Fluid Particle Interaction Parameter Research Articles

Unsteady MHD dusty fluid flow over a non-isothermal cone embedded in a porous medium

An investigation of the impacts of magnetic field, heat generation/absorption and thermal radiation on unsteady free convection dusty fluid flow over a non-isothermal vertical cone enclosed inside a porous medium is explored. The Crank–Nicolson approach is used to get the numerical solutions for these nonlinear, coupled partial differential equations (PDEs). The interaction of physical parameter range on temperature and velocity distribution is calculated and graphically presented. The results demonstrate that when the porosity, heat generation/absorption, and thermal radiation parameters are increased, the velocities rise, whereas the magnetic and mass concentration of particle phase parameters have an opposite effect. Furthermore, raising the fluid-particle interaction parameter causes a rise in dust phase velocity but a reduction in fluid phase velocity.

Application of central composite design (CCD)-response surface methodology (RSM) for optimization of heat transfer in dusty nanofluid flow with velocity slip

Background and Purpose The consequence of thermal radiation is scrutinized on the heat transport of Nano-diamond/silicon oil and silver/silicon oil nanofluids through a stretching endless plate. The single phase (Tiwari and Das) model is employed for nanofluid. The major objective of this study is to optimize the RSM-based Central composite design modeling to optimization of the heat transfer in dusty Oldroyd-B nanofluid across stretching surface. Additionally the velocity slip effect is considered. The dust particle phase is also taken into account. The significance of viscous dissipation, joule heating, inclined magnetic field with convective condition is investigated. Methodology The partial differential equations are developed under consideration, then transform to ODE’s by utilizing similarity tools. The transformed model of ODE’s is tackled numerically via bvp4c MATLAB tool with shooting algorithm. The effect of magnetic parameter, fluid interaction parameter, nanoparticle volume fraction, slip parameter and temperature interaction parameter on velocity field and temperature distribution of fluid phase and dust phase is investigated. Furthermore the Nusselt number on the wall is observed for interactive parameters of mass concentration of dust particles, fluid particles interaction parameter for velocity and unsteady parameters utilizing the face-centered Central Composite design (CCD) of the Response Surface Methodology (RSM). Additionally, Analysis of Variance (ANOVA) algorithm and 3D plots are utilized to examine the consequence of experimental design parameters via the response. The recommended model significance has been analyzed in conditions of correlation coefficient ( R 2 ), mean square error (MSE), root means square error (RMSE), prediction standard error to acknowledge the most excellent strong. Results The difference between the Predicted R2 of 0.9467 and the Adjusted R2 of 0.9867 is less than 0.2, which is assumed to be a reasonable concurrence. Furthermore results of the current analysis indicate that velocity gradient for nanofluid is diminishes for larger fluid particle interaction parameter for velocity, while the dust phase velocity is improved. The increment in Temperature gradients is observed via increasing values of the nanoparticle fraction and temperature base fluid particle interaction parameter. From the results it is concluded that skin friction coefficient is reduced with larger magnetic parameter for both mono nanofluids. Furthermore the heat transfer rate is increased by increasing the thermal radiation parameter for both mono nanofluids. It is concluded that silver/silicon oil nanofluid play a higher role in heat transportation as compare to Nano-diamond/silicon oil.

Unsteady MHD dusty fluid flow over a cone in the vicinity of porous medium: a numerical study

This research presents an unsteady free convection magnetohydrodynamics (MHD) dusty fluid flow over a vertical cone enclosed inside a porous medium. The Crank–Nicolson approach is used to get the numerical solutions for these non-linear partial differential equations (PDEs). The velocity and temperature distributions are graphed numerically for a wide range of physical parameters to highlight important characteristics of the solutions. The results showed that increasing the porosity parameter leads to a rise in the velocity profile for the fluid and dust phases, while doing the reverse with the rise of the magnetic parameter, fluid-particle interaction parameter, and mass concentration of the particle phase parameter. Additionally, it is shown that the temperature profile rises as the magnetic parameter and the mass concentration of particle phase parameter grow, whereas the fluid-particle interaction parameter and porosity parameter show the opposite tendency.

EMHD stagnation point flow of dusty hybrid nanofluid over a permeable stretching sheet: Radiative solar applications

The primary objective of this paper is to investigate the impact of dusty hybrid nanofluid electromagnetohydrodynamics (EMHD) on the stagnation point flow in the presence of solar radiation. Base fluids contain ethylene glycol, water, silver, titanium alloy, and suspended dust particles. Nonlinear differential equations with two or more independent variables define fluid flow phenomena. The governing equations can be solved by the MATLAB solver by employing a suitable numerical method, like R–K fourth order via shooting method. The isothermals for various parametric values have been explained. Because it has the potential to greatly advance the disciplines of industrial and thermal engineering, this proposed model is useful. When compared to using a single base fluid, the combination of two additional base fluid qualities provides noteworthy results. Because we were able to acquire a lower freezing point than water and better heat conductivity than pure ethylene glycol when we employed the combination of the two base fluids. Glycol water is used in car coolant and solar heating systems for a variety of purposes. Impact of embedded physical quantities like electric field parameter, ratio of specific heat, porosity parameter, stagnation parameter, radiation parameter, heat source parameter, and fluid particle interaction parameter for both velocity and temperature are illustrated graphically. Dust particles have a notable impact on various sectors, including the food and pharmaceutical industries. Specifically, they are special importance in applications such as wastewater treatment, solids drying, and the presence of plastic-coated metal items. In the present work, we observe that the stagnation parameter enhances the momentum boundary layer (MBL) thickness because the dusty fluid dominates the dusty hybrid nanofluid while incorporating the Ag + Ti alloy/EG + Water. The radiation becomes more efficient at evenly spreading heat, potentially resulting in a more uniform temperature distribution. Silver and titanium alloy particles may affect the thermal conductivity of dusty hybrid nanofluid when compared to the dusty fluid. The porosity parameter enhances the fluid flow and penetration by the porous medium, which lowers friction between the skin and the surface and reduces resistance.

An exact solution for unsteady three-dimensional magnetohydrodynamic Casson flow of dusty nanofluid over a porous stretching sheet

The unsteady three-dimensional (3D) Casson flow of a nanofluid containing dust particles over a porous, linearly stretching sheet in the presence of an external magnetic field is studied. It is assumed that the sheet is stretched in both directions along the xy plane. The governing equations of the two-phase model are partial differential equations that are transformed into ordinary equations using similarity transforms. The nanofluid is a suspension of water-based nanoparticles. In this study, we look at how nanoparticle size affect the properties of dusty nanofluid flow. The mathematical model contains the basic equations for the fluid and dust phases in the form of three-dimensional partial differential equations, which are transformed into dimensionless ordinary-dimensional equations using an appropriate similarity transformation. An exact analytical solution to this boundary value problem is obtained. The effects of various physical values on dust and nanofluid velocities are discussed in detail, including the Casson parameter, magnetic parameter, porosity parameter, fluid-particle interaction parameter, mass concentration of dust particles, and nanoparticle size. In a few specific instances, the current analytical solution demonstrates a good agreement with previously published numerical investigations.

Dual solutions for the two-dimension copper oxide with silver (CuO–Αg) and zinc oxide with silver (ΖnO–Αg) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip

PurposeThis paper aims to present dual solutions for the two-dimension copper oxide with silver (CuO–Ag) and zinc oxide with silver (ZnO–Ag) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip.Design/methodology/approachThe governing partial differential equations for the two dust particle phases are reduced to the pertinent ordinary differential equations using a similarity transformation. Closed-form analytical solutions for the reduced skin friction and reduced Nusselt number, as well as for the velocity and temperature profiles, were presented, both graphically and in tables, under specific non-dimensional physical parameters such as the suction parameter, Prandtl number, slip parameter and shrinking parameter, which are also presented in both figures and tables.FindingsThe results indicate that for the shrinking flow, the wall skin friction is higher in the dusty fluid when compared with the clear (viscous) fluid. In addition, the effect of the fluid–particle interaction parameter to the fluid phase can be seen more clearly in the shrinking flow. Furthermore, multiple (dual, upper and lower branch solutions) are found for the governing similarity equations and the upper branch solution expanded with higher values of the suction parameter. It can be confirmed that the lower branch solution is unstable.Practical implicationsIn practice, the study of the stretching/shrinking flow is crucially important and useful. Both the problems of steady and unsteady flow of a dusty fluid have a wide range of possible applications in practice, such as in the centrifugal separation of particles, sedimentation and underground disposal of radioactive waste materials.Originality/valueEven though the problem of dusty fluid has been broadly investigated, very limited results can be found for a shrinking sheet. Indeed, this paper has succeeded to obtain analytically dual solutions. The stability analysis can be performed by following many published papers on stretching/shrinking sheets. Finally, the critical values and plotting curves for obtaining single or dual solution are successfully presented.

Effect of Non-Linear Radiation and Non-Uniform Heat Source/Sink on Flow over a Linear Stretching Sheet with Fluid Particle Suspension

In this paper, the flow and heat transfer of dusty flow over a linear stretchable sheet has been analyzed. The effects of non-linear radiation and non-uniform heat source or sink have been studied. Considering the mentioned terms and conditions, the problem has been formulated. The formulation consists of systems of nonlinear PDEs which has been converted to a system of ODEs by taking suitable similarity transformations. Then the systems of ODEs have been solved by using Rungakutta method of 4th order. The computations work has been carried out by using BVP4C tool of MATLAB. The impact of flow parameters like radiation parameter, prandtl number, eckret number, fluid Particle interaction parameter β and diffusivity parameter on flow and heat transfer are investigated. The results are presented through graphs and tables. From the graphs, it is concluded that the presence of particles in fluid has some impact of different parameters in flow and heat transfer. The parameters like Eckert number, Fluid- particle interaction parameter, diffusivity parameter have remarkable effects of presence of particles

Two-phase hydromagnetic Eyring-Powell fluid flow over a stretching sheet suspended to a dusty particle

ABSTRACT The thermophysical feature of a 2D flow of a dusty Eyring-Powell fluid caused by a stretched sheet in the presence of magnetic field was assessed in the present study. The similarity transformation had been considered for transforming the dimensionless heat and fluid flow basic partial differential equations into simple ordinary equations. After that, the Runge-Kutta-Fehlberg 45 solver utilizes numerical methods to resolve the altered equations. We study and discuss in depth the flowing and heating attributes under various parameters, including the magnetic parameter, Eyring Powell fluid parameter, fluid particle interaction parameter and Prandtl number. In order to validate the reliability of the numerical solution, the findings that were produced are contrasted with the results that were achieved in the past. It has been proven numerically that the velocity of the fluid phase and particle phase both increases when the Eyring Powell fluid parameter is increased.

Two-Phase Flow of Eyring–Powell Fluid with Temperature Dependent Viscosity over a Vertical Stretching Sheet

In this work, the mixed convection flow of non-Newtonian Eyring–Powell fluid with the effects of temperature dependent viscosity (TDV) were studied together with the interaction of dust particles under the influence of Newtonian Heating (NH) boundary condition, which assume to move over a vertical stretching sheet. Alternatively, the dusty fluid model was categorized as a two-phase flow that consists of phases of fluid and dust. Through the use of similarity transformations, governing equations of fluid and dust phases are reduced into ordinary differential equations (ODE), then solved by efficient numerical Keller–box method. Numerical solution and asymptotic results for limiting cases will be presented to investigate how the flow develops at the leading edge and its end behaviour. Comparison with the published outputs in literature evidence verified the precision of the present results. Graphical diagrams presenting velocity and temperature profiles (fluid and dust) were conversed for different influential parameters. The effects of skin friction and heat transfer rate were also evaluated. The discovery indicates that the presence of the dust particles have an effect on the fluid motion, which led to a deceleration in the fluid transference. The present flow model can match to the single phase fluid cases if the fluid particle interaction parameter is ignored. The fluid velocity and temperature distributions are always higher than dust particles, besides, the opposite trend between both phases is noticed with β. Meanwhile, both phases share the similar trend in conjunction with the rest factors. Almost all of the temperature profiles are not showing a significant change, since the viscosity of fluid is high, which can be perceived in the figures. Furthermore, the present study extends some theoretical knowledge of two-phase flow.

Flow and Heat Transfer of MHD Dusty Nanofluid Toward Moving Plate with Convective Boundary Condition

This paper considers the flow and heat transfer characteristics of dusty nanofluid over a moving plate in the presence of magnetohydrodynamic (MHD) with convective boundary condition. Two types of nanofluid namely CuO-water and Al2O3-water permeated with dust particles are considered. The governing partial differential equations are converted into a system of non-linear ordinary differential equations using similarity transformation, then the non-linear ordinary differential equations are solved using shooting method with fourth-fifth order Runge-Kutta Fehlberg method (RKF45). The influence of non-dimensional governing parameters such as velocity ratio parameter, magnetic field parameter, volume fraction of the nanoparticle, volume fraction of the dust particle, mass concentration of the dust particle, fluid particle interaction parameter for velocity, fluid particle interaction parameter for temperature and Biot number on the velocity and temperature profiles for fluid and dust phases of CuO-water and Al2O3-water dusty nanofluids are discussed and presented through graphs. The skin friction coefficient and Nusselt number are discussed and presented in tabular form.

Internal heat generation impact on MHD natural convection of dusty hybrid nanomaterials within a porous cavity

AbstractThe numerical contribution of the natural heat flow of dusty hybrid nanofluid due to a square cavity filled with a porous medium with the effects of internal heat generation and the magnetic field is presented in this paper. The system of the problem equations is divided into hybrid nanofluid (Al2O3–Cu) phase equations and dusty phase equations, which are converted to a dimensionless form to be suitable for solving them numerically using the finite difference method. The results manifest in the streamlines, isotherms contours for both hybrid nanofluid phase and dust phase as well in local and average Nusselt numbers profiles. The numerical computations are performed and presented via graphs and tables due to the influence of governing physical parameters like , , , (0 ≤ Σ ≤ /2), , , , and . The results indicate that increasing of fluid–particle interaction parameter for velocity leads to increment of the streamlines and isotherms of both the dust and hybrid nanofluid phases. A notable enhancement is found in the streamlines of the hybrid nanofluid phase and dust phase for high values of the Rayleigh number. The average Nusslet number ameliorates due to suspended dust particles in the hybrid nanofluid while deteriorates with increasing nanoparticle volume fraction. Furthermore, rising values of Hartmann number lead to reducing streamlines of the hybrid nanofluid and dust phases but an increase occurs with an increment of the inclined angle of the magnetic field. A notable agreement is obtained between the data of the present study and other previously published work.

Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

Thermal non-equilibrium model subjected to thermal radiation impact and dust particles suspension in a porous square cavity

Heat transfer due to a square Darcy porous cavity in the presence of dust particles and thermal radiation effect by applying the thermal non-equilibrium model is investigated numerically in the current paper. The square cavity is maintained at a hot temperature at the left side wall, and the right side wall is maintained at cold temperature. While the bottom and top walls of the cavity are considered adiabatic. The impact of governing physical parameters on the streamlines, isotherms contours for the fluid and dust phases and isotherms for the solid phase are tested and represented through Graphic. In addition, the profiles of the average Nusselt numbers for solid and fluid phases and the total average Nusselt number are presented. The finite difference method is convenient to obtain a numerical analysis of the non-dimensionalized equations via the influence of mass concentration of the dust particles, fluid-particle interaction parameter for velocity, fluid-particle interaction parameter for temperature, Eckert number, radiation parameter, Rayleigh number, modified conductivity ratio, and inter-phase heat transfer coefficient. The results urge that the presence of dust particles leads to reduces the heat transfer rate at the left wall of the enclosure.

Role of hybrid nanostructures and dust particles on transport of heat energy in micropolar fluid with memory effects

Constitutive models exhibiting viscoelastic and micro-inertia with vortex viscosity effects are used for modeling of transport of heat energy, (angular and linear) with conservation laws for dust phase flow. The governing models are solved via the finite element method. The convergence of numerical solutions is guaranteed and mesh-free results are computed in view of a variation of physical parameters. Micro-rotations have shown a remarkable impact on shear stress and wall heat flux. The momentum relaxation (memory effects) time has shown a remarkable decrease in velocity associated with macro-flow. An increase in vortex viscosity increases angular motion. The Deborah number has shown a decreasing trend on flow. This causes a significant decrease in convective transport of heat energy. The temperature of dust particles increases when the ratio of specific heat and fluid particle interaction parameter for temperature is increased. However, the opposite behavior is noted for the case of increasing the relaxation time of the particle phase. The hybrid nanofluid transports much momentum than the momentum transported by mono-nanofluid.

Dynamics of dust particles in a conducting dusty nanomaterials: A computational approach

Subject introduced in the present analysis is the role of dust particles in a conducting dusty nanofluid, past a stretching surface. Thermal conductivity which affects the nanofluid heat transfer is conducted by a suitable model known as Maxwell model. Both the dust and nano particles considered here are spherical. The entire flow phenomena i.e. the momentum and energy is characterizes by taking cupper- and silver- nano particles. The nonlinear fluid phase and dust phase governing equations are transformed to ordinary differential equation with the suitable choice of transformed variables which arises the characterizing parameters for the flow phenomena. Solutions of the coupled ODEs are performed numerically. The role of nanoparticle volume fraction and number density of dust particle along with magnetic field are also important for the heat transfer. The influence of parameters such as dust particle mass concentration, fluid particle interaction parameter, Eckert number, effective specific heat parameter, on momentum and heat profiles are presented through graphs. Verification of current study is obtained by comparing with the earlier study in particular cases and found to be in good agreement

Jeffrey Fluid Embedded with Dust Particles over a Shrinking Sheet: A Numerical Investigation

This study examines the flow behaviour of Jeffrey fluid together with uniform distribution of dust particles that moves over the vertical shrinking sheet. This intriguing mixture employs the two-phase model which mathematically describes the characteristic of both fluid and solid particles in a flow system by a set of partial differential equations. A convenient form of these equations is expressed in the form of ordinary differential equations through the use of similarity transformation and can subsequently be solved by applying the Keller-box method. Numerical solutions for several influencing parameters, namely suction, fluid-particle interaction, magnetic field and aligned angle on the flow and temperature fields of the two components (fluid and dust particles) are presented in graph form. In addition, the results of skin friction coefficient and Nusselt number at surface of sheet are summarized in the table and analysed in details. It is found that, the velocity and temperature profiles of fluid and dust phases show a similar behaviour in response to all involved parameters except for fluid-particle interaction parameter, respectively.

The Investigation of a Fluid-Solid Interaction Mathematical Model under Combined Convective Jeffrey Flow and Radiation Effect Embedded Newtonian Heating as the Thermal Boundary Condition over a Vertical Stretching Sheet

The investigation on the interaction between solid and fluid under combined convective flow has been carried out mathematically. The Jeffrey fluid model is taken as the fluid phase and the model is being embedded with the dust particles (solid phase). This two-phase model is constructed by introducing the fluid-particles interaction forces in the momentum equations of the fluid and dust phases, respectively. The natural and forced convections together with the aligned magnetic field are considered on the fluid flow. Also, the Newtonian heating as thermal boundary condition is induced on the vertical stretching sheet. In order to reduce the complexity of the model, the governing equations are transformed from partial differential equation into ordinary differential equation via suitable similarity transformation. The solutions are obtained in terms of velocity and temperature profiles for the fluid and particles phases respectively whereby the Keller-box method is utilized to obtain the desired outcomes. The influences of several significant physical parameters are visualized graphically to clarify the flow and heat transfer characteristic for both phases. The investigation found that the fluid’s velocity is affected by the presence of the dust particles which led to decelerate the fluid transference. The present flow model is able to be compared with the single-phase fluid cases if the fluid-particle interaction parameter is ignored.

Unsteady natural convection flow of a dusty non-Newtonian Casson fluid along a vertical wavy plate: numerical approach

The present contribution provides a numerical treatment for the flow of unsteady natural convection of non-Newtonian Casson fluid model loaded with dusty particles over a vertical wavy plate. It is assumed that the fluid is incompressible and the dusty particles are considered to be spheres with the same size. Via the help of primitive variable formulation, the dimensionless boundary layer governing equations are reduced into a convenient coordinate system. The transformed resulting system of governing equations is tackled numerically employing the fully implicit finite difference method. The impact of various controlling physical parameters such as the amplitude of the wavy plate, the dimensionless time and fluid–particle interaction parameters on the velocity and temperature of both fluid and particle phase is analyzed. It is found that the magnitude of the velocity of both fluid and particle phase diminishes with increasing amplitude of the wavy plate parameter, while an opposite behavior is observed on temperature distributions as the amplitude of the wavy plate parameter rises. A significant impact is noticed for the heat transfer rate with enhancement values of fluid–particle interaction parameter. The numerical solutions are compared with the available data in the literature. Quantitative comparison illustrates good compatibility between the current and previous results.

Analysis of dusty Casson fluid flow past a permeable stretching sheet bearing power law temperature and magnetic field

Purpose This study aims to present an analysis on heat transfer attributes of fluid-particle interaction over a permeable elastic sheet. The fluid streaming on the sheet is Casson fluid (CF) with uniform distribution of dust particles. Design/methodology/approach The basic steady equations of the CF and dust phases are in the form of partial differential equations (PDEs) which are remodeled into ordinary ones with the aid of similarity transformations. In addition to analytical solution, numerical solution is obtained for the reduced coupled non-linear ordinary differential equations (ODEs) to validate the results. Findings The solution seems to be influenced by significant physical parameters such as CF parameter, magnetic parameter, suction parameter, fluid particle interaction parameter, Prandtl number, Eckert number and number density. The impact of these parameters on flow field and temperature for both fluid and dust phases is presented in the form of graphs and discussed in detail. The effect on skin friction coefficient and heat transfer rate is also presented in tabular form. It has been observed that an increase in the CF parameter curtails the fluid velocity as well as the particle velocity however enhances the heat transfer rate at the wall. Furthermore, comparison of the numerical and analytical solution is also made and found to be in excellent agreement. Originality/value Although the analysis of dusty fluid flow has been widely examined, however, the present study obtained both analytical and numerical results of power law temperature distribution in dusty Casson fluid under the influence of magnetic field which are new and original for such type of flow.

Numerical Analysis of Unsteady Magneto-Biphase Williamson Fluid Flow with Time Dependent Magnetic Field

Numerical investigation of the dusty Williamson fluid with the dependency of time has been done in current disquisition. The flow of multiphase liquid/particle suspension saturating the medium is caused by stretching of porous surface. The influence of magnetic field and heat generation/absorption is observed. It is assumed that particle has a spherical shape and distributed uniformly in fluid matrix. The unsteady two-dimensional problems are modeled for both fluid and particle phase using conservation of mass, momentum and heat transfer. The finalized model generates the non-dimensioned parameters, namely Weissenberg number, unsteadiness parameter, magnetic parameter, heat generation/absorption parameter, Prandtl number, fluid particle interaction parameter, and mass concentration parameters. The numerical solution is obtained. Locality of skin friction and Nusselt number is deliberately focused to help of tables and graphs. While inferencing the current article it is clearly observed that increment of Williamson parameter, unsteadiness parameter, magnetic parameter, volume fraction parameter, and mass concentration parameter reduces the velocity profile of fluid and solid particles as well. And increment of Prandtl number, unsteadiness parameter, volume fraction parameter, and mass concentration parameter reduces the temperature profile of fluid and solid particles as well.