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This present aims to present the numerical study of the unsteady stretching/shrinking flow of a fluid-particle suspension in the presence of the constant suction and dust particle slip on the surface.

The governing partial differential equations for the two phases flows of the fluid and the dust particles are reduced to the pertinent ordinary differential equations using a similarity transformation. The numerical results are obtained using the bvp4c function in the Matlab software.

The results revealed that in the decelerating shrinking flow, the wall skin friction is higher in the dusty fluid when compared to the clean fluid. In addition, the effect of the fluid-particle interaction parameter to the fluid-phase can be seen more clearly in the shrinking flow. Other non-dimensional physical parameters such as the unsteadiness parameter, the mass suction parameter, the viscosity ratio parameter, the particle slip parameter and the particle loading parameter are also considered and presented in figures. Further, the second solution is discovered in this problem and the solution expanded with higher unsteadiness and suction values. Hence, the stability analysis is performed, and it is confirmed that the second solution is unstable.

In practice, the flow conditions are commonly varying with time; thus, the study of the unsteady flow is very crucial and useful. The problem of unsteady flow of a dusty fluid has a wide range of possible applications such as in the centrifugal separation of particles, sedimentation and underground disposable of radioactive waste materials.

Even though the problem of dusty fluid has been broadly investigated, limited discoveries can be found over an unsteady shrinking flow. Indeed, this paper managed to obtain the second (dual) solutions, and stability analysis is performed. Furthermore, the authors also considered the artificial particle-phase viscosity, which is an important term to study the particle-particle and particle-wall interactions. With the addition of this term, the effects of the particle slip and suction parameters can be investigated. Very few studies in the dusty fluid embedded this parameter in their problems.

The purpose of this paper is to explore the impact of thermal radiation, viscous dissipation and Joule heating effects on the flow of a magneto-nanofluid between two horizontally placed plates. Three distinct shapes of nanoparticles in a base fluid (water) are considered to compose the nanofluid.

Introducing feasible similarity variables, the flow model is transformed into a nonlinear and coupled system of ordinary differential equations. The consequent system is solved by using homotopy analysis method.

Furthermore, the influence of embedded parameters on velocity and temperature profiles is highlighted graphically. The same is done for showing the variations in skin friction coefficient and local rate of heat transfer. Under certain conditions, present results compared with already existing results in the literature. Some main findings are pinpointed in the last section before the bibliography. From presented work, it is analyzed that the velocity field along y-axis and x-axis are increasing and decreasing functions of suction/injection parameter. The velocity of the fluid starts increases for Reynolds number and declines for volumetric fraction of the nanoparticles. Significant variations in angular velocity are observed for volumetric fraction and Reynolds number, respectively. Thermal field increases rapidly for brick-shaped nanoparticles, and for platelet-shaped nanoparticles, it decreases rapidly. Local rate of heat transfer increases for radiation and Reynolds number and starts decreasing for Eckert number.

The study presented is original and has not been submitted to any other journal for the publication purpose. The contents are original and proper references have been provided wherever applicable.

This paper aims to study the impacts of viscous dissipation, thermal radiation and Joule heating on squeezing flow current and the heat transfer mechanism for a magnetohydrodynamic (MHD) nanofluid flow in parallel disks during a suction/blowing process.

First, the governing momentum/energy equations are transformed into a non-dimensional form and then the obtained equations are solved by modified Adomian decomposition method (ADM), known as Duan–Rach approach (DRA).

The effect of the radiation parameter, suction/blowing parameter, magnetic parameter, squeezing number and nanoparticles concentration on the heat transfer and flow field are investigated in the results. The results show that the fluid velocity increases with increasing suction parameter, while the temperature profile decreases with increasing suction parameter.

A complete analysis of the MHD fluid squeezed between two parallel disks by considering Joule heating, thermal radiation and adding different nanoparticles using the novel method called DRA is addressed.

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.

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.

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.

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.

Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many applications, the variability of these properties plays a significant role in modifying transport characteristics while the temperature difference in the boundary layer is notable. These include drag reduction in heavy oil transport systems, petroleum purification and coating manufacturing. The purpose of this study is to develop, a comprehensive mathematical model, motivated by the last of these applications, to explore the impact of variable viscosity and variable thermal conductivity characteristics in magnetohydrodynamic non-Newtonian nanofluid enrobing boundary layer flow over a horizontal circular cylinder in the presence of cross-diffusion (Soret and Dufour effects) and appreciable thermal radiative heat transfer under a static radial magnetic field.

The Williamson pseudoplastic model is deployed for rheology of the nanofluid. Buongiorno’s two-component model is used for nanoscale effects. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. Extensive validation with earlier studies in the absence of nanoscale and variable property effects is included.

The influence of notable parameters such as Weissenberg number, variable viscosity, variable thermal conductivity, Soret and Dufour numbers on heat, mass and momentum characteristics are scrutinized and visualized via graphs and tables.

Buongiorno (two-phase) nanofluid model is used to express the momentum, energy and concentration equations with the following assumptions. The laminar, steady, incompressible, free convective flow of Williamson nanofluid is considered. The body force is implemented in the momentum equation. The induced magnetic field strength is smaller than the external magnetic field and hence it is neglected. The Soret and Dufour effects are taken into consideration.

The variable viscosity and thermal conductivity are considered to investigate the fluid characteristic of Williamson nanofluid because of viscosity and thermal conductivity have a prime role in many industries such as petroleum refinement, food and beverages, petrochemical, coating manufacturing, power and environment.

This fluid model displays exact rheological characteristics of bio-fluids and industrial fluids, for instance, blood, polymer melts/solutions, nail polish, paint, ketchup and whipped cream.

The outcomes disclose that the Williamson nanofluid velocity declines by enhancing the Lorentz hydromagnetic force in the radial direction. Thermal and nanoparticle concentration boundary layer thickness is enhanced with greater streamwise coordinate values. An increase in Dufour number or a decrease in Soret number slightly enhances the nanofluid temperature and thickens the thermal boundary layer. Flow deceleration is induced with greater viscosity parameter. Nanofluid temperature is elevated with greater Weissenberg number and thermophoresis nanoscale parameter.

The purpose of this paper is to numerically study the boundary layer problem for the case of two-dimensional flow of dusty fluid over a shrinking surface in the presence of the fluid suction at the surface.

The governing equations of the problem are reduced to the system of ordinary differential equations using the similarity transformation and then solved using the bvp4c method in the Matlab software.

The effects of the drag coefficient parameter L, the fluid–particle interaction parameter δ, the suction parameter s and the particle loading parameter ω on the flow of the permeable shrinking sheet are investigated. It is found that the aforementioned parameters have different effects in the shrinking sheet flow. This study has also succeeded in discovering the second solution, and through the stability analysis, it is suggested that the solution is unstable and not physically realizable in practice.

The current findings add to a growing body of literature on the boundary layer problem in the dusty fluid. The dusty fluid is significant in various practical applications such as in the transporting suspended powdered materials through pipes, propulsion and combustion in rockets, the flow of blood in arteries, wastewater treatment and as corrosive particles in engine oil flow.

Even though the dusty fluid problem has been extensively studied in the flow of the stretching sheet, limited findings can be found over a shrinking flow. In fact, this is the first study to discover the second solution in the dusty fluid problem.

The hydrodynamic development of non‐Newtonian fluid flow in the entrance region of a duct with porous walls is examined numerically by solving the modified Navier‐Stokes equations. Cases involving blowing, suction, and no mass transfer through the walls are considered. Velocity distributions, pressure drops, and skin friction coefficients are presents for each case. A definite concavity is found in the velocity profile near the duct entrance for all cases. Results for Newtonian fluids are compared with previous studies in which boundary‐layer theory was used. In the region away from the entrance it is found that the present results are in good agreement with previous works. In the region close to the entrance, or in the case of suction, boundary‐layer theory is shown to be inappropriate.

The purpose of this paper is to investigate numerically mixed convection of Al₂O₃-water nanofluids flowing through a horizontal ventilated cavity heated from below by a temperature varying sinusoidally along its lower wall. The simulations focus on the effects of different key parameters, such as Reynolds number (200 ≤ Re ≤ 5,000), nanoparticles’ concentration (0 ≤ ϕ ≤ 0.1) and phase shift of the heating temperature (0 ≤ γ ≤ π), on flow and thermal patterns and heat transfer performances.

The Navier–Stokes equations describing the nanofluid flow were discretized using a finite difference technique. The vorticity and energy equations were solved by the alternating direction implicit method. Values of the stream function were obtained by using the point successive over-relaxation method.

The simulations were performed for two modes of imposed external flow (injection and suction). The main findings are that the dynamical and thermal fields are affected by the parameters Re, ϕ, γ and the applied ventilation mode; the addition of nanoparticles leads to an improvement of heat transfer rate and an increase of mean temperature inside the enclosure; the heat exchange performance and the better cooling are more pronounced in suction mode; the phase shift of the heating temperature may lead to periodic solutions for weaker values of Re and contributes to an increase or a decrease of heat transfer depending on the value of ϕ and the convection regime.

To the best of the authors’ knowledge, the problem of mixed convection of a nanofluid inside a vented cavity using the injection or suction technics and submitted to non-uniform heating conditions has not been treated so far.

The purpose of this paper is to investigate the steady flow of a non‐Newtonian power‐law type fluid over a permeable stretching surface. The surface is stretched with a prescribed skin velocity following a power‐law variation along its length.

Using appropriate similarity variables and boundary layer approximations, the continuity and momentum equations are reduced to an ordinary differential equation subject to appropriate transformed boundary conditions, with three dimensionless parameters: the power‐law index of the non‐Newtonian fluid, suction/injection parameter and the power law index of the skin velocity. These equations are solved numerically by using the fourth‐order Runge‐Kutta integration algorithm coupled with a conventional shooting procedure. Comparisons with closed form analytical solutions obtained for the case of Newtonian fluid by previous authors are also performed.

It was found that the dimensionless entrainment velocity decreases with the power exponent m, of the prescribed skin velocity, irrespective of the non‐Newtonian fluid nature, for both impermeable and permeable surfaces. Large rates of injection lead to very large values of the skin friction, the effect being more intense for small values of the dimensionless flow index n. At the same rate of the injection/suction, the skin friction S is increased when the surface is stretched linearly than uniformly.

This type of problem has potential to serve as a prototype for many manufacturing processes such as rolling sheet drawn from a die, cooling and/or drying of paper and textile, manufacturing of polymeric sheets, sheet glass and crystalline materials, etc.

A thorough analysis of the hydrodynamics of a stretching surface is performed in the present paper, by combining analytical and numerical means. The topics covered here (Ostwald‐de Waele power‐law fluid + prescribed skin velocity + permeability of the stretching surface) seem to be not reported till now in the literature.

The purpose of this paper is to propose a prediction method of gas-liquid two-phase flow patterns and reveal the flow characteristics in the suction chamber of a centrifugal pump.

A transparent model pump was experimentally studied, and the gas-liquid two-phase flow in the pump was numerically simulated based on the Eulerian–Eulerian heterogeneous flow model. The numerical simulation method was verified from three aspects: the flow pattern in the suction chamber, the gas spiral length and the external characteristics of the pump. The two-phase flow in the suction chamber was studied in detail by using the numerical simulation method.

There are up to eight flow patterns in the suction chamber. However, at a certain rotational speed, only six flow patterns are observed at the most. At some rotational speeds, only four flow patterns appear. The gas spiral length has little relationship with the gas flow rate. It decreases with the increase of the liquid flow rate and increases with the increase of the rotational speed. The spiral flow greatly increases the turbulence intensity in the suction chamber.

A method for predicting the flow pattern was proposed. Eight flow patterns in the suction chamber were identified. The mechanism of gas-liquid two-phase flow in the suction chamber was revealed. The research results have reference values for the stable operation of two-phase flow pumps and the optimization of suction chambers.