Solid Temperature Profiles Research Articles

On thermal non-equilibrium (TNE) model for heat transfer in ternary ferro-nanofluid with rectangular porous fin

The heat transmission in a rectangular porous fin affected by a thermal non-equilibrium model with radiation and magnetic field influences is studied in this study. A ferrofluid containing ferroparticles (Fe3O, CoFe2O4, and Cu) and a mixture of 50 % water and 50 % ethylene glycol coats the fin. Dimensionless form is later achieved by formulating the governing equations for both the solid and ferrofluid phases. In order to get the answer, the Runge–Kutta–Fehlberg (RK-45) scheme is used. Visual and tabular representations are used to investigate the effect on heat transmission of the Biot and Rayleigh numbers as well as the porous and convective parameters. The results show that the solid phase temperature profile is inferior for lower Hartmann numbers (H) and Rayleigh numbers (Ra). The disparity in temperature between the solid and ferrofluid phases decreases in proportion to the Ra. Applications for this type of device include heat exchangers, air conditioners, and cooling towers.

Comparison of discriminant analysis coupled with principal component analysis (PCA-DA) and back propagation neural network (BPNN) as classification model for decision support system in porous ceramic matrix (PCM) based burner

Two classification models discriminant analysis coupled with principal component analysis (PCA-DA) and back propagation neural network (BPNN), are for the first time applied for decision support system in porous ceramic matrix (PCM) based burner. The PCM based burner is simulated numerically, and 121 pairs of gas and solid temperature profiles are generated as input data. The operation of PCM based burner is classified into four, on the basis of important properties of PCM like extinction coefficient and convective coupling. With the help of the data, the classification models are developed. The classification models are monitored and analyzed through different plots and classification parameters like specificity, sensitivity and precision. Further, new samples are correctly allocated to their corresponding class by the classification models. The classification models are also explored and compared under noisy data (2% and 5%). The performances of both the classification models are found to be good for no noise case with all the parameters like sensitivity, specificity, and precision values greater than 0.69, for both the models. However, with 2% noise case, BPNN performs better than PCA-DA. The minimum value of parameters (sn, sp, & pr) is 0.67 with BPNN and 0.50 with PCA-DA, respectively. Under 5% noise, the minimum values of the parameters dropped to 0.47 for PCA-DA and 0.50 for BPNN, respectively. With the help of plots though, the new samples are easily identified to their correct class 3.

Experimental and Computational Evidence of Damped Axial Conduction with Reciprocating Flow

Abstract Axial conduction is a crucial performance deteriorating factor in miniaturized heat transfer devices, primarily due to the low fluid flow rates, high solid cross-sectional to free-flow area ratio, and use of high thermal conductivity materials. These causative factors, inherent to micro-scale systems, should be such that the axial conduction is minimum. The reciprocating flow of the convective fluid (instead of steady unidirectional flow) is proposed per se as an alternative, which directly alters the solid temperature profile, the root cause of axial conduction. An experimental setup is built as a proof of the concept. In the test rig, a double-acting reciprocating pump generates a fully reversing periodic flow of air through a flow channel carved into a steel block embedded with a heater. The experimental temperature profile in the solid at the cyclic steady state is bell-shaped, indicating a virtual adiabatic plane capable of restricting axial heat transfer. The experimental results are verified taking the help of an independent finite-element-based numerical analysis. Similarly, the non-dimensional interfacial flux ratio (?_0 ), integrally related to axial conduction, for unidirectional and reciprocating flow is significantly different. This ratio in the vicinity of the inlet is ~53% less with the reciprocating compared to the equivalent unidirectional flow. The optimal thermal performance with the reciprocating flow is correlated through a critical Strouhal number expression, Sr ≤ (pDh)/L. In thermal management applications employing reciprocating flow, the limiting relation can be used to determine flow parameters and optimum geometry design.

Hydrogen direct reduction ironmaking process for zero CO2 emission: A study on the effect of particle properties changes during the multiple non-catalytic gas-solid reactions

Direct hydrogen reduction (H-DR) is one of the most attractive technologies for decarbonization in the iron and steelmaking industries. Improvements in process efficiency depend on a multi-scale evaluation since the industrial performance is significantly affected by transient non-catalytic gas–solid reactions at the pellet scale. This study investigated the effect of temperature-dependent morphological changes in industrially produced pellets during isothermal reduction temperatures from 600 to 900 °C. A 2D axisymmetric pellet grain model using the finite element method and considering the three reduction reactions and the mass and heat transfer phenomena was developed to evaluate the evolution of the solid transformations along the pellet radius during the reduction time. Based on the experimental results, structural properties of the pellets, such as grain size, tortuosity, and transient porosity, were incorporated into the proposed pellet model. The simulation results under different conditions show good agreement with experimental data when changes in the pellet tortuosity are considered, particularly at higher temperatures. Furthermore, predictions of solid and gas concentration and temperature profiles over the pellet radius during the reduction process evidenced the transient behavior of the process. The findings represent an important contribution to the degree of knowledge on the H-DR process application by providing information on the effect of structural parameters of the pellets for the current status of mathematical models of the process.

Magnetohydrodynamic chemically reactive viscoelastic fluid flow through an inclined porous layer

AbstractAnalysis of a time‐independent magnetohydrodynamic viscoelastic fluid flow in a deformable inclined porous layer with first‐order chemical reaction has been investigated. Walters' fluid model has been used to study viscoelastic fluid. The walls are suctioned/injected at a constant rate. The expression representing the solution for solid displacement, fluid velocity, temperature, and concentration distribution is obtained. The effect of applicable parameters on solid displacement, fluid velocity, temperature, and concentration are discussed graphically, while skin friction, heat transfer, and mass transfer are revealed in a tabular structure. It is noticed that solid displacement, fluid velocity, and temperature profiles decrease when the viscoelastic parameter increase. Solid displacement enhances and the velocity of the fluid reduces owing to the influence of increasing drag parameter, whereas the reverse effect is seen for the volume fraction parameter. Nusselt number at the walls shows the opposite behavior for the viscoelastic parameter and Eckert number. Sherwood number at the walls shows opposite behavior for Reynolds number, Schmidt number, and radiation parameter. Also, the entropy generation number rises as a result of the influence of viscoelasticity and Eckert number.

Ignition of thermally-thick blunt body PMMA samples using a heated wire

Ignition limits and ignition delay times of thermally-thick polymethyl methacrylate (PMMA) spheres (4-cm diameter) and cylinders (5.08-cm diameter) are investigated by placing an electrically-heated wire coil beneath the sample in a slow forced flow. The wire serves as both a heater for the solid sample and a gas-phase hot spot to ignite the oxidizer-fuel vapor mixture. In the experiments, the wire's electrical current and power-on time, its distance from the sample surface, the forced flow velocity, oxygen percentage, and pressure are systematically varied. Ignition limits as a function of the oxygen percentage, pressure, and igniter current are determined. Two ignition delay times are determined: igniter-assisted ignition and self-sustained ignition. These critical times are also functions of the degree of heat-up of the sample interior. Solid temperature profiles are measured using embedded thermocouples to determine the sub-surface temperature gradients at the moment of ignition. The heat transfer modes from the igniter to the solid sample are numerically investigated during the pre-pyrolysis heat-up period. At the forward stagnation-point region where ignition occurs, radiation is greater than convection and accounts for approximately 60% of the total heat input. This is consistent with the experimental findings on ignition delay times and heat flux measurements.

Forced Convection in a Transpired Passage With a Porous Medium Insert

Abstract Forced convective heat transfer in a passage with a porous medium matrix subjected to uniform blowing has been fully analyzed, using a local thermal nonequilibrium approach, in application of transpiration systems on the basis of porous medium. An exact solution was found for the asymptotic case of infinitely high interstitial Biot number. In order to extend the problem to general local nonthermal equilibrium cases, an analytical solution procedure has been developed, introducing six unknown parameters to describe both fluid and solid temperature profiles, which are then determined by solving six independent differential and integral equations based on the two energy equations for individual phases and their corresponding boundary conditions. The important performance index for the problem, namely, the overall cooling effectiveness is found quite sensitive not only to the blowing ratio, but also to the interstitial Biot number and fluid to solid effective thermal conductivity ratio. It rises with the blowing ratio and effective thermal conductivity ratio, while it drops as increasing the interstitial Biot number toward the local thermal equilibrium. The present analysis reveals that the local nonthermal equilibrium analysis is definitely needed for accurate estimation of the transpiration-cooled wall temperature.

Analytical closed-form solution for fluid flow through microchannel heat sinks including axial conduction

An analytical study on the convective heat transfer through a rectangular microchannel heat sink including solid axial conduction, has been performed. The system has been split into two coupled boundary value problems, each addressing the heat transfer to the fluid through different routes (namely, the sidewall or fin and the base wall or substrate). The results are derived in the form of a net wall and fluid temperature rise. The validation of the proposed analytical model has been done using existing experimental data and a three-dimensional conjugate computational model. The results show excellent agreement in terms of solid and fluid temperature distributions. The parametric studies show an increasingly non-linear behaviour in the solid and fluid temperature profiles in the microchannel, if axial conduction is dominant. The simulated results are consistent with the CFD and experimental outcome. It has also been noted that a uniform heat flux applied at the bottom of the microchannel (substrate) cannot ensure the transfer of heat uniformly to the fluid. If axial conduction is high, a significant fraction of the applied heat influx is transmitted to the fluid near the channel entry region with a corresponding reduction in the flux distribution at the channel exit.

CFD modelling of coal gasification in a fluidized bed with the effects of calcination under different operating conditions

This paper investigates the thermochemical and physical conversion processes of coal gasification numerically with particular interest on calcination in a bubbling fluidized bed furnace. A comprehensive Eulerian-Eulerian three-dimensional model is developed for studying the gasification process. Three calcination cases are carried out under different operating conditions while one inert case is conducted to evaluate the effect of calcination. The presented numerical results aim at determining the mechanism of coal gasification in an air-steam environment with different flowrates. Evidence of particle segregation is found in the bed of coal and limestone due to density reduction and diameter shrinkage. Char conversion is investigated for different air-coal and steam-coal ratios, also the effect of bed temperature, fluid flowrate and fuel feeding rate on the carbon conversion is studied comprehensively. The highest char conversion rate is observed in the airflow rate of 17.0 kg/h where the bed temperature is found to be maximum. A noticeable impact of calcination is found in the gaseous emission while increasing CO2 concentration. Time averaged solid and gas temperature and species concentration profiles indicate the steady-state condition of numerical simulation.

Heat transfer analysis of rectangular porous fins in local thermal non-equilibrium model

• Analytical solutions on convective-radiative porous fin in LTNE is accomplished. • Darcy model and Boussinesq approximation are used to simulate the porous medium. • The two energy equations are solved using the Adomian Decomposition Method. • Results are given as temperature profiles and total Nusselt numbers. • Criteria to compare LTNE and LTE hypothesis are given for both scale analysis and ADM. In this study, an analytical solution of a porous fin with natural convection and radiation heat transfer is carried out. For the first time, the analysis is accomplished in Local Thermal Non-Equilibrium (LTNE) model. The investigation is carried out on a porous fin with finite length and adiabatic tip. The Darcy model and Boussinesq approximation for buoyancy effects are used to evaluate the infiltration velocity in the porous medium. Two energy equations are solved using the Adomian Decomposition Method (ADM). The solution is validated with the numerical solution of the finite difference method, and with the asymptotic solution for the Local Thermal Equilibrium (LTE) model. The results are presented in terms of temperature profiles and total average Nusselt numbers. They pointed out the effects of internal and external radiation and convection heat transfer, as well as thermal conductivity ratio and dimensionless thickness. It was found that solid phase temperature profiles decrease as the Biot, Bi , and Rayleigh, Ra *, numbers decrease, whereas the difference between the solid phase and fluid phase temperatures, for assigned Bi , decreases for lower Ra . Thermal conductivity ratio and dimensionless thickness increase engender higher solid phase temperature for assigned Bi and Ra *. The total Nusselt number increases as Ra *, Bi and external radiation increase, whereas it decreases with the thermal conductivity ratio. Criteria to compare LTNE and LTE assumptions are proposed, and they highlight the fact that the minimum Biot number to accept the LTE assumption becomes lower as the Rayleigh number decreases.

Identification of Coating Thickness in Cement Rotary Kiln

The cement industry is one of the major industries in every country. This industry is the driving force behind the development of a nation. The heart of this industry is the rotary kiln. One of the significant concerns about a rotary kiln is forming a cover of molten materials on the kiln's inner wall called coating. The low thickness of this coating cause burns to the wall refractory bricks and heavy damage to the kiln, while its high thickness reduces the production volume and quality of products. Currently, the kilns are checked by experienced technicians for empirical coating estimation. This paper aims to identify the thickness of the coating for the automatic control purpose of the kiln. The identification problem of coating thickness is based on thermal resistances in different layers of the kiln and heat transfer equations between these layers. For this purpose, the linear and nonlinear identification methods such as Ordinary Least Squares (OLS), Recursive Least Squares (RLS), global search method, and genetic algorithm are used. The coating can be identified in the proposed identification approach by having the kiln's ambient and internal solid temperature profiles. The raw data for the identification process has been extracted by Finite Element Analysis (FEA) for a given solid temperature profile along with the kiln and different kiln coating thicknesses. The modeling and simulations carried out in this paper show that the identification methods were able to determine the amount of coating with acceptable errors depending on the method.

Local thermal non-equilibrium (LTNE) model for developed flow in porous media with spatially-varying Biot number

The local thermal non-equilibrium (LTNE) model has been extensively used to model convective heat transfer in porous media. Most of the past LTNE-based models account for thermal interactions between fluid and solid phases in the form of a constant Biot number (Bi). This work presents a local thermal non-equilibrium model for fully developed flow in a channel filled with a porous medium where Bi itself varies across the channel. A set of differential equations for fluid and solid phase temperature fields are derived under this condition, which are shown to be generalizations of previously presented results for constant Bi. Results from the present analysis are shown to reduce to and agree with past work for the special case of constant Bi. The variable Bi model is used to investigate the effect of thermal properties such as thermal conductivity on the fluid and solid temperature profiles. The nature of temperature distributions are correlated with the spatial variation in Bi, including for parabolic and sinusoidal variation. Specifically, for periodic Bi, the locations of maxima and minima in temperature fields are found to be well correlated with corresponding maxima and minima in Bi. Nusselt number (Nu) for different values of thermal conductivities and heat generation rates are determined for variable Bi. This work accounts for an important physical consideration in porous media and generalizes previously-presented LTNE models for porous media in a channel.

Simulation and Optimization of Coal Gasification in a Moving-bed Reactor to Produce Synthesis Gas Suitable for Methanol Production Unit

This paper presents process simulation and optimization of coal gasification process<br /> in a moving-bed reactor using Pittsburgh No. 8 coal as feed. The system of differential<br /> equations for the mass and energy balances was solved using 4th-order Runge-Kutta method and optimized by non-dominated sorting genetic algorithm-II (NSGA-II) method.<br /> The simulation was used to predict solid and gas temperature profile and gas composition<br /> along the reactor. The simulation results were compared successfully with experimental<br /> data relevant to Westfield plant in Scotland. In addition, the effect of operating parameters such as coal-to-oxygen molar ratio, steam-to-oxygen molar ratio, inlet gas temperature, reactor pressure, and oxygen mole fraction in inlet air on amount of synthesis gas (syngas) production, hydrogen to carbon monoxide molar ratio (HCMR) in produced syngas, and coal conversion was investigated. Finally, the reactor performance was optimized to produce the highest syngas production with a HCMR of two using NSGA-II method.

Modeling batch fluidized bed drying of pharmaceutical powder: Influence of hydrodynamic regime and sorption isotherms

A mathematical modeling, based on the two-phase theory of batch fluidized bed drying of type A particles and type B particles pharmaceutical powders, was performed. A perfectly mixed flow bubbling regime and an axially dispersed plug flow turbulent regime with a freeboard section were assumed. The experiments were carried out in a pilot-scale bed and in an industrial scale bed. The experimental sorption isotherms were used to model the falling rate drying period. The influence of the particles hygroscopic properties on the drying rate and on the temperature profile was discussed. The simulated solid moisture content and temperature profiles are in good agreement with the experimental results.

Concentration and temperature profiles in a fixed bed column based on an analytical solution of the axial dispersion model for binary and multicomponent non-isothermal adsorption processes

An analytical solution to model dynamic adsorption of multicomponent mixtures in packed beds is presented. The analytical solution describes transient concentration profiles together with gas and solid phase temperature profiles during adsorption and desorption processes. The breakthrough curves predicted by the analytical solution are in satisfactory agreement with numerical simulations and experimental data reported in the literature.

Facile lipase-catalyzed synthesis of a chocolate fat mimetic

A cocoa butter equivalent (CBE) was synthesized enzymatically from readily available edible fats with fatty acid and triacylglycerol compositions that closely resemble the fat present in chocolate, cocoa butter. A commercially available immobilized fungal lipase, Lipozyme RM IM, was used as the reaction catalyst. Reaction parameters were a temperature of 65 °C, water activity of 0.11, a 4 h reaction time, and a substrate mass ratio of a commercial enzymatically synthesized shea stearin (SS) to palm mid-fraction (PMF) of 6:4 (w/w). Fractionation was also used after reaction completion to further approach the triacylglycerol composition of cocoa butter by removing trisaturated and unsaturated triacylglycerols. The yield of the triglyceride 1-palmitoyl-2-oleoyl, 3-stearoyl-glycerol (POS) produced was 57.7% (w/w). The amounts of 1,3-dipalmitoyl-2-oleoyl-glycerol (POP), (POS) and 1,3-stearoyl-2-oleoyl-glycerol (SOS) in the final CBE were 11.2%, 36.3%, and 34.8%, respectively. In comparison, the amounts of POP, POS and SOS in the cocoa butter used in this study were 15.2%, 38.2%, and 27.8%, respectively. No significant differences (P > 0.05) in melting point and enthalpy of fusion between CB and the CBE were observed. In comparison, a non-interesterified blend of SS and PMF (60:40 w/w) showed significantly (P < 0.05) higher melting point and lower enthalpy of fusion compared to CB. The crystal polymorphic form V of CB (β2-3L) was similar to that of CBE and SS/PMF (60:40 w/w). The solid fat content (SFC) vs. temperature profile of the CBE generally resembled that of CB, except that the CBE had significantly (P < 0.05) higher SFCs at 5, 10, 15, 20 and 25 °C compared to both CB and SS/PMF (60:40 w/w). Addition of 15% (w/w) CBE to CB did not cause any changes in physical properties (melting point, SFC and crystal polymorphic forms) of the CB. This study demonstrates the potential for synthesizing a CB-like CBE using a green, rapid, straightforward one step enzymatic conversion followed by fractionation from widely available edible fats.

Experimentally Verified Mathematical Model of Polymer Plasticization Process in Injection Molding.

The mathematical model of the polymer plasticization in the reciprocating screw injection moulding machine is presented in this paper. Methods of calculation of the most important flow characteristics, such as the solid bed profile, the pressure and temperature profiles, the mass flow rate, the power demand, the screw torque and the energy consumption were analysed. According to the mathematical model, a computer program was developed. Based on the computer program, simulation studies of the injection moulding process were conducted. Thereafter, the experimental studies, evaluating the theoretical model from the accuracy and usefulness point of view, were carried out. Important output quantities, such as the temperature and pressure profiles, the power demand by the screw, the torque on the screw and the screw rotation time were measured. The studies were performed on a specially made research office. The simulation results were compared with the experimental data measured for the most popular polymers and different operating parameters of the injection machine. The experimental studies have indicated the need to introduce some corrections to the mathematical model. Several modifications have been made to the model, mainly related to the methods of stress determining in the polymer layer. Finally, the output characteristics of the plasticization process in the injection moulding are now correctly determined by the model with an average error less than 10%.

Coupling of an acoustic emissions system to a laboratory torrefaction reactor

This article describes the use and characterization of an acoustic system coupled to a torrefaction reactor. The reactor, including phase shift and frequency, was characterized by applying both Lissajous/Hilbert and cross-spectrum techniques. Optimum acoustic frequencies were identified and an exploratory torrefaction test combining frequencies and temperatures was performed. The results from dynamic solid yields, conversion rates and temperature profiles showed that acoustic fields may improve torrefaction treatment.

Effects of Replica Ceramic Foam Microstructure on Porous Media Combustion Temperature Distribution

Replica ceramic foam (RCF) is a widely used material in porous media combustion. The macro-structural and thermal properties such as porosity and effective thermal conductivity are governed by RCF’s micro-structure and the properties of the material. The aim of this paper is to study the essential influence of the cell structure and the material on porous media combustion temperature distribution. Kelvin model is adopted to describe the micro-structure of the RCF and to establish the correlations between micro-structure with porosity and effective thermal conductivity. Based on these correlations, the effects of strut length, strut cross sectional size, vertex shape together with different materials (include alumina, zirconia and silicon carbide) on the gas and solid temperature profiles are numerically investigated. Results indicate that the SiC RCF burner has the highest temperature peaks of both gas and solid at the same operating parameters. The temperature profiles of gas and solid are significantly affected by the strut length, the strut cross sectional radius and the length of nodes.

Effect of distributor on performance of a continuous fluidized bed dryer

Proper gas distribution is very important in fluidized bed drying in industrial practice. Improper distribution of gas may lead to non-idealities like channeling, short circuiting and accumulation which gives rise to non-uniform quality of dried product. Gas distribution depends on the distributor plate used. Gas distribution mainly depends on orifice diameter, number of orifices and opening area of the distributor plate. Small orifice diameter leads to clogging, and a large orifice diameter gives uneven distribution of gas. The present work involves experimental studies using different distributor plates and simulation studies using ASPEN PLUS steady state simulator. The effect of various parameters such as orifice diameter, number of orifices and the opening area of the distributor plate on the performance of fluidized bed dryer have been studied through simulation and experimentation. Simulations were carried out (i) with increasing air inlet temperature to study the characteristics of solid temperature and moisture in outlet (ii) with increasing orifice diameter and (iii) with increase in number orifices to study the solid outlet temperature profiles. It can be observed from the simulation that, an increase in orifice diameter and number orifices increases solid outlet temperature upto certain condition and then after there is no effect with further increase. Experiments were carried out with increasing opening area (3.4 to 42%) in the form of increasing orifice diameter keeping the number of orifices constant and increasing number of orifices of the distributor plate keeping the orifice diameter constant. It can be seen that the drying rate and solid outlet temperature increase upto certain condition and then after with further increase in the orifice diameter and number of orifices, the change in the drying rate and solid outlet temperature observed is little. The optimum values of orifice diameter and number of orifices from experimentation are found to be 5 mm and 60 (22% opening area).