Infinite Viscosity Research Articles

Heterogeneous/homogeneous and inclined magnetic aspect of infinite shear rate viscosity model of Carreau fluid with nanoscale heat transport

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.

Infinite shear rate viscosity of cross model over Riga plate with entropy generation and melting process: A numerical Keller box approach

This paper presents the effects of cross fluid model associated with entropy generation and melt process. The Cross-fluid viscosity model based on the infinite shear rate effect is taken with attaching Riga plate. Physical interpretation generates a system of partial differential equations (PDEs), and further, these are processed with similarity variables to attain a system of ordinary differential equations (ODEs). The numerical experiments are presented compared and discussed. Here, the numerical Keller Box approach is utilized. The obtained results indicate that the melt process loses the temperature and entropy generation enlarges the temperature visibility.

Accurate prediction of magnetorheological damper characteristics based on a new rheological constitutive model

Physical modeling of magnetorheological dampers (MRDs) plays a crucial role in understanding the dynamic characteristics, optimizing design, and developing control algorithms of MRDs. The systematic study of various factors indicates that an accurate magnetorheological fluid (MRF) rheological model can effectively improve the estimation accuracy of the MRD physical model. The difficulty in establishing an accurate MRF model lies in the rheological behavior of MRFs at low and medium shear rates (0.01 ∼ 103 s−1) measured by commonly used rheometers exhibits notable differences from that at extremely high shear rates (105 ∼ 107 s−1) in MRDs. Therefore, this paper proposes to estimate the rheological behavior of MRFs at extremely high shear rates using the exponential linear mixed analytical (ELMA) model with excellent description and prediction capabilities, combined with the infinite viscosity and nonlinear term decay rate constraints determined based on rheology and related limited rheological data. This paper constructs a series of predictive MRD physical models combined with other relevant information, from the simple analytical model to the complex numerical model. The simulation results of the monotube MRD physical model, constructed based on the ELMA model identified by the above method and considering all deformation and inertial effects, are consistent with the corresponding dynamic test results of the MRD, reflecting the effectiveness and prospect of the parameter identification method and physical model.

Effect of a double-chain surfactant on the stabilization of suspensions of silica and titania particles against agglomeration and sedimentation

Dispersions of vesicles of didodecyldimethylammonium bromide (DDAB) were prepared with magnetic stirring of multilamellar liposomes followed by ultrasonication (SS) in order to generate dispersions that contained only unilamellar vesicles, unlike the stirring-only (S) method which also produces many large liposomes. With the SS method, the vesicles had average diameters ranging from 68 to 80 nm, which were much smaller than the diameters generated with the S method. The new vesicle dispersions had nearly infinite viscosities at very low shear stresses at DDAB weight fractions wD from 0.025 to 0.027, even though they were not close-packed, in contrast to the S dispersions. The new SS vesicle dispersions stabilized completely against sedimentation polydisperse nonspherical crystalline titania particles with sizes ranging from ca. 96–156 nm, as well as suspensions of monodisperse spherical amorphous silica particles with diameters of dsed = 454 nm, 691 nm, and 826 nm. These results establish that DDAB vesicle dispersions can stabilize against sedimentation a broad range of particle types and sizes. In addition, at the low values of wD = 0.009 and 0.018, the effective viscosities, ηeff, of the DDAB dispersions, determined from the sedimentation velocities, ranged from 1.35-1.87 cP and 4.34–5.57 cP, respectively. At higher shear stresses, however, these dispersions were highly shear-thinning and still flowable in a capillary under gravity. This behavior is critical for the practical applications of such dispersions for inkjet printing and possibly paints.

Steady shear rheological properties, microstructure and stability of water in water emulsions made with basil seed gum and waxy corn starch or high pressure-treated waxy corn starch

The water in water (W/W) emulsions were prepared by mixing basil seed gum (BSG) with waxy corn starch (WCS) or high pressure-treated waxy corn starch (HWCS) at different concentrations. Increasing the concentration of WCS or HWCS increased the zeta potential, consistency index, infinite shear viscosity, and apparent viscosity, while it decreased the Z-average droplet size, polydispersity index, separation index, and flow behavior index of the W/W emulsions. After increasing the concentration of WCS and HWCS, the micrographs captured by an optical microscope indicated that the number of follicular droplets increased more than individual droplets. However, coalescence did not occur due to electrostatic repulsion. When the concentration of WCS and HWCS was increased from 0.5 to 2 wt% (at a constant concentration of 0.25 wt% and 0.2 wt% of BSG, respectively), the consistency index of the emulsions was increased significantly (p < 0.05) from 0.109 to 0.436 Pa. sn and from 0.032 to 0.743 Pa. sn, respectively. The results simply revealed the capability of 0.2 wt% BSG+ 0.5, 1, or 2 wt% HWCS and 0.25 wt% BSG+ 0.5, 1, or 2 wt% WCS for being utilized as stable W/W emulsions; these emulsions were stable for at least a week.

Infinite shear rate aspect of the cross-nanofluid over a cylindrical channel with activation energy and inclined magnetic dipole effects

The posture of fluid flow at a high or low shear rate is characterized by the infinite shear viscosity concept based on the Cross-fluid (CF). This dynamical system has some characteristics to examine the extreme levels of the fluid along with the effects of inclined magnetic dipole mechanics. The current research is examines the infinite shear rate based on the CF past over the cylindrical channel. The velocity through an inclined magnetic field, based on the cylindrical geometry and the activation energy, is provided using mass transport along with the chemical reactions. Moreover, the thermophoresis effects, Brownian motion based on the nanoparticles, and binary chemical procedures are also provided in this study. The CF model is provided through the tensor of Cauchy stress along with the partial differential equations (PDEs). Similarity transformations have been used to convert the PDEs into ordinary differential equations. The numerical performances of the obtained system have been obtained by using the bvp4c method.

Cross electromagnetic nanofluid flow examination with infinite shear rate viscosity and melting heat through Skan-Falkner wedge

Abstract This demonstration of study focalizes the melting transport and inclined magnetizing effect of cross fluid with infinite shear rate viscosity along the Skan-Falkner wedge. Transport of energy analysis is brought through the melting process and velocity distribution is numerically achieved under the influence of the inclined magnetic dipole effect. Moreover, this study brings out the numerical effect of the process of thermophoresis diffusion and Brownian motion. The infinite shear rate of viscosity model of cross fluid reveals the set of partial differential equations (PDEs). Similarity transformation of variables converts the PDEs system into nonlinear ordinary differential equations (ODEs). Furthermore, a numerical bvp4c process is imposed on these resultant ODEs for the pursuit of a numerical solution. From the debate, it is concluded that melting process cases boost the velocity of fluid and velocity ratio parameter. The augmentation of the minimum value of energy needed to activate or energize the molecules or atoms to activate the chemical reaction boosts the concentricity.

Hydrodynamic cavitation reduction in semidilute turbulent polymer solution flows

The hydrodynamic cavitation in semidilute solution flows of a flexible polymer additive in water was experimentally explored in a mesoscale converging–diverging nozzle to elucidate the cavitation reduction effects of polymer additives. Rheological measurements demonstrated that polymer solutions were shear-thinning, with infinite viscosities larger than pure water. The polymer additives significantly mitigated the intensity of cloud cavitation and the growth of violent cavity structures in the tested solution concentrations. Under conditions of supercavitation, the tested polymer solutions could not suppress the growth of large structures but showed a reduction in the population of cavitation bubbles. The temporal evolution and spatial variation of cavitation structures in different concentrations were captured using high-speed imaging. Statistical analysis of the images showed that polymers reduce cavitation via three main mechanisms. (1) The longitudinal expansion of cavities downstream is attenuated relative to the pure water. The streamwise distribution of vapour-ratio fluctuations was flattened, and its peak was shifted upstream in the solutions. (2) Mean collapse and growth rate of cavitating bubble pockets and their fluctuations were noticeably relaxed by polymer additives. For a 400 p.p.m. solution (parts per million (p.p.m.)), a reduction of 65 % was measured relative to pure water flow at the highest tested flow rate. (3) Spectral analysis of the downstream pressure indicated that the shedding frequency at the cavitation inception was reduced as the solution's concentration increased. This reduction was as high as 70 % for a 400 p.p.m. solution. These results highlight the strong interplay between polymer additives and the generation of cavitation-related structures.

Rheological Characterization of High-Molecular-Weight Polyethylene Oxide—An Extensive Parametric Experimental Study

Abstract A comprehensive study of the rheological characterization of the aqueous solutions of polyethylene oxide (PEO) with molecular mass of 4 × 106, 5 × 106, and 8 × 106 g/mol, respectively, named (4 miDA), (5 miDA), and (8 miDA) was conducted. A large batch of samples of 4 miDA PEO with concentrations varying from 0.1% to 3%, representing the range of dilute solutions to very high viscous hydrated gels, were tested. Steady-state shear flow and oscillatory measurements are reported. Cross, Carreau, and Carreau–Yasuda models were used to describe the shear-thinning behavior within the shear rate range (0.001 ≤ γ˙ ≤ 3000 s−1). Experimental findings were validated with published results under the same operating conditions within specified shear rate ranges (0.1 ≤ γ˙ ≤ 100 s−1). We find that the behavior of PEO under shear is highly dependent on the rheometer, material, and operating procedures. Oscillatory measurements were carried out to determine the complex properties of the PEO solutions in the frequency ω and strain amplitude γ ranges of 0.01 ≤ ω ≤ 100 rad/s and 0.01 ≤ γ ≤ 1000%, respectively. Higher magnitudes of dynamic moduli (G/ and G//), zero (η0) and infinite (η∞) shear rate viscosities, resonant frequencies (ωres), linear viscoelastic regions (LVER), and higher relaxation time constants (λ) were observed with increasing concentration and molecular weight. The rheological response of the PEO polymeric solutions was further clarified via Lissajous curves. The aim of this work is to characterize the behavior of the 4 miDA PEO prior to its use in an experimental investigation of the secondary flows of viscoelastic fluids in noncircular channels.

Evaluation of L-ascorbic acid as a green low dosage hydrate inhibitor in water-based drilling fluid for the drilling of gas hydrate reservoirs

Hydrate plug formation in the drilling fluid flow line is a significant issue in the oil and gas industry. Green hydrate inhibitors have recently gained much interest in flow assurance problems as they are being used as alternatives for existing hydrate inhibitors. The present study described that L-ascorbic acid (LA), a natural organic compound, has been identified as a Low Dosage Hydrate Inhibitor and has exhibited better results than Polyvinylcaprolactum (PVCap) and Polyvinylpyrrolidone (PVP). The temperature-augmented visual method and a self-fabricated set-up have been used to determine the first hydrate crystal formation in the tetrahydrofuran (THF)-water hydrate system. LA has shown a better inhibition effect in terms of induction time (i.e., >1440 min) than PVCap (119.67–180.67 min) and PVP (85.33–240.67 min). Carboxymethyl cellulose (CMC), polyanionic cellulose (PAC), xanthan gum (XG), and potassium chloride (KCl) are mixed with water to make the water-based drilling fluids used in this study. The R2 values showed a good agreement with the Herschel-Bulkley Model (R2 ranges from 0.993 to 0.999 for 0.5 w/v% PVCap and 0.1 w/v% PVP-containing fluids) than Bingham Plastic Model (R2 ranges from 0.836 to 0.952 for 0.1 w/v% PVP and base fluids). The MPE values are less for Herschel-Bulkley Model (From 1.418 to 6.015 for 0.5 w/v% PVCap and 0.1 w/v% PVP) than for Bingham Plastic (From 9.985 to 29.718 for 1.0 w/v% PVP and 0.1 w/v% PVP). Cross Model is also used to determine the zero and infinite shear viscosities for the formulated fluid system, which showed the viscosities are in the permissible range. These observations suggest that L-ascorbic acid (LA) may be an effective hydrate inhibitor in drilling fluids.

Activation Energy and Inclination Magnetic Dipole Influences on Carreau Nanofluid Flowing via Cylindrical Channel with an Infinite Shearing Rate

Background: The infinite shear viscosity model of Carreau fluid characterizes the attitude of fluid flow at a very high/very low shear rate. This model has the capacity for interpretation of fluid at both extreme levels, and an inclined magnetic dipole in fluid mechanics has its valuable applications such as magnetic drug engineering, cold treatments to destroy tumors, drug targeting, bio preservation, cryosurgery, astrophysics, reaction kinetics, geophysics, machinery efficiency, sensors, material selection and cosmology. Novelty: This study investigates and interprets the infinite shear rate of Carreau nanofluid over the geometry of a cylindrical channel. The velocity is assumed to be investigated through imposing an inclined magnetic field onto cylindrical geometry. Activation energy is utilized because it helps with chemical reactions and mass transport. Furthermore, the effects of thermophoresis, the binary chemical process and the Brownian movement of nanoparticles are included in this attempt. Formulation: The mathematics of the assumed Carreau model is derived from Cauchy stress tensor, and partial differential equations (PDEs) are obtained. Similarity transformation variables converted these PDEs into a system of ordinary differential equations (ODEs). Passing this system under the bvp4c scheme, we reached at numerical results of this research attempt. Findings: Graphical debate and statistical analysis are launched on the basis of the obtained computed numerical results. The infinite shear rate aspect of Carreau nanofluid gives a lower velocity. The inclined magnetic dipole effect shows a lower velocity but high energy. A positive variation in activation energy amplifies the concentration field.

Effect of Williamson parameter on Cu-water Williamson nanofluid over a vertical plate

The objective of this study is to analyze the augmentation of thermal conductivity and mass transfer rate over a semi-infinite vertical plate on account of nanoparticles suspended in Williamson fluid. Tiwari and Das model for nanofluids involving infinite shear rate viscosity is used in the current review to explain the heat transfer performance of nanofluids. The finite difference method of an implicit type is used to solve the governing dimensionless equations numerically. Graphical illustrations demonstrate the effects of the Williamson parameter on momentum, energy, and concentration, the behavior of skin friction coefficient and heat, and mass transfer rate. According to the present study, higher values of the Williamson parameter increases the skin friction, heat and mass transfer rate.The visualization of velocity, temperature, and concentration in the contour plots are also depicted. It is observed that Weissenberg number increases the velocity temperature and concentration of fluid flow near the plate significantly.

Polymer-Induced Drag Reduction in Dilute Newtonian and Semi-Dilute Non-Newtonian Fluids: An Assessment of the Double-Gap Concentric Cylinder Method.

Polymer-induced drag reduction (DR) in fluids was studied using a rotational rheometer with double-gap concentric cylinder geometry. Although both polymers (polyacrylamide (PAM) and 2-acrylamido-2-methylpropane sulfonic acid (SPAM)) had molecular weights of several MDa, the contrasting polymer charge, nonionic and anionic, led to different polymer overlap concentrations (c*), PAM ≫ SPAM, and fluid rheology, with PAM fluids mostly Newtonian and SPAM fluids non-Newtonian (shear-thinning). Based on these differences, it was important to account for the infinite shear viscosity and normalize the polymer concentration by the intrinsic concentration (cint) so that the DR performance of the two polymer fluids could be accurately compared. Both polymers induced DR, and the maximum DR by SPAM (DR% = 28) was slightly higher than that by PAM (DR% = 22) when Rep ∼ 1700. For PAM, the loss of DR with time diminished at higher polymer concentrations (≥100 ppm, at Rep = 3149) but was found to be sensitive to high Rep, with polymer chain scission the likely cause of the reduced performance. For the semi-dilute SPAM fluids, the shear stability contrasted that of PAM, showing negligible dependence on the polymer concentration and Rep. The apparent rapid loss of DR was predominantly attributed to a time-dependent effect and not polymer degradation. In pipe flow, the maximum DR for SPAM was higher than that measured by rheometry and was attributed to differences in the flow conditions. However, changes in the normalized DR/c with polymer concentration were found to be consistent between the two flow geometries. Furthermore, the high fluid stresses in pipe flow (at high Rep) led to drag reduction losses consistent with PAM, as the time-dependent effect was not seen.

Characterization of Cross nanofluid based on infinite shear rate viscosity with inclination of magnetic dipole over a three‐dimensional bidirectional stretching sheet

AbstractFluid viscosity manages several engineering processes and keeps its leading role in lubrication models, biological models, polymer processes, melt solutions, colloidal suspensions, and mayonnaise. The cross viscosity model is the most appropriate model, which interprets the key features of non‐Newtonian fluids in the region of shear‐thinning/thickening when very high and very low shear rates are applied. This article focuses on the mathematical model of three‐dimensional Cross nanofluid and interprets its aspect of infinite shear rate of viscosity over the expanding sheet. Velocity is studied through placing inclined magnetic dipole effect, transportation phenomenon is brought by considering the radiation effects, heat generation and chemical process is engaged for concentration of nanoparticles. The geometry of this mathematical model is expanding the stretching sheet with velocity slip, and convective heat conditions are associated. Similarity variables are being utilized for conversion dimensional mathematical model into nondimensional one. For the pursuit of numerical solution of the system of nondimensional mathematical model, the numerical technique Bvp4c is utilized. Furthermore, Matlab graphs and statistical analysis for all physical parameters and physical quantities are shown in the result and debate section. Due to inclination of angle Lorentz force producing in increasing manner, hence flow is opposed, and velocity of fluid is dropped for () and () and for increasing value of n index, the velocity of fluid flow is decreasing.

Melting and entropy generation of infinite shear rate viscosity Carreau model over Riga plate with erratic thickness: a numerical Keller Box approach

The current investigations are related to presenting the characteristics of flow at very high and low shear rates along with the melting process over the geometry of Riga plate. Carreau nanofluid is most appropriate mathematical viscosity model that can deal with low and high shear rates. Transportation of energy is discussed through melting conditions, thermal radiation and viscous dissipation. In this study, electromagnetic hydrodynamic aspect of nanofluid is discussed by using electromagnetic surface (Riga plate) and this system generates Lorentz force parallel to wall that keeps its effect on velocity of nanofluid. Partial differential equations (PDEs) are moved in ordinary differential equations and numerical approach named Keller Box and Shooting scheme are exercised to fetch the numerical solution of the system. An augmentation in Q leads to an enrichment in an external magnetic field. The velocity as well as momentum boundary layer booms by the virtue of an improvement in an external magnetic field. The viscosity of the nanofluid increases by the virtue of a magnification in β. Nanofluid becomes more radiated and absorbs more heat as a result of magnification in Nr, which escalates the heat transfer rate.

Sol-gel transition induced by alumina nanoparticles in a model pulmonary surfactant

Inhaled airborne particles smaller than 100 nm entering the airways have been shown to deposit in significant amount in the alveolar region of the lungs. The interior of the alveoli is covered with a ~ 1 µm thick lining fluid, called pulmonary surfactant. Inhaled nanoparticles are susceptible to interact with the lung fluid and modify pulmonary functions. Here we evaluate the structural and rheological properties of the pulmonary surfactant substitute Curosurf® which is administered to premature babies for the treatment of respiratory distress syndrome. Curosurf® is considered a reliable model of endogenous pulmonary surfactant in terms of composition, structure and function. Using active microrheology based on magnetically actuated wires, we find that Curosurf® dispersions exhibit a Newtonian behavior at lipid concentration from 0 to 80 g L−1, and that the viscosity follows the Krieger-Dougherty law observed for a wide variety of colloids. Upon addition of 40 nm alumina nanoplatelets, a significant change of the Curosurf® rheology is noticed. The dispersions then enter a soft solid phase characterized by an infinite viscosity and a non-zero equilibrium elastic modulus. The sol-gel transition induced by the nanoparticles is interpreted as the result of the alumina/vesicle interaction, which are illustrated by transmission electron microscopy. It also suggests a potential toxicity associated with the modification of the lung fluid structural and dynamical properties.

Aspects of infinite shear rate viscosity and heat transport of magnetized Carreau nanofluid

Aspects of infinite shear rate viscosity and heat transport of magnetized Carreau nanofluid

Inclined magnetic dipole and nanoscale energy exchange with infinite shear rate viscosity of 3D radiative cross nanofluid

AbstractWorking nanoliquids are used in bionomical concerns and to enhance the energy in the refrigeration system. The unique thermophysical characteristics of nanoliquids made nanoscience interesting and beneficial for fields of engineering, medical, and industry with real applications, like, food science, employing nanoparticles to deliver drugs, food microbiology, detection of foodborne pathogens, detection of foodborne pathogens, electronic device cooling, controlling fusion, magnetic cell separation, cancer therapeutics, nanocryosurgery, and so forth. The aim of this study is to deliver a broad analysis on nanoscale energy exchange and inclined magnetic dipole impact with the mathematical model of cross nanofluid. Scrutiny of movement of fluid is made by placing the magnetic dipole and buoyancy force. Transport of energy is investigated by thermal radiation, nonuniform heat sink–source while checking of mass transfer facts of activation energy and the chemical process is taken into consideration. Moreover, the nanostructured concepts of thermophoresis and Brownian movement along with zero‐mass flux constraint are also utilized for the comprehensiveness of this study. Mathematical relations of cross nanofluid are processed with similarity transformation, shooting methodology, and bvp4c Matlab procedure is rehearsed to get the numerical results of this attempt.

Rheological characterization of cemented paste backfills containing superabsorbent polymers (SAPs)

The addition of superabsorbent polymers (SAP) to cemented paste backfill (CPB) made from tailings slurries may offer a good alternative to the dewatering components of the conventional CPB production owing to their high-water absorption and retention capacities. Therefore, an experimental program was implemented to characterize the rheological behavior of CPB incorporating an SAP. Two types of binder comprising a general use Portland cement (GU) and a blended binder (GUSL) consisting of 80% ground granulated blast furnace slag (GGBFS) and 20% GU were used. Two different binder proportions, Bw (=100 × Mbinder/Mdry-tailings) of 4.5 and 7% were tested. An SAP dosage (ratio of the dry mass of SAP to the volume of the tailings slurry) of 30 and 34 kg/m3 was assessed in this study. Results showed that the SAP addition distinctly reduced the yield stress (τ0) and the infinite shear viscosity (μ∝) and increased the small cone (H = 150 mm) slump height (s) of such mixtures over time. Moreover, The SAP-thickened tailings CPB (SAP-TT CPB) showed a severe shear-thinning behavior marked by a negative flow index (n < 0) and moderate to extremely low yield stress (τ0 in the range 21–78 Pa), while the corresponding reference CPB without SAP added (Ref) exhibited a normal shear-thinning behavior with moderate to slightly high yield stress (τ0 in the range 76–206 Pa).

Inclined magnetized and energy transportation aspect of infinite shear rate viscosity model of Carreau nanofluid with multiple features over wedge geometry

AbstractHeat transference in fluid mechanism has a deep influence in real‐life applications like hot‐mix paving, recovery of energy, concrete heating, heat spacing, refineries, distillation, autoclaves, reactors, air conditioning, and so forth. In this attempt, findings related to energy exchange with features of infinite shear rate viscosity model of Carreau nanofluid by placing inclined magnetic dipole over the wedge are made. The main role in the transportation of heat is exercised by incorporating facts of radiation, nonuniform heat sink source, Brownian motion, thermophoresis, and chemical reaction. The mathematical system of the infinite shear rate viscosity model of Carreau nanofluid gives a system of partial differential equations and furthermore, these are moved into ordinary differential equations. A numerical procedure is applied via shooting/bvp4c to obtain numerical results. Inclined magnetic dipole gives a lower velocity of Carreau nanofluid. Due to the relaxation time factor velocity of Carreau fluid gets down. A* causes to generate the heat internally, so due to this, temperature increases rapidly. The increasing rate of temperature is found very high for the growing Hartmann number. The rate of mass transport becomes low for gradual increment in the parameter of thermophoresis, wedge angle, and Prandtl. Inclined magnetic dipole gives a lower velocity of Carreau nanofluid. Due to the relaxation time factor, the velocity of the Carreau fluid goes down. The absence and presence of magnetic numbers have no influence on velocity, temperature, and concentration files for Le, Rd, θf, γ, We, β, Pr, Nb, Nt, A.