Mass Biot Number Research Articles

Study of Nano-Powell-Erying fluid flow past a porous stretching sheet by the effects of MHD, thermal and mass convective boundary conditions

The object of this research is to examine the combined effects of mass and thermal Biot numbers on the properties of a Powell-Erying fluid flow that is two-dimensional, constant, viscous, incompressible, and non-Newtonian. In the direction of the flow is an extending sheet encircled by a porous medium. Further consideration is given to the existence of a chemical reaction, thermophoresis, Brownian motion, and velocity lapse, among other factors. Utilizing the Powell-Erying Cauchy non-Newtonian model, the viscoelastic effect is accounted for. When establishing concentration and temperature boundary conditions, thermal and mass Biot numbers are incorporated. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. Furthermore, the Nusselt number, Skin-friction, and Sherwood number coefficients are evaluated and shown in a tabular format utilizing the same parameters. In the end, the numerical outcomes obtained from this investigation are substantiated and considered to be highly consistent with the findings that were previously documented.

Finite element solutions of Double diffusion effects on three-dimensional MHD Nano-Powell-Erying fluid flow in presence of thermal and mass Biot numbers

This work uses a numerical method to investigate the effects of diffusion on the flow of three-dimensional magnetohydrodynamic (MHD) nanofluids. The applicable equations for this problem are derived from the Nano-Powell-Erying fluid model. The result of the differential equation is calculated by solving the problem using the finite element method. The numerical solutions are used to study the three-dimensional structures with the flow of nanofluid to investigate the influence of well-known fluid parameters. The study found that the Hartmann number and buoyancy ratio parameter have a significant impact on the velocity profile, while the Brownian motion and thermophoresis parameters, as well as the thermal and mass Biot numbers, are the main factors influencing the temperature and concentration fields. This study aims to analyse the effect of two different parameters on the flow of MHD nanofluids to improve our basic understanding of this phenomenon. The findings that were produced are compared to the previous work and incipiently, the present numerical results are veritably in good agreement with the previous results. The results of this study can be useful for the optimization and design of various engineering applications.

Flow analysis of radiated micropolar nanofluid on a stretching/shrinking wedge surface under chemical reaction and multiple convective conditions

This paper reports the flow features and distributions of concentration and temperature of a micropolar type nanofluid (water-based) past a stretchable and shrinkable wedge, influenced by variable magnetic force, nonlinear sort thermal radiation and chemical reaction. Along with the consideration of multiple convection, the model of Buongiorno is stated. The Brownian motion and thermophoresis have been kept in the analysis. Suitable similarity alteration is approached to renovate the foremost equations to dimensionless ordinary differential equations (ODEs). Associated conditions became nondimensional forms according to this conversion. Then the numerical solutions of the reduced governing equations with boundary conditions are obtained by adopting the RK-4 technique with shooting criteria. The language MAPLE 17 assisted in developing this solution. Significant upshots of prime parameters on the fluid transmission, mass and heat transport properties are represented with suitable tables and graphs. In tabular form, we have reckoned the physical quantities of heat, mass transfer rates and drag friction coefficients to fulfill the engineering interest. This study acquaints that the material parameter negatively influenced nanofluid’s angular velocity. The fluid’s temperature improves with thermal and mass Biot numbers, but this response goes opposite for the parameter of wedge angle. Chemical reaction and wedge angle parameters amplify mass transport. This study can be beneficial in the blowing of chilled air by AC panels, the abstraction of crude oils, the nuclear power hub, the working of warships, making flaps on the wings of aeroplanes for advanced lift, submarines, the extraction of polymers and several other sectors in advanced science and industrial developments.

Magnetically driven chemically reactive Casson nanofluid flow over curved surface with thermal radiation

AbstractDuring this exploration, Casson nanofluid is taken over a sheet that is curved and stretching in nature and its flow equations are analyzed. Radiation and slip provisions are also taken into consideration. A magnetic field of uniform rate is provided. Convective heat and mass transference extract dominant conclusions from the system. The Brownian migration together with thermophoresis is also included in the flow structure. Moreover, the chemical reaction of higher‐order within the nanoingredients also generates interest. Guiding equations furnished by the selected model are resettled to ordinary differential equations of nonlinear type by significant similarity transformation. We have worked on MAPLE‐19 software to work out this with a suitable accuracy rate. Upshots are shown with diagrams and tables. Corresponding physical consignment such as Nusselt number has been analyzed. Determination of skin friction and moreover Sherwood's number is also in the area of interest. Magnificent advancement in heat sifting is dealt with by magnetic and Brownian motion specification. The graphs prescribed the upshots of thermophoresis and slip parameters. Outcomes convey that temperature together with concentration are reduced for stretching parameters but velocity lines are enhanced. Heat transport goes up for magnetic and Brownian motion framework but elevated outcomes are spotted for radiative flow in contrast to nonradiative flow. Mass transfer is reduced for chemical reaction components but the rate of augmentation is elevated for higher‐order chemically reactive flow. Mass Biot number and temperature Biot number both increase the concentration and temperature transport, respectively.

Analysis of energy transport considering Arrhenius activation energy and chemical reaction in radiative Maxwell nanofluid flow

Nanofluids have innovative possessions that create them hypothetically worthwhile in numerous heat transportation uses, comprising apparatus chilling/vehicle thermal controlling, firewood cells, curative progressions, hybrid-energetic devices, internal freezer and chiller etc. Here the thermo-solutal possessions of convective conditions on nonlinear radiated magnetized Maxwell nanofluid with activation energy in the stagnation region. The homotopic process has been implemented for solutions. The physical parameters are plotted graphically. These outcomes reported that the radiation factor and Prandtl number decline; however, thermophoretic factor intensifies the temperature field of Maxwell nanofluid. Moreover, activation energy factor and mass Biot number exaggerate the concentration field. Additionally, the outcomes for Newtonian case with assessment of former prose are structured in this analysis.

OHAM analysis of fourth-grade nanomaterial in the presence of stagnation point and convective heat-mass conditions

ABSTRACT In this paper stagnation point flow of fourth-grade fluid toward a porous stretching sheet is modeled. Convective conditions of heat and mass transfer are utilized. Problem formulation consists of Brownian motion and thermophoresis effects. Two-dimensional expressions for flow, temperature and concentration are presented. Resulting systems are reduced into ordinary differential equations (ODEs). Computations to the nonlinear system are organized by employing the optimal homotopy analysis method (OHAM). Average residual error (ARE) and average square residual error (ASRE) are computed and analyzed. Physical interpretations to velocity, temperature, concentration, skin friction, and Nusselt and Sherwood numbers are arranged. Velocity profile boosts with higher estimations of material parameters (fluid parameters), injection, and velocity ratio parameters. Decay in temperature in noticed for higher Prandtl number. Intensification in concentration is examined with higher thermophoresis parameter and mass Biot number. Skin friction coefficient reduces for higher velocity ratio parameter. Heat transfer rate (Nusselt number) boosts with Prandtl and thermal Biot numbers. Sherwood number increases with higher Schmidt and mass Biot numbers.

Innovations in Eyring–Powell radiative nanofluid flow due to nonlinear stretching sheet with convective heat and mass conditions: Numerical study

ABSTRACT The augmentation of heat and mass transfer in an industrial process due to convective boundary conditions plays an important role which cannot be ignored and the study lead to saving energy, reducing process time and increasing thermal rating. The impact of nonlinear thermal radiation on Eyring-Powell nanofluid flow over a nonlinear elongating sheet with Joule and viscous dissipation is investigated. The well-posed boundary layer problem is reduced into a highly nonlinear coupled ordinary differential system by adopting similarity transformations. The resultant equations subject to convective temperature and concentration conditions are then solved by employing a Runge-Kutta-Fehlberg 45 order numerical scheme combined with shooting technique. The flow characteristics affected by the pertinent parameters are calculated and presented through the graphs. It is witnessed that the increase in mass Biot number and Lewis number aggregates to rise in the Sherwood number. Also, the rate of heat transfer coefficient rises with growing values of thermal Biot number and radiation parameter. These investigations are of great importance in food processing, crystal growth, fibre and wire coating, production of glass fibres and in many possible areas.

Effect of Convective Heat and Mass Conditions in Magnetohydrodynamic Boundary Layer Flow with Joule Heating and Thermal Radiation

A free convection viscous MHD flow over a semi-infinite vertical sheet with convective heat and mass conditions has been considered. The effects of thermal radiation, chemical reaction and Joule heating on flow are also accounted. The governing nonlinear partial differential equations have been transformed into a set of highly non-linear coupled ordinary differential equations (ODEs) using appropriate similarity transformations. Numerical solutions of transformed equations are obtained by employing the 5<sup>th</sup> order Runge-Kutta Fehlberg technique followed by the shooting technique. The influences of different flow parameters on the momentum, energy and mass field are discussed and shown graphically. Results reveal that temperature and concentration profiles enhance due to increasing heat and mass Biot number parameters.

Kinetics of Starch Degradation during Extrusion Cooking of Steady State Flow Konjac (Amorphophallus oncophyllus) Tuber Flour in a Single Screw Extruder

The presence of glucomannan in Konjac (Amorphophallus oncophyllus) tuber flour has promoted its various applications, especially in the food, drink, drug delivery and cosmetics. Starch is the main impurity of Konjac tuber flour. Although the common wet refining method may result in a high purity Konjac tuber flour, it is very tedious, time consuming and costly. This research aimed to study the kinetics of starch degradation in the extrusion cooking process of dry refining method to produce high quality Konjac tuber flour. In this research, Konjac tuber flour with 20% (w/w) moisture was extruded in a single screw extruder by varying screw speeds (50, 75, 100, 125, 150 and 175 rpm) and barrel temperatures (353, 373, 393, 413 and 433 K). The results showed that the starch extrusion cooking obeys the first reaction order. The reaction rate constant could be satisfactorily fitted by Arrhenius correlation with total activation energy of 6191 J.mol−1 and pre-exponential factor of 2.8728×10−1 s−1. Accordingly, thermal degradation was found to be the primary cause of starch degradation, which shared more than 99% of the energy used for starch degradation. Based on mass Biot number and Thiele modulus evaluations, chemical reaction was the controlling mechanism of the process. The results of this research offer potential application in Konjac tuber flour refining process to obtain high quality flour product. Copyright © 2020 by Authors, Published by BCREC Group. This is an open access article under the CC BY-SA License (https://creativecommons.org/licenses/by-sa/4.0).

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.

Spectral quasi linearization simulation of radiative nanofluidic transport over a bended surface considering the effects of multiple convective conditions

This article enlightens on the hydrothermal performance of radiative nanofluid flow over a curved stretched surface. The curved surface is coiled inside a circular segment of radius R. The surface has been presumed to be permeable and slippery. Effects of multiple convective conditions i.e. convective conditions at the surface caused by both heat and mass transport are incorporated to explore the outcomes. The permeability characteristic of the surface that affects the hydrothermal integrity of the flow has been discussed in detail. The leading equations are renovated into its non-dimensional form by applying similarity conversion. After then, the spectral quasi linearization method (SQLM) is introduced to solve those foremost nonlinear ordinary differential equations (ODEs). Residual error analysis is depicted to show the convergence rate of SQLM. The impact of the pertinent factors on the flow is illustrated through graphs and tables. Several streamlines and three-dimensional plots are provided to enrich the result section. Results assured that temperature reduces for curvature parameter, but intensifies for both thermal and mass Biot numbers. Nanofluidic motion increases for curvature parameter and declines for slip factor. Curvature parameter and Lewis number provide reduction in mass transfer, whereas thermal and mass Biot numbers, slip parameters provide the enhancement. Heat transfer is enhanced for curvature parameter, thermal and mass Biot number.

Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm

A precise determination of the mass diffusion coefficient and the mass Biot number is indispensable for deeper mass transfer analysis that can enable finding optimum conditions for conducting a considered process. The aim of the article is to estimate the mass diffusion coefficient and the mass Biot number by applying nondominated sorting genetic algorithm (NSGA) II genetic algorithms. The method is used in drying. The maximization of coefficient of correlation (R) and simultaneous minimization of mean absolute error (MAE) and root mean square error (RMSE) between the model and experimental data were taken into account. The Biot number and moisture diffusion coefficient can be determined using the following equations: Bi = 0.7647141 + 10.1689977s − 0.003400086T + 948.715758s2 + 0.000024316T2 − 0.12478256sT, D = 1.27547936∙10−7 − 2.3808∙10−5s − 5.08365633∙10−9T + 0.0030005179s2 + 4.266495∙10−11T2 + 8.33633∙10−7sT or Bi = 0.764714 + 10.1689091s − 0.003400089T + 948.715738s2 + 0.000024316T2 − 0.12478252sT, D = 1.27547948∙10−7 − 2.3806∙10−5s − 5.08365753∙10−9T + 0.0030005175s2 + 4.266493∙10−11T2 + 8.336334∙10−7sT. The results of statistical analysis for the Biot number and moisture diffusion coefficient equations were as follows: R = 0.9905672, MAE = 0.0406375, RMSE = 0.050252 and R = 0.9905611, MAE = 0.0406403 and RMSE = 0.050273, respectively.

Stratified electromagnetohydrodynamic flow of nanofluid supporting convective role

This study numerically examined unsteady double stratified EMHD mixed convection flow of nanofluid via permeable stretching sheet. It also looked at the convective heat and mass boundary conditions as well as the Navier velocity slip. In the thermal field, the effects of radiative heat transfer, heat generation/absorption, viscous dissipation, together with Ohmic heating (both magnetic and electric fields) were considered. The concentration field accounts for the chemical reaction. These show the physical behavior of electromagnetohydrodynamic flow associated with the problem formulation. The characteristics in regard to convective heat and mass, Navier slips conditions, as well as double stratification, were imposed. Such structure arises in energy efficiency and performance, which is achievable without higher pumping power, serves in the extrusion manufacturing process involving the thermal system for efficient devices particularly in polymeric, paper production, and food processing. The governing equations, which are nonlinear partial differential equations, were modelled by ordinary differential equations using suitable transformations. The ODEs were solved numerically, using implicit finite difference method (Keller box method). The physical implications deliberated on the behavior via the velocity, thermal energy, and concentration fields as well as the skin friction coefficient; the Nusselt and Sherwood numbers were scrutinized in relation to several parameters via mathematical model. The analysis shows that thermal and concentration stratifications decrease the distributions adjacent to the sheet surface, indicating decrease in the concentration nanoparticles and reduction in thermal energy. Augmentation occurs with convective heat and mass Biot numbers with the fields. The electric and magnetic parameters exhibit opposite flow behavior to the velocity and temperature. Chemical reaction and viscous dissipation weaken the concentration profile. Numerical results were compared with the published data available in the literature for limiting cases, and good agreement was noticed.

Chemically reactive flow and heat transfer of magnetite Oldroyd-B nanofluid subject to stratifications

As an emerging technology owing to countless worthy properties, nanofluids have been concerned by numerous scientists and developed a very energetic arena. Nanofluids, a colloidal assortment of nanoparticles and widespread analysis have disclosed applications of heat transfer because of their intensified aspects of thermal conductivity. The present article explores the nanofluid characteristics on MHD flow of an Oldroyd-B liquid. The convective and stratification mechanisms in the manifestation of thermal radiation and chemical reaction have been utilized for heat and mass transfer features. Additionally, the phenomenon of heat sink/source is accounted. The mathematical relation is established by means of usual boundary layer estimates. Homotopic approach has been utilized for the computation of resultant non-linear ODEs. Thermophysical properties of numerous somatic parameters on velocity, temperature and concentration are scheduled in plots as well as in tabular form. The present interruption reports that the liquid temperature declines for thermal stratification parameter, although conflicting trend is being noted for radiation parameter and thermal Biot number on temperature of Oldroyd-B fluid. The mass Biot number and chemical reaction parameter displays diminishing tendency on concentration field. Additionally, for authentication of current derived elucidations an assessment table of skin friction coefficient is prepared in restrictive cases.

The impact of convective drying on the color, phenolic content and antioxidant capacity of noni (Morinda citrifolia L.)

The effect of thin-layer drying temperature on color, phenolic content and antioxidant capacity of noni slices was investigated. Noni slices were air-dried at 50, 60 and 70 °C under natural convection conditions. Drying curves were fitted to thin-layer drying models in order to evaluate the drying characteristics of the product. In addition, an unsteady-state diffusion equation was numerically solved considering both product shrinkage and a variable mass Biot number in boundary condition to accurately estimate water diffusivity in a process with external resistance to mass transfer. Results revealed that the Aghbashlo model accurately reproduced the experimental behavior. As expected, water diffusivities, corrected for shrinkage, increased with the use of higher drying temperatures, with values in the range of 1.80-3.19 to ×10 -9 m 2 /s. On the other hand, while drying caused a reduction in product lightness (24-31%) and total phenolic content (20-28%), the antioxidant capacity of dried noni was high (82-93% DPPH inhibition), which is advantageous for the further storage or processing of this fruit.

Extension to nonlinear adsorption isotherms of exact analytical solutions to mass diffusion problems

Analytical solutions with algebraic expressions are proposed for one-dimensional nonlinear mass diffusion problems. The solutions proposed to solve sorption/desorption problems are rigorously exact for piecewise linear isotherms. They provide an efficient methodology to devise analytical solutions to nonlinear isotherms, and instantly time-varying boundary conditions, with arbitrary accuracy. An exact solution is calculated for each linear piece of the isotherm and is then propagated iteratively to the next linear piece. For end-user convenience and efficiency, three exact analytical expansions are proposed: a new short and intermediate contact time expansion obtained using the Laplace transform (erfc solution), a modified version of Eq. (33) in Sagiv (2002) with improved stability (Sagiv solution), and a new expansion with a decreasing energy norm (energy solution). All expansions are compared in terms of their accuracy and number of terms for typical nonlinear isotherms, mass Biot numbers and volume ratios covering a broad range of applications. When the thermodynamic conditions are changed at the interface, only the “erfc” and the “energy” solutions retain overall accuracy (machine precision) with few terms (<30). New strategies to enable the simultaneous estimation of diffusion coefficients, isotherms and mass Biot numbers are finally derived.

Mathematical simulation of convective drying: Spatially distributed temperature and moisture in carrot slab

A one-dimensional unsteady state mathematical model of coupled heat and mass transfer equations is developed to simulate the convective drying of individual food. The semi-analytical proposed solution method considers fundamentals of the drying process and takes internal resistances to temperature and moisture into account. Present study describes a novel solution approach of thin layer drying for spatially distributed temperature and moisture content within carrot slices. Temperature and moisture differences of surface and center, heat, and mass Biot numbers are calculated during the drying. In addition, the effects of Biot number and relative humidity on drying kinetics of carrot slices are investigated. The procedure of solution approach and obtained results are expected to be useful to drying industry. The predicted temperature and moisture history of food in drying process is validated with a set of published experimental data. A comparison between the theoretical and experimental results has shown a remarkable agreement.

Identification of Diffusion Transport Properties from Desorption/Sorption Kinetics: An Analysis Based on a New Approximation of Fick Equation during Solid−Liquid Contact

The identifiability of three diffusion properties (diffusion coefficient D, partition coefficient K, and convective mass transfer coefficient hm) from desorption kinetics (or equivalently sorption kinetics) was investigated from a new approximated analytical solution of 1D diffusion coupled with a Robin boundary condition. A generalized least-squares criterion, which extends classical identification techniques, was proposed. The robustness of classical and modified criteria was compared on both experimental and simulated data including different sampling strategies and noise levels. Confidence intervals and bias were calculated for a large set of conditions: desorption levels ranged between 30% and 100% (equilibrium), the dilution factor ranged between 10 -3 and 10 -1 , mass Biot numbers ranged between 10 -1 and 10 4 , and the K value ranged between 10 -3 and 5.

MATHEMATICAL MODEL FOR LIQUID-LIQUID PHASE-TRANSFER CATALYSIS

A mathematical model for liquid-liquid phase transfer catalysis concerning diffusion and reaction in a single organic droplet was developed. The reversibility of reaction in the aqueous phase was taken into account to investigate its effect on the role of phase transfer catalytic intermediate. The modified Hatta number (φ) which characterizes the phenomena of diffusion within droplets and mass Biot number of the active intermediate reflecting the importance of interfacial mass transfer resistance, were defined to interpret their effects on the organic reaction rate. Comparisons of the behaviors of active intermediate in the organic droplets for reversible and irreversible aqueous reactions were proposed. From the simulation results, the reversibility of the aqueous phase reaction affects the overall reactivity not much except for a lower distribution coefficient of the intermediate. The quantity of the active intermediate in the organic phase slightly increases as decreasing the equilibrium constant of the aqueous reaction. The published experimental data were employed to demonstrate the present model successfully. From the present study, the behaviors of diffusion and reaction within liquid droplets in phase transfer catalysis can be understood and are useful for proper reactor design.

A theoretical model for phase transfer catalyzed reaction with the third‐liquid phase

The behaviors of phase transfer catalysts under the formation of a third‐liquid phase were analyzed in the present work. A mathematical model concerning mass transfer with reaction in an organic droplet was developed. The third‐liquid phase was considered to form between the aqueous/organic interface. The diffusion resistance of active intermediate (QY) in the catalyst phase and mass transfer resistance between the droplet and the bulk aqueous phase were all considered. The surface conversion factor (?) and mass Biot number (Bi) were defined to interpret their relative importance on the overall reaction rate. The system equations were solved by finite difference and fourth‐order Runge‐Kutta methods. From the simulation results, the conversion increases with increasing Bi and decreases with increasing ?. The overall reaction rate is influenced not only by the diffusivity of organic reactant but also by its surface reaction rate. In addition, the diffusion rates of QY and QX in the third liquid phase are not important to the overall reaction rate because QY and QX are highly concentrated within the thin catalyst layer. These results exhibit the phenomena of phase transfer reaction catalyzed by the third‐liquid phase.