Non-dimensional Variables Research Articles

Case study of autocatalysis reactions on tetra hybrid binary nanofluid flow via Riga wedge: Biofuel thermal application

Ethanol and biodiesel, which both belong to the first generation of biofuel technology, are the two most popular forms of biofuels now in use. In order to create next-generation biofuels using waste, cellulosic biomass, and algae-based resources, the Bioenergy Technologies Office (BETO) is working with business. The present article is designed to study the effect of tetra hybrid nanoparticles with the utilization of the novel Hamilton and Crosser model and catalytic reaction on binary fluid with the consideration of ethanol biofuel as a base fluid. Ethanol comprising tetra hybrid nanoparticles and heterogeneous catalytic reaction amplifies thermal conductivity and significantly increases brake thermal efficiency and reduces brake-specific fuel consumption in diesel engines. Therefore, the aim of this article is a theoretical checkup that is related to heat and mass transport of biofuel flow considering binary fluid accompanied with autocatalysis reaction and novel tetra hybrid nanoparticles on biofluid flow subjected to a Riga wedge. Transportation of heat via nonuniform heat source/sink, thermal radiation, and thermal conductivity are in our consideration. The mathematics of the assumed problem generates the system of non-linear partial differential equations from basic equations of momentum, energy, and mass. The usage of non-dimensional variables gave a system of non-linear ODEs with boundary conditions which are further dealt with in the Lobatto111A scheme. The results are obtained for stretching/shrinking wedge with several parameters. From obtained results, it is observed that the velocity field diminishes owing to magnification in Weissenberg number and Casson fluid parameter. The temperature field diminishes by amplifying heat generation, thermal radiation, and variable thermal conductivity parameter. Concentration distribution escalates by rising homogeneous reaction parameters.

Analysis of auto cubic catalysis and nanoscale heat transport using the inclined magnetized Cross fluid past over the wedge

In this study, the chemical procedure is presented in the nanomaterial flow, which contains the astonishing topographies. Nanoparticles contain physical and chemical properties, which are continuously used in almost every field of nanotechnology and nanoscience. Therefore, the idea to implement of these investigations is related to the heat and mass transport based on the nanomaterial flow along with the Cross model, chemical process via autocatalysis and an inclined magnetic dipole over shrinking/stretching wedge. Moreover, heat transportation with non-uniform heat source/sink, thermophoretic diffusion impacts, and Brownian motion are also studied. The assumed problems in the mathematics generate the system of nonlinear partial differential equations using the basic form of momentum, energy, and mass. Non-dimensional variables provide the system of equations using the boundary conditions, which are further updated with the shooting method to reduce into the initial value problem. The solution of the nonlinear model is presented through the MATLAB built-in procedure Bvp4c to find the numerical solutions.

Dissipative flow features of Carreau nanofluid with thermal radiation inside plane wall channel: Jeffery-Hamel analysis

The current article communicates a numerical investigation on laminar flow of dissipative generalized Newtonian Carreau nanofluid flowing through vertical conduit with converging and diverging plane walls. Thermal and concentration characteristics due to enthalpy change, activation energy, and non-linear thermal radiation have been examined in the presence of buoyancy forces. The channel walls for both temperature and volumetric fraction are assumed to be isothermal. The instability mechanism of nanofluids is reported using a two-phase nanofluid model, which works reasonably well for nanoparticle concentrations below a certain threshold. A Jeffery-Hamel (J-H) flow model is developed by assuming an incompressible purely radial flow of Carreau nanofluids with heat and mass transportation. Using the suitable non-dimensional variables, the resulting nonlinear partial differential equations are turned into a system of ordinary differential equations. The modified governing equations are then numerically solved using the built-in boundary value problem solver bvp4c, on the template form of commercial software MATLAB. The impacts of material, geometrical and thermophysical parameters governing the J-H problem are discussed and illustrated. Results indicate that higher buoyance forces incline the velocity profiles in converging enclosure, while a slight reduction is perceived in opposing forces. A significant decrease of wall heat transmission is reflected for larger values of activation energy and radiation parameter. For endorsing this communication, a comparison analysis is established with existing research and noticed a remarkable agreement. Practically, the flow inside converging and diverging channels are deployed in nuclear reactors that use plate-type nuclear energies, high heat-flux condensed heat exchangers, high-performance micro-electronic cooling systems, jets, rockets nozzles, and jet propulsion inlet.

Sustainable gene expression programming model for shear stress prediction in nonprismatic compound channels

Open channel flow resistance and channel stability can be determined from boundary shear stress distribution. Overbank floods cross the main channel and pours the floodplain. The momentum change between the main channel and floodplains creates complicated flow shapes in compound channels. This alters floodplain and main channel shear stress. River floodplains also support agriculture and development activities due to which floodplain shape changes along the flow length, creating a converging, diverging or skewed compound channels. Traditional empirical formulas cannot accurately estimate shear force distribution. Thus, creative and accurate methods remain in demand. Gene expression programming, an innovative approach, has been utilized in this study to develop a new equation for compound channel with converging floodplains in terms of nondimensional geometric and flow variables to estimate the boundary shear force carried by floodplains. The proposed GEP-based method is best when compared to previously developed methods. The findings indicate that the predicted percentage shear force carried by floodplains determined using GEP is in good agreement with the experimental data (R2 = 0.96 and RMSE = 3.395 for the training data and R2 = 0.95 and RMSE = 4.022 for the testing data).

Numerical simulation of mass and heat transport phenomena of hydromagnetic flow of Casson fluid with sinusoidal boundary conditions

AbstractA magnetic field might interact with its surroundings, influencing chemical and physical processes in materials processing, heat exchangers, and other scientific study. Therefore, a computational study of non‐Newtonian (Casson) free convective MHD unsteady fluid flow has been highlighted in this article with mass and heat transit property through a vertical infinite porous plate. A sinusoidal boundary conditions as well as chemical reaction and thermal radiation have been considered. Using a collection of nondimensional variables, the flow related equations are also turned into nondimensional form. The EFDM algorithm is employed in order to arrive at a numerical solution via Compaq Visual Fortran. The reliability of the numerical solution has been confirmed using stability testing and convergence analysis. The whole system is convergent when the values of Prandtl number and Lewis number are greater than or equals to 0.075 and 0.025, respectively. A visual depiction of the impact of the pertinent factors on dimensionless velocity, temperature, and concentration profiles are displayed through graphical representation as well as with tabular representation. It has been inspected that when the magnetic component is regarded, it greatly affects the heat transfer factors of Casson nanofluid and the heat also rises when Eckert number, heat source and radiation parameter accelerate. It is also found that the Sherwood number is increased as the impact of chemical reaction parameter and the Lewis number, also the skin friction is decreased as the influence of porosity term got accelerated. The comparison of the current findings with the data that were previously published serves as the final stage in validating the present study.

The maximum solubility product marks the threshold for condensation of multivalent biomolecules

Clustering of weakly interacting multivalent biomolecules underlies the formation of membraneless compartments known as condensates. As opposed to single-component (homotypic) systems, the concentration dependence of multicomponent (heterotypic) condensate formation is not well understood. We previously proposed the solubility product (SP), the product of monomer concentrations in the dilute phase, as a tool for understanding the concentration dependence of multicomponent systems. In this study, we further explore the limits of the SP concept using spatial Langevin dynamics and rule-based stochastic simulations. We show, for a variety of idealized molecular structures, how the maximum SP coincides with the onset of the phase transition, i.e., the formation of large clusters. We reveal the importance of intracluster binding in steering the free and cluster phase molecular distributions. We also show how structural features of biomolecules shape the SP profiles. The interplay of flexibility, length, and steric hindrance of linker regions controls the phase transition threshold. Remarkably, when SPs are normalized to nondimensional variables and plotted against the concentration scaled to the threshold for phase transition, the curves all coincide independent of the structural features of the binding partners. Similar coincidence is observed for the normalized clustering versus concentration plots. Overall, the principles derived from these systematic models will help guide and interpret in vitro and in vivo experiments on the biophysics of biomolecular condensates.

Effect of Thermal Radiation and Variable Viscosity on Bioconvective and Thermal Stability of Non-Newtonian Nanofluids under Bidirectional Porous Oscillating Regime

The bioconvective flow of a Jeffrey fluid conveying tiny particles under the effect of an oscillating stretched bidirectional surface is considered in this paper. The effects of thermal radiation and a porous medium are also investigated. The Cattaneo–Christov diffusion theories are used to analyze the heat and mass transfer phenomena. The activation energy effects are included in the concentration equation. The solved dimensionless equations system is established, based on non-dimensional variables. The analytical findings are evaluated using the homotopic analysis technique. The convergence of solutions is ensured. The results are validated by already available published findings and a good concordance is encountered. The fundamental physical aspect of flow parameters is graphically evaluated. The main results reveal that the velocity is reduced by increasing the permeability of the porous medium. An increase in the temperature occurs when the viscosity of the fluid is varied. The obtained results can be useful in thermal systems, energy production, heat transfer devices, solar systems, biofuels, fertilizers, etc.

Chemical reaction and magnetohydrodynamics effects on heat absorbing fluid past an inclined porous plate

AbstractThe study of a heat‐absorbing, chemically bonding fluid over a porous channel in a conducting field with ramped wall temperature is considered. The Dufour effect presence is also considered with thermal radiation. The novelty is the consideration of radiation absorption and the angle of inclination. In this approach, the dimensional governing equations and boundary forms are transformed into a dimensionless form using standard nondimensional parameters and variables. The simplified governing equations and boundary forms are then calculated using the Laplace transform method. We get accurate answers in the speed, temperature, and concentration spaces. Calculations of surface friction, the Nusselt number, and the Sherwood number are also performed. Several physical parameters' influences on the quantified flows are analysed using graphics. A comparison is also made with the results available in the literature and found a good agreement in the absence of radiation absorption. When a chemical is added to a fluid to dilute it, the velocity area and concentration area both decrease, but the temperature area increases as a result of an increase in the Schmidt Number, the Nusselt Number, and the skin friction. Our research revealed that the Dufour effect and arbitrarily ramped temperatures had a similar effect on fluid velocity.

Effect of thermal radiation on nonDarcy hydromagnetic convective heat and mass transfer flow of a water–SWCNT’s and MWCNT’s nanofluids in a cylindrical annulus with thermo-diffusion and chemical reaction

The examined through analysis of the movement of water-based single wall carbon nanotube (SWCNT) and multiwall carbon nanotube (MWCNT) nanofluids in a coordinate annulated zone under influence of non-uniform heat source/sink. By imposing the appropriate nondimensional variables, the governing partial differential equations are converted into a system of coupled nondimensional partial differential equations. By means of the usage of quadratic polynomials and the Galerkin finite element detail approach, the nonlinear equations have been executed. The expressions representing fluid velocity, temperature and concentration are discussed graphically. While skin friction, heat transfer and mass transfer are revealed in tabular structure. The proposed scheme is shown to have faster convergence than the existing scheme with excellent accuracy. Various parametric values have been analyzed and observed that higher temperatures and concentrations are produced with lower velocities with and bigger velocities with higher radiative heat flux or nanoparticle volume fraction.

Peristaltic pumping of hybrid nanofluids through an inclined asymmetric channel: A biomedical application

This analysis addresses the application of highly effective nanomaterials namely single walled carbon nanotubes, copper dioxide and titanium dioxide in medical field from different aspects. The nanomaterials are brought into consideration with aiming to focus heat transfer enhancement of base liquid. Further the characteristics of nanomaterials are compared in terms of single phase nanofluid and hybrid nanofluid models. This inspiration leads to mathematical modeling of the problem subjected to Sorret and Dufur effects. Convection phenomenon is used to investigate heat transfer at the walls of channel. The mathematical formulation has been performed in asymmetric inclined channel. The equations are simplified by using small Reynolds number and long wavelength estimation. The governing equations with associated boundary conditions are solved via Mathematica software. The non-dimensional variables appeared in equations are discussed against velocity, temperature, concentration, streamline, skin friction, Nusselt number and Sherwood number. The results are compared for single phase nanoliquid (SWCNTs+water) and hybrid nanofluid (Cu+TiO2) models against physical variables. Hybrid nanofluid model leads higher temperature against inclination angle and Dufur number. Opposite trend is noted for mass transport against Sorret number. Furthermore, heat transfer in case of hybrid nanofluid model is noted higher than single phase nanoliquid model. The considered nanomaterials could be useful to boost heat transfer rate for targeted maligned tissues. The current study will help researchers to investigate other nanomaterials that could be used effectively as an alternative in medical fields.

Mechanics of heated Rabinowitsch fluid in elliptic vertical duct: Peristalsis and analytical study

This work consists of the analytical study of the peristaltic flow of heated non-Newtonian fluid flow through an elliptical duct. The flow characteristics of Pseudoplastic and Dilatant fluids are analyzed in a vertically held elliptic duct by considering the Rabinowitsch fluid model. The mathematical model is processed to a dimensionless analysis by employing adequate nondimensional variables and extended wavelength approximation. The resulting PDEs are solved analytically in the elliptic domain using the explicit boundary condition form. A simpler second-degree polynomial is presented to get the solution of temperature. These analytical solutions are examined in detail by graphical analysis. It is found that the flow velocity of Pseudoplastic fluid is more prominent than Dilatant fluid in the vicinity of the centerline. The earlier and later fluids have a maximum axial speed at the channel’s mean and close to the peristaltic boundary. The greater buoyancy force (Grashof number) enhances the Pseudoplastic fluid’s velocity but diminishes the flow velocity of Dilatant fluid. Moreover, it is noticed that the aspect ratio has less impact, and the Grashof number has an effective influence on pressure rise. The streamlines of Rabinowitsch fluid break into vortices near the deformed wall. The vortices are comparatively less in the count for Dilatant fluid than Pseudoplastic fluid for quick flow and a more significant Grashof number.

Finite Difference Method to Evaluate the Characteristics of Optically Dense Gray Nanofluid Heat Transfer around the Surface of a Sphere and in the Plume Region

The current research study is focusing on the investigation of the physical effects of thermal radiation on heat and mass transfer of a nanofluid located around a sphere. The configuration is investigated by solving the partial differential equations governing the phenomenon. By using suitable non-dimensional variables, the governing set of partial differential equations is transformed into a dimensionless form. For numerical simulation, the attained set of dimensionless partial differential equations is discretized by using the finite difference method. The effects of the governing parameters, such as the Brownian motion parameter, the thermophoresis parameter, the radiation parameter, the Prandtl number, and the Schmidt number on the velocity field, temperature distribution, and mass concentration, are presented graphically. Moreover, the impacts of these physical parameters on the skin friction coefficient, the Nusselt number, and the Sherwood number are displayed in the form of tables. Numerical outcomes reflect that the effects of the radiation parameter, thermophoresis parameter, and the Brownian motion parameter intensify the profiles of velocity, temperature, and concentration at different circumferential positions on the sphere.

Numerical investigation of jet-wedge combinatorial initiation for oblique detonation wave in supersonic premixed mixture

The jet-wedge combinatorial initiation (JWCI) is a novel functional form for initiating an oblique detonation wave (ODW) with reduced total drag within the oblique detonation combustor under the conditions of a low Mach number and low static pressure inflow. It can suppress the instability of the detached ODW. The evolution of the combustion wave during combinatorial initiation is dominated by the intersection between the bow shock wave and the oblique shock wave and consists of four stages: the shock-induced combustion stage, the shock–deflagration coupling stage, the hybrid combustion stage, and the oblique detonation stage. Three combustion regimes can be formed by using the JWCI: the shock-induced combustion regime, the hybrid combustion regime, and the oblique detonation combustion regime. These regimes have distinct characteristics of combustion and flow structure that can be controlled by changing two non-dimensional variables: the ratio of momentum flux (J) and the penetration ratio (PR). This is significant as it can facilitate the application of different combustion regimes under a variety of realistic flight conditions. In this study, the criterion for the transformation of the combustion regime is quantitatively investigated, and it is shown that the structure of the combustion wave does not transform until both non-dimensional variables have reached their respective thresholds. J is crucial for determining the combustion regime and facilitating its transformation, but the PR accounts only for the height of the combustion wave structure. The work is beneficial for research on the initiation of the ODW in applications of oblique detonation engines.

Induced by heat source on unsteady MHD free convective flow of Casson fluid past a vertically oscillating plate through porous medium utilizing finite difference method

In this research, the unsteady MHD flow of a Casson fluid past a vertical plate that oscillates while maintaining a constant wall temperature and the heat source is the subject of this article. The fluid is electrically conductive and moves through a porous media. Partial differential equations with initial and boundary conditions are used to model this phenomenon. There are a few appropriate non-dimensional variables introduced. Using the finite difference method(FDM), the consistent dimensionless equations with circumstances are resolved. The energy and velocity equations are solved precisely. Expressions for Nusselt number and skin friction are also assessed. The outcomes of computations are analyzed for newly developing flow parameters. Additionally, skin friction and the Nusselt number effects are explained using table values. Furthermore, increasing the heat source parameter causes a rise in temperature and velocity.

The concentration threshold for condensation of multivalent molecules is set by by the maximum solubility product.

Clustering of weakly interacting multivalent biomolecules underlies the formation of membrane-less compartments known as condensates. As opposed to single component (homotypic) systems, the concentration dependence of multi-component (heterotypic) condensate formation is not well understood. We previously proposed the solubility product (SP), the product of monomer concentrations in the dilute phase, as a tool for understanding the concentration dependence of multi-component systems. In the current study, we further explore the limits of the SP concept using spatial Langevin dynamics and rule-based stochastic simulations. We show, for a variety of idealized molecular structures, how the maximum SP coincides with the onset of the phase transition, i.e., the formation of large clusters. We reveal the importance of intra-cluster binding in steering the free and cluster phase molecular distributions. We also show how structural features of biomolecules shape the solubility product profiles. The interplay of flexibility, length and steric hindrance of linker regions controls the phase transition threshold. Remarkably, when solubility products are normalized to non-dimensional variables and plotted against the concentration scaled to the threshold for phase transition, the curves all coincide independent of the structural features of the binding partners. Similar coincidence is observed for the normalized clustering vs. concentration plots. Overall, the principles derived from these systematic models will help guide and interpret in vitro and in vivo experiments on the biophysics of biomolecular condensates. (Supported by NIGMS grants R24 GM137787 and R01 GM132859.)

Analytical Solution of Unsteady MHD Casson Fluid with Thermal Radiation and Chemical Reaction in Porous Medium

One of non-Newtonian fluid, Casson fluid, has a diversify application in the manufacturing and engineering sector due to its elasticity behaviour. This study provides the analytical solution of unsteady Casson fluid with the presence of thermal radiation and chemical reaction in a porous medium. Formulation of this fluid model is initiated with the partial differential equation (PDE) of the momentum and energy equations as well as the concentration equation. By applying the proper non-dimensional variables, these equations are then converted into dimensionless form. Subsequently, the derivation of the exact solutions for the concentration, temperature and velocity profiles is conducted with the operation of the Laplace transform method that satisfies both initial and boundary equations. Graphical illustrations, which portray the various effects on this study are generated. It has been revealed that as the thermal radiation, chemical species and porosity increases, so does the velocity profile. However, MHD and Casson parameter shown opposite behaviour in the velocity profiles.

Effect of Cattaneo-Christov heat flux case on Darcy-Forchheimer flowing of Sutterby nanofluid with chemical reactive and thermal radiative impacts

The Darcy-Frochheimer flow scheme is important in industries where a higher stream rate impact is a prominent occurrence, for illustration in, petroleum engineering. In this article, we examine the influence of Cattaneo-Christov heat fluxing on the Darcy-Frochheimer flowing of Sutterby nanofluid via stretchable surface with chemical reactive and heat radiative impacts. The highest-order nonlinear partial differential equation is addressed by utilizing the similarity function and a new set of the ordinary differential equation is developed. The obtained equations are then numerically examined by using the bvp4c technique in MATLAB. The graphical behavior for numerous aspects, such as velocity, solutal, thermal, drag coefficient, and heat transport are illustrated for particular non-dimensional variables. Skin fraction and velocity curve decline with the higher valuation of the Frochheimer number. An augmentation in the thermal curve due to the heat source/sink parameter, but a reverse pattern is observed for the Nusselt number. The reverse pattern is observed for the thermal curve and solutal curve via a higher Brownian motion parameter. Compared with the existing research, the outcomes demonstrate excellent congruence.

Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear

Cavitation damage and hard particle erosion are some of the main sources of wear in most hydraulic machines, such as pumps or hydroturbines. However, the synergic effect of these two phenomena leads to a wear phenomenon that is often more severe than the sum of the individual effects of cavitation and hard particle erosion and that has been scarcely studied. Therefore, in this work, simplified computational fluid dynamics (CFD) simulations using 2D and 3D approaches were performed to investigate the behaviour of a particle interacting with a cavitation bubble near a solid wall under several conditions of pressure, position, bubble maximum size, and mass of the particle. All the involved variables were combined into three nondimensional variables: the dependent variable includes the impact velocity of the particle normal to the surface, while the other two variables include the particle position relative to the eroded wall and the particle mass. Through this approach, several correlations were identified, and a dimensionless function of two variables and six fitting factors was proposed to comply with those correlations. Then, this function was returned to its dimensional form to obtain an expression to predict the impact velocity of a particle normal to the solid wall due its interaction with a collapsing bubble.

A Curve-fit Traction Coefficient Relation of Mixed EHL Line Contact with Hydraulic Fluid and Steel Surfaces

Accurate modeling of hydraulic gear machine meshing torque loss, considering possible asperity contact, is required for better prediction of its hydromechanical efficiency. A model for predicting the mixed thermal EHL line contact traction coefficient is implemented in this study, considering experimental density and viscosity properties. Simulation results of traction coefficient are validated with experiments at two operating conditions. The defining components of the traction coefficient, the asperity load ratio and the hydrodynamic component are obtained at wide range of inputs. Finally, explicit curve-fit formulations of the asperity load ratio and the hydrodynamic component of traction coefficient are created in terms of input non-dimensional variables, which can be used for modeling the torque loss in a simple yet accurate way.

Heat Transfer Analysis of Generalized Nanofluid with MHD and Ramped Wall Temperature Using Caputo–Fabrizio Derivative Approach

The aim of the present work is to apply the fractional derivative to the heat transformation of a nanofluid along with ramped wall temperature. The flow is analyzed under the effect of magnetohydrodynamic together with heat transfer. A nanofluid under the application of fractional‐order differential equations by Caputo–Fabrizio derivatives with respect to time has the ability to explain the behavior of nanofluid under the influence of memory concept. For the same purpose, Caputo–Fabrizio time‐fractional derivative is applied to investigate the behavior of nanoparticles on the thermal conductivity of a fluid. Appropriate nondimensional variables are engaged in the equation which governs the problem and guides us to obtain the exact solutions for the fields of velocity and temperature. These obtained solutions for the nondimensional set of governing equations are found by extracting them from the governing equations by applying Laplace transform techniques along with Caputo–Fabrizio time‐fractional derivative. The influence of the fractional variable on the velocity, temperature, and Nusselt number is graphically exposed and discussed. The velocity for the state of wall temperature as ramped falls down with the enlarging values of the fractional parameter. Variation in Nusselt number is shown in the tabular form. Solutions are visualized graphically to make an analysis of how the variation is taking place in the physical behavior of the nanofluid flow with respect to the change in distinct physical parameters. The obtained results here will have useful industrial and engineering implementations. It is found that fluid velocity in the flow direction decreases with the increase in the magnetic parameter. The relationship of fractional parameter with the velocity and temperature of the nanofluid is found as direct proportional for a smaller time. However, this direct proportionality converts into inverse proportionality for larger values of time. It is observed that the increase in the nanoparticles volume fraction causes an increase in temperature distribution. It is due to lower specific heat of nanoparticles and its higher thermal conductivity than that of the base fluid.