ability and accuracy. Moreover, identification of conduction and keyhole mode welding during fiber laser welding process is a promising task. Therefore, aim of the present work is identification of weld limits viz, conduction, transition and keyhole in Ti6Al4V alloy and SS 316L welds with respect to fundamental dimensional and non-dimensional parameters. Also, the influence of laser welding process variables and thermal physical properties of Ti6Al4V alloy and SS 316L welds are investigated using linear energy, laser interaction energy and absorbed heat flux. Moreover, the effect of non-dimensional numbers viz. melting efficiency, non-dimensional heat input index, non-dimensional linear energy, Marangoni number and Fourier number are examined. The non-dimensional numbers correlated the combined effect of laser welding process variables and alloy properties with thermal and fluid flow characteristics to analyze its impact on weld pool development. And, evaluation of weld characteristics in definitive weld regimes relative to dimensional and non-dimensional numbers. Moreover, macro and micro-structural analysis and micro-hardness estimation is carried out at distinct weld regimes to examine the weld behaviour.

Simplified methods for characterizing dynamic sorption of SVOCs on viscous particles

Abstract Exposure to indoor and outdoor semi-volatile organic compounds (SVOCs) poses a significant threat to human health. The dynamic mass transfer of SVOCs between gas and particles, especially those containing high-viscosity organic matter, plays an important role in determining the behavior of indoor and outdoor SVOCs and their exposure risk to human health. In this study, four simplified methods are proposed to characterize the dynamic interaction of SVOCs between gas and particles based on an analytical solution of the mass transfer model. The methods entail neither complex series calculations nor solutions to transcendental equations to estimate the SVOC dynamic behavior between the gas and particle phases. Through analysis, the critical value of mass Fourier number, i.e., 0.18, and the critical values of mass Biot number, i.e., 0.1 and 20, are used to divide the ranges of application of the different methods into six zones. The results calculated demonstrate that the simplified methods are sufficiently accurate to estimate the saturation state of SVOCs in viscous particles with different organic species. Based on these methods, the internal SVOC distribution in the particles and the time to reach equilibrium are discussed. The results calculated for benzo[a]pyrene between the gas phase and different particles show that the viscosity of the organic species in the particles has a significant impact on the sorption saturation degree of the SVOCs. Thus, caution should be exercised when the equilibrium assumption is made for studying the interaction of SVOCs between gas and particle phases, especially in the case of particles comprising organic species of high viscosities.

Simplified prediction model of the discharging time of a shell-and-tube LHTES

We present a simplified theoretical model able to predict the discharging performance of a shell-and-tube latent heat thermal energy storage. The model is validated against two-dimensional axi-symmetric numerical simulations. Here, the heat exchange area, A, the whole PCM volume, V, and the heat exchange wall temperature have been kept constant. According to these constraints, the shell-and-tube shape depends on just one geometrical parameter. Thus, six values of the ratio between the external and internal radius of the PCM module, re/ri, in the range between 2 and 6, are considered. The simplified model matches the discharging time predicted by the numerical simulations. Details of the sensible and the latent heat contribution to the discharging time is provided with respect to the radius ratio. Hence, the latent heat contribution represents about the 70% of the overall discharging time in the range 2⩽re/ri⩽6. The results reveal a scaling law between the Fourier number related to the complete solidification and the radius ratio, Fo∝(re/ri)-5.5, supported by the numerical simulations. Moreover, the rescaled dimensionless time, Fo/(re/ri)-5.5, leads to the self-similar behaviour of the liquid fraction βl time series for all the geometries here investigated. Thus, it represents a promising prediction tool for the design of latent heat thermal energy storage in shell-and-tube configuration.

General correlation for frost thermal conductivity on parallel surface channels

Growth of frost layer on cold fins of tube-fin heat exchangers leads to an increase in the pressure drop and a decrease in the frost thermal conductivity and thereby the heat transfer rate. There is a lack of a general model in the literature for estimating the frost thermal conductivity on parallel plate channels, including almost all parameters affecting this factor. In this study, for the first time, the general explicit semi-empirical correlations consist of dimensionless parameters are developed, which apply to parallel surface channels. The dimensionless input parameters include the wall temperature, air temperature, air velocity, frost porosity, relative humidity, specific heat of moist air, latent heat of sublimation, and operating time. The comparative results indicate that the best correlation predicts data points with an coefficient of determination, average absolute relative error, and relative root mean square error equal 0.9921, 2.755%, and 3.713%, respectively. Other available published correlations present higher deviations using the same dataset. Furthermore, to provide a good insight into this study, a sensitivity analysis is carried out employing the validated model. It is shown that the effective thermal conductivity of the frost layer is not only a function of frost density but also depends on a group of dimensionless parameters. It is observed that the thermal conductivity of the frost layer increases with the increase in the Reynolds number, Fourier number, air humidity, and it decreases with the increase in the dimensionless temperature, modified Jakob number, and porosity.

Determination of thermal diffusivity of the material by numerical-analytical model of a semi-bounded body

A mathematical description of the material thermal diffusivity aт in a semi-bounded body is proposed with a relatively simple algorithm for its numerical and analytical by solving the inverse problem of thermal conductivity. To solve the problem, it is necessary to obtain the temperature values of the unbounded plate as a result of a thermophysical experiment. A plate can be conditionally considered as a semi-bounded body as long as the Fourier number Fo ≤ Foк (Foк ≈ 0.04–0.06). It is assumed that the temperature distribution over cross-section of the heated layer of the plate R is sufficiently described by a power function whose exponent depends linearly on the Fourier number. A simple algebraic expression is obtained for calculating aт in the time interval ∆τ from the dynamics of temperature change T(Rп , τ) of a plate surface with thickness Rп heated under boundary conditions of the second kind. Temperature of the second surface of the plate T(0, τ) is used only to determine the time of the end of experiment τк. The moment of time τк, in which the temperature perturbation reaches the adiabatic surface x = 0, can be set by the condition T(Rп , τк) – T(0, τ = 0) = 0,1 K. The method of approximate calculation of dynamics of changes in depth of the heated layer R by the values of Rп , τк , and τ is proposed. Calculation of a т for the time interval ∆τ is reduced to an iterative solution of a system of three algebraic equations by matching the Fourier number, for example, using a standard Microsoft Excel procedure. Estimation of the accuracy of a т calculation was made by the test (initial) temperature field of the refractory plate with the thickness Rп = 0.05 m, calculated by the finite difference method under the initial condition T(x, τ = 0) = 300 (0 ≤ x ≤ Rп) at radiation-convective heating. The heating time was 260 s. Calculation of aт, i was performed for 10 time moments τi + 1 = τi + Δτ, τ = 26 s. Average mass temperature of the heated layer for the whole time was T = 302 K. The arithmetic-mean absolute deviation of aт(T = 302 K) from the initial value at the same temperature was 2.8 %. Application of the method will simplify the conduct and processing of experiments to determine the thermal diffusivity of materials.

Low Frequency Pulsating Jet Impingement Boiling and Single Phase Heat Transfer

Experiments are carried out to characterize the influence of jet pulsations on the single phase and boiling heat transfer under a confined and submerged impinging jet, using water and FC-72. A novel jet pulsation mechanism is developed for introducing the mean flow pulsations at different jet flow rates. The effects of jet Reynolds number, pulsation frequency and amplitude are studied by comparison of the time-averaged Nusselt numbers and boiling curves against steady state data. The root-mean-squared dimensionless temperature oscillations in the heater are correlated to the jet Strouhal number, mean Reynolds number and the diffusion Fourier number of the heater that is based on the frequency of jet oscillations. Under both boiling and single phase cooling conditions, temperature oscillations are found to be inversely related to the Strouhal number with an exponent in the range 0.63-0.75. During pulsating jet impingement boiling, a periodic renewal of the boiling process is observed, where the bubbles on the heater surface are cyclically flushed downstream of the stagnation point in-phase with the pulsating flow. For the cases considered, the root-mean-squared dimensionless temperature is found to be negligible during fully developed nucleate boiling, indicating that the heat transfer process is pseudo-stationary. Here, vigorous ebullition is the dominant mechanism of heat transfer and suppresses any temperature oscillations that can arise due to the flow oscillations. For heat fluxes in the partial nucleate boiling regime and close to critical heat flux however, temperature oscillations decrease with an increase in jet Strouhal number. No marked influence of low frequency jet pulsations is found on the time averaged single phase or boiling heat transfer characteristics (including critical heat flux) for the range of parameters studied.

Revisiting thermal penetration depth for caloric cooling system

Thermal penetration depth is a physical quantity identifying the distance that heat can diffuse through the domain material, which has been widely adopted for thermoacoustic cryocoolers in the past, where the diffusive thermal resistance is the only dominating factor for gaseous refrigerant. By ignoring the surface convection thermal resistance, we show that the conventional thermal penetration depth significantly overestimates the cooling performance of the caloric material. This paper modifies the conventional thermal penetration depth with the consideration of convection thermal resistance and applies this concept to caloric cooling devices. The modified thermal penetration depth can be computed by the approximate fitting formula, which is numerically validated by CFD simulation results. The influence of physical properties and geometric parameters of materials on thermal penetration depth is discussed. In addition, the modified thermal penetration depth can be visualized on Biot number and Fourier number chart, which can guide design of future caloric cooling systems. This design approach is supported by the experimental data from the literature.

Analytical solution for quenching of hot rolled aluminium plates without passing through C-curve

At the end of the hot rolling process, quenching is deployed for obtaining the desired microstructure and mechanical properties. During the quenching of aluminium plates, it is essential to optimize the process parameters such as the plate speed and cooling intensity for surpassing the C-curve. In this study, 1-D steady-state analytical model has been developed with the constant heat transfer boundary condition. The Eulerian computational domain contains the precooling and water cooling regions. Temperature drop starts in the precooling region itself due to back diffusion of heat, which originates from the water cooling region. Based on the analytical solution, the effect of plate speed and heat transfer coefficient on the cooling time has been investigated with the three non-dimensional parameters such as Peclect, Biot, and Fourier numbers. Typically, for the 2xxx (Al–Cu) alloys, every material point in the plate has to reach 350 °C within 0.2 s, which surpasses the nose of the C-curve where the phase transformation (CuAl2) severity can be reduced. This sets the limit for the maximum Fourier number and while keeping Peclect number as the independent variable, the minimum required water cooling in terms of Biot number is identified. The presented analytical solution provide the guidelines for selecting the appropriate combinations of plate speed and heat transfer coefficient for the quenching of continuously moving hot rolled plates. The results indicate that the nose of the C-curve can be surpassed easily by increasing the plate speed instead of reducing which contradicts the common notion.

Determination of Thermal Diffusivity of Material by the Numerical-Analytical Model of a Semi-Bounded Body

A mathematical description of a material’s thermal diffusivity ae in a semi-bounded body is proposed with a relatively simple algorithm for its numerical and analytical calculation by solving the inverse problem of thermal conductivity. To solve the problem, it is necessary to obtain the temperature values of the unbounded plate as a result of a thermophysical experiment. A plate can be conditionally considered as a semi-bounded body as long as Fourier number Fo ≤ Foe (Foe = 0.04–0.06). It is assumed that the temperature distribution over a cross-section of the heated layer of the plate with thickness R is sufficiently described by a power-like function whose exponent depends linearly on the Fourier number. A simple algebraic expression is obtained for calculating ahc in time interval Δτ from the dynamics of temperature change T(Rp, τ) of a plate surface with thickness Rp heated at boundary conditions of the second kind. Temperature T(0, τ) of the second surface of the plate is used only to determine end time τe of the experiment. Moment of time τe, at which the temperature perturbation reaches adiabatic surface x = 0, can be set by the condition T(Rp, τe) – T(0, τ = 0) = 0.1 K. An approximate method of calculating the dynamics of changes in depth of heated layer R by values of Rp, τe, and τ is proposed. The calculation of ahc for time interval Δτ is reduced to an iterative solution of a system of three algebraic equations by matching the Fourier number, for example, using a standard Microsoft Excel procedure. Estimation of the accuracy of calculation of ahc at radiation-convective heating was performed using the initial temperature field of the refractory plate with thickness Rp = 0.05 m, calculated by the finite difference method under initial condition T(x, τ = 0) = 300 (0 ≤ x ≤ Rp). The heating time was 260 s. Calculation of ahc, i has been performed for ten time moments τi + 1 = τi + Δτ, Δτ = 26 s. Average mass temperature of the heated layer for the entire time was τe T = 302 K. The arithmetic-mean absolute deviation of ae (T = 302 K) from the initial value at the same temperature was 2.8%. Application of the method will simplify conducting and processing experiments to determine thermal diffusivity of materials.

Criteria for the onset of convection in the phase-change Rayleigh–Bénard system with moving melting-boundary

Here, for the first time, we report the criterion for the onset of convection in a low Prandtl number phase-change Rayleigh–Bénard (RB) system with an upward moving melt interface in a two-dimensional square box for a wide range of Rayleigh number Ra and Stefan number Ste (defined as the ratio between the sensible heat to the latent heat). High fidelity simulations were performed to study the phenomenon of the onset of convection. Unlike the classical RB system in the phase-change RB system, it was found that the onset of convection depended on Ste and Fourier number τ, in addition to Ra. The phase-change RB system with upward moving melt interface can be classified into two groups: slow expanding phase-change RB system (Ra ≤ 104) and moderate/fast melting phase-change RB system (Ra > 104). The slow melting phase-change RB system becomes unstable when the effective Rayleigh number based on the melt height is ≈1295.78, consistent with the finding by Vasil and Proctor [“Dynamic bifurcations and pattern formation in melting-boundary convection,” J. Fluid Mech. 686, 77 (2011)]; however, moderate and fast melting phase-change RB systems become unstable when the product of the local Rayleigh number Ra based on the melt-layer height hyt and the Fourier number based on the melt-layer height reaches a threshold value. Interestingly, it is seen that the criteria for the onset of convection for moderate and fast melting phase-change RB systems show a power law kind of form such that Racrτcr = aSteb + c. In addition, during the initial conduction regime before the onset of convection, it is seen that the Nusselt number at the hot wall is Nuh ∼ τ0.5, and during the onset of convection, i.e., during the formation of the initial convection rolls, the Nusselt number at the hot wall is Nuh ∼ τd, where the value of the exponent d is 2 for low Rayleigh numbers and 4 for higher Rayleigh numbers. This study reports some general characteristics of the onset of convection and some organized behavior in the transient melting phase-change RB system, which are not yet explored and reported in the open literature. This work may lead to significant understanding of different applications of fluid-dynamical melting phase-change RB systems in both natural and engineering systems.

Experimental study and ANN-based prediction of melting heat transfer in a uniform heat flux PCM enclosure

Abstract In this paper, heat transfer during the melting process of n-octadecane as a phase change material (PCM) is experimentally studied. This study is followed by an artificial neural network (ANN) to predict the melting characteristics of PCM. Experiments are performed in a rectangular enclosure subjected to a uniform heat flux in one vertical side. Melting heat transfer is characterized by observing the solid-liquid interface and recording the temperature distribution in the enclosure. Experimental results indicate that heat transfer during the melting process is dominated by natural convection. A multilayered perceptron feed-forward neural network trained by the Levenberg-Marquardt algorithm is used to predict the Nusselt number and the melted volume fraction. Rayleigh, Fourier and Stefan numbers are set as input parameters of the network. The optimal structure of the ANN to predict the Nusselt number show high accuracy in estimating the heat transfer characteristics during melting by achieving the mean square error and the correlation coefficient of 4.42 × 10−6 and 0.999, respectively. Based on the proposed ANN, the majority of the data falls within ±6.23% and ±6.54% of the Nusselt number and the melted volume fraction, respectively.