Governing Flow Equations Research Articles

Theoretical analysis of two-layered electro-osmotic peristaltic flow of FENE-P fluid in an axisymmetric tube

This article presents the theoretical analysis of two-dimensional peristaltic transport of two-fluids in a flexible tube under the influence of electro-osmotic force. The flow domain is composed of two regions, namely, the core region and the peripheral region. The Newtonian and the FENE-P models are used to describe the rheology of fluids in the peripheral and the core regions, respectively. Governing flow equations corresponding to each region are developed under the assumption of long wavelength and low-Reynolds number. The interface between the two regions is computed numerically by employing a system of non-linear algebraic equations. The influence of relevant controlling parameters on pressure gradient, interface, trapping, and reflux is highlighted graphically and explained in detail. Special attention is given to estimate the effects of viscoelastic parameter of the core region fluid in the presence of electro-osmotic environment. Our investigation indicates an augmentation in the pressure loss at a zero volumetric flow rate with growing the viscoelastic and occlusion parameters. Moreover, trapping, reflux, and pumping efficiency are found to increase by increasing the electro-osmotic and viscoelastic parameters. The analysis presented here may be helpful in controlling the micro-vascular flow during the fractionation of blood into plasma (in the peripheral layer) and erythrocytes (core layer). This study may also have potential applications in areas such as electrophoresis, hematology, design, and improvement of bio-mimetic electro-osmotic pumps.

Oldroyd-B nanofluid-flow between stretching disks with thermal slip and multiple flow features

This novel investigation deals with the thermal slip in magnetized axi-symmetric flow of Oldroyd-B liquid configured by infinite stretchable disks. With appliance of fundamental laws, the flow model equations are constructed. The governing flow equations are altered into no-dimensional form by using similarity quantities. The solution procedure is followed by using famous homotopy analysis technique. The convergence analysis is performed to evaluate the solution accuracy. The signifi?cance of flow parameters in the pattern of velocity, temperature and concentration are graphically illustrated. The novel numerical simulations for wall shear stress, Nusselt number, and Sherwood number are also performed at both surfaces of disks. It is noted the effects of relaxation time and retardation constants on radial and normal velocity components is opposite. The thermal slip parameters enhance the nanoparticles temperature. The concentration profile is decreases with Brown?ian motion parameter.

NUMERICAL SOLUTION OF MAGNETOHYDRODYNAMIC (MHD) RADIATIVE BOUNDARY LAYER FLOW AND HEAT TRANSFER ALONG A WEDGE IN THE PRESENCE OF SUCTION/INJECTION

An approximate numerical solution for the two dimensional laminar MHD radiative boundary layer flow along a wall of wedge with appropriate suction and injection in the presence of viscous dissipation and porous medium is considered in the present article. The fluid is considered to be viscous and incompressible. By applying appropriate similarity transformation, the governing flow equations have been transformed into corresponding higher order ordinary differential equations. The flow model is shown to be controlled by a number of flow parameters, viz. the radiation parameter, magnetic parameter, the permeability parameter, Prandtl number, Eckert number, the Hartree pressure gradient parameter and suction-injection parameter. The system of governing differential equations is solved numerically by shooting method and numerical calculations are carried out for different values of above mentioned dimensionless parameters. An analysis of the drawn results predicts that the velocity boundary layer and thermal boundary layer are influenced appreciably by the suction-injection, radiation and viscous dissipation at the wall of wedge.

Oldroyd-B nanofluid-flow between stretching disks with thermal slip and multiple flow features

This novel investigation deals with the thermal slip in magnetized axi-symmetric flow of Oldroyd-B liquid configured by infinite stretchable disks. With appliance of fundamental laws, the flow model equations are constructed. The governing flow equations are altered into no-dimensional form by using similarity quantities. The solution procedure is followed by using famous homotopy analysis technique. The convergence analysis is performed to evaluate the solution accuracy. The signifi?cance of flow parameters in the pattern of velocity, temperature and concentration are graphically illustrated. The novel numerical simulations for wall shear stress, Nusselt number, and Sherwood number are also performed at both surfaces of disks. It is noted the effects of relaxation time and retardation constants on radial and normal velocity components is opposite. The thermal slip parameters enhance the nanoparticles temperature. The concentration profile is decreases with Brown?ian motion parameter.

Non-Newtonian heat and mass transfer on MHD blood flow through a stenosed artery in the presence of body exercise and chemical reaction

A mathematical model of non-Newtonian blood flow, heat and mass transfer through a stenosed artery is studied. The non-Newtonian model is chosen to suit the Herschel-Bulkley fluid characteristics, taking into account the presence of body acceleration, magnetic fields and chemical reaction. The study assumed that, the flow is unsteady, laminar, two-dimensional and axisymmetric. The governing flow equations of motion were solved numerically using explicit finite difference schemes. The study found that velocity profile diminishes with increase in Hartman number and increases with body acceleration. The temperature profile is raised by the increase of body acceleration and the Eckert number, while it diminishes with the increase of the Peclet number. It was found also that the concentration profile increases with the increase of the Soret number and decreases with the increase of the chemical reaction. It was further observed that the shear stress deviates more when n > 1 than when n < 1. Shear stress for power law fluid when n > 1 exhibited higher magnitude value than Newtonian, Bingham and Herschel-Bulkley fluids.

Design and modelling of dust capturing system in thermally stratified flowing conditions

An improved understanding of the spreading and deposition of particles in a thermally buoyant flow environment i.e. melting hall is a key prerequisite to plan new strategies for dust capturing and reduced diffuse emissions. Accurate modeling of dust spreading and deposition requires accurate prediction of turbulence, particles dynamics, and particle-flow interactions. Widely used Reynolds-averaged Navier-Stokes (RANS) turbulence model, such as k-epsilon model, have shortcomings when modeling transient flow phenomena in thermally buoyant flow conditions. To overcome this shortcoming, a filtered VLES model (Very Large Eddy Scale model) have been applied where turbulent structures larger than a given filter size (typically grid size) is captured by the governing flow equations and smaller structures are modelled with a modified filtered k-epsilon model. This modeling approach provides more details description of the stratified flow and small turbulence structures. Both Drift-Flux Model (DFM) in a Eulerian framework and discrete phase model (DPM) in a Lagrangian framework have been applied to model the particle phase. Three coupled modelling approaches VLES-DPM, k-epsilon-DPM, and VLES-DFM are applied to understand the dust spreading and deposition. These methods are also used for designing a dust capturing system. The parameters which influence the dust capturing efficiency are also identified. The result from these three approaches are compared and the study showed that the VLES-DFM produces similar results to the VLES-DPM with lower computational time. Furthermore, the studies show that dust capturing efficiency depends on hood shape, particle size, particle density, hall-wind, and suction rate.

Activation Energy and Second Order Slip in Bioconvection of Oldroyd-B Nanofluid over a Stretching Cylinder: A Proposed Mathematical Model

The thermal performances based on the interaction of nanoparticles are the topic of great interest in recent years. In the current continuation, we have utilized the activation energy and thermal radiation consequences in the bioconvection flow of magnetized Oldroyd-B nanoparticles over a stretching cylinder. As a novelty, the second order slip features (Wu’s slip) and convective Nield boundary assumptions are also introduced for the flow situation. The heat performances of nanofluids are captured with an evaluation of the famous Buongiorno’s model which enables us to determine the attractive features of Brownian motion and thermophoretic diffusion. The suggested thermal system is based on the flow velocity, nanoparticles temperature, nanoparticles volume fraction and motile microorganisms. The governing flow equations for the flow problem are constituted with relevant references for which numerically solution is developed via shooting algorithm. A detailed graphically analysis for the assisted flow problem is performed in view of the involved parameters. Although some studies are available in the literature which deals with the flow of various fluids over-stretching cylinder, the phenomenon of bioconvection and other interesting features are not reported yet. Therefore, present scientific computations are performed to fill this gap and the reported results can be more useful for the enhancement of thermal extrusion processes, solar energy systems, and biofuels.

Effects of Viscous Dissipation and Wall Conduction on Steady Mixed Convection Couette Flow of Heat Generating/Absorbing Fluid

This article theoretically investigated mixed convection flow of heat generating/absorbing fluid in the presence of viscous dissipation and wall conduction effects. The flow is considered to be steady in a vertical channel with some boundary thickness. One of the plates is heated while the other is kept at ambient temperature. The governing flow equations were solved analytically using Homotopy Perturbation Method (HPM). The influences of the governing parameters were captured in graphs, tables and a table was constructed for validation of the work. It is worthwhile to stress that, both the velocity and temperature profiles decrease near the heated plate with an increase in boundary thickness (&lt;i&gt;d&lt;/i&gt;) while the reverse cases were observed toward the cold plate. The velocity profile increases near the heated plate with increase in mixed convection parameter (&lt;i&gt;Gre&lt;/i&gt;) and decreases towards the cold plate. Rate of heat transfer has been observed to decrease with increase in boundary plate thickness (&lt;i&gt;d&lt;/i&gt;) while the critical value of (&lt;i&gt;Gre&lt;/i&gt;) increases with growing boundary plate thickness. The study therefore established the importance of boundary plate thickness in mixed convection investigation.

Magnetohydrodynamic oscillatory flow of a physiological fluid in an irregular channel

The impact of heat source on magnetohydrodynamic oscillatory flow of a chemically reacting viscoelastic fluid in an asymmetric wavy channel is analysed. The governing flow equations are transformed into ODEs by utilizing proper non-dimensional variables. The subsequent ordinary differential equations are solved analytically. The effects of different flow parameters on the fluid flow, thermal and species distributions as well as rate of heat and mass transfer coefficients are examined graphically. It is pointed out that the velocity of fluid is parabolic with extreme value along the channel centreline and minimum at the walls. The magnitude of fluid velocity increases with an increase in porous parameter and high heat transport of a system is due to the presence of oscillatory flow.

An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations

We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). We verify the accuracy of the numerical scheme for commonly used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and unbounded flow past a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method.

Unsteady Hydromagnetic Flow of Eyring-Powell Nanofluid over an Inclined Permeable Stretching Sheet with Joule Heating and Thermal Radiation

The present analysis deals with an unsteady magnetohydrodynamic flow of Eyring-Powell nanofluid over an inclined permeable stretching sheet. Effects of thermal radiation, Joule heating, and chemical reaction are considered. The effects of Brownian motion and thermophoresis on the flow over the permeable stretching sheet are discussed. Using Runge-Kutta fourth-order along with shooting technique, numerical and graphical results were obtained for the governing flow equations. The influence of various parameters on flow variables have been examined in detail. The results reveal that the temperature of the fluid enhanced with increasing Brownian and thermophoresis parameters. The increase of fluid velocity with the local Grashof number, the solutal Grashof number has been noticed. Further, the nanoparticles concentration decreased for a given increase in Brownian motion and chemical reaction parameters, while it increased with an increase in the thermophoresis parameter.

Heat transfer and flow analysis of Casson fluid enclosed in a partially heated trapezoidal cavity

In this article, we are reporting the mechanism of natural convection flow in a partially heated trapezoidal cavity containing non-Newtonian Casson fluid. A non-Newtonian model of Casson fluid is used to develop the governing flow equations. The thermal control inside the enclosure is managed using the partially heated lower wall. Most physical and significant conditions are used at the inclined walls of the cavity to attain the performance of heat management and streamlines. The Galerkin finite element technique (GFEM) is adopted to examine the solution of dimensionless PDEs system. The thermal and flow fields are envisioned through isotherms and streamlines while the simulations are performed for flow and thermal fields via various ranges of Rayleigh number (104 ≤ Ra ≤ 105.5), and different lengths of the heated part. Furthermore, outcomes are visualized for Nusselt number over the cavity wall under the influence of the Casson parameter. It is observed that as Casson fluid parameter decreases the velocities in x-direction and y-direction exhibit the dominant behavior. The influence of lower values of Casson fluid parameter on Nusselt number is significant at the middle of the cavity while the Nusselt number increases as increases the heated bottom wall in length.

Magnetized squeezed flow of time‐dependent Prandtl‐Eyring fluid past a sensor surface

AbstractThe present numerical investigation describes the influence of a transverse magnetic field on the heat and mass transfer characteristics of time‐dependent squeezed flow of Prandtl‐Eyring fluid past a horizontal sensor surface. The current physical problem is modeled based on the considered flow configuration. Also, the present problem is analyzed under the influence of Lorentz forces, to explore the impact of a magnetic field on the flow behaviour. The considered physical problem in the present study gives highly nonlinear coupled time‐dependent, two‐dimensional partial differential equations. The governing flow equations are reduced to the system of nonlinear ordinary differential equations by imposing the suitable similarity transformations on the laws of motion. Due to the inadequacy in the analytical methods, the present problem is solved by using the Runge‐Kutta fourth order integration scheme with shooting method. The flow and heat transfer behaviour of various control parameters are studied and presented in terms of graphs and tables. From the current investigation it is noticed that, the increasing magnetic parameter enhances the velocity field and diminishes the temperature profile in the flow region. Also, the magnifying permeable velocity parameter decreases the temperature field. The present similarity solutions are found to be in good agreement with previously published results.

Response to (Comment on the paper “Theoretical & Applied Mechanics Letters 7 (2017) 235–242”)

RD is absent from the dimensional Eqs. (1)–(6) in Ref. [1], which we included in Ref. [1] as reference to the study of the related flow behaviors of the nanofluid. These equations constitute the governing flow equations of nanofluid over a stretching sheet in Ref. [1], and these dimensional equations are independent from the entropy generation Eq. (1) from Ref. [1] with RD as mentioned above. Entropy generation measures the degree or level of available (existing) irreversibilities within a process. The entropy generation equation is an extension from the governing flow Eqs. (1)–(6).

MHD oblique stagnation point flow of nanofluid over an oscillatory stretching/shrinking sheet: existence of dual solutions

An unsteady magnetohydrodynamic oblique stagnation point flow of an incompressible nanofluid towards a stretching/shrinking surface with the effect of mass suction on the oscillatory surface is analyzed. Water is considered as a base fluid while single wall carbon nanotubes are assumed as nanoparticles. The governing flow equations are transformed into a system of coupled nonlinear ordinary differential equations via suitable transformation. Dual solutions of these nonlinear coupled equations are obtained by utilizing the bvp4c package in MATLAB. It is also found that these solutions survive in a certain domain of controlling parameters. The physical influence of several controlling parameters like nanoparticle volume fraction parameter, Hartmann number, stretching/shrinking parameter and suction parameter on heat transfer characteristics and flow field are discussed in detail and are demonstrated through graphs. We find that dual solutions exist in both the stretching case and the shrinking case. Also, the lower solution branch shows singular behavior for the skin friction coefficient in the shrinking domain whereas the upper solution branch has smooth behavior in both the stretching and shrinking domains.

Natural convection effects on heat and mass transfer of slip flow of time-dependent Prandtl fluid

Abstract We proposed a mathematical model for an incompressible, viscous, natural convection, and stagnation point slip flow of MHD Prandtl fluid over an infinite plate. The governing flow equations are constructed using the Prandtl rheological model. In account of physical relevance, we investigated the Soret and Dufour effects on the flow field. The complex natured flow equations are transformed to a set of PDEs using a suitable similarity variables. The non-dimensionalized ruling problem together with physical boundary conditions is numerically analyzed via Crank-Nicolson scheme. The velocity, temperature and concentration of the diffusing species distributions are enhanced for higher values of unsteadiness parameter. It is noted that velocity is slightly decreasing for higher values of Reynolds number while smaller values of Re providing more dominant effects on the velocity, temperature and concentration of the diffusing species profiles and enhanced heat and mass transfer rates is noticed. The physical behavior of reduced Nusselt and Sherwood numbers, friction factor, for distinct values of emerging parameters is examined and representative set of graphs are presented. Highlights Flow model is presented for MHD Prandtl fluid flow over an infinite plate. Mathematical model is performed for unsteady flow with Soret and Dufour effects. The proposed model is solved via crank Nicolson finite difference scheme. Simulations are performed for skin friction, Nusselt and Sherwood numbers.

Entropy generation on the interaction of nanoparticles over a stretched surface with thermal radiation

This communication examines the entropy generation on the interaction of nanoparticles over a stretching porous sheet with nonlinear thermal radiation. The water-based Nanofluid having Nimonic 80a metal nanoparticles of Bricks shape. Similarity transformations are used for the simplification of governing flow equations. Numerical results for temperature, velocity, Bejan number, and entropy profiles are obtained and investigated by Successive linearization technique and Chebyshev spectral collocation scheme. Simultaneous effects of the porous medium, Radiation parameter, nanoparticle volume fraction, Prandtl number, Brinkman number, and Reynolds number are demonstrated through graphs. Additionally, the outcomes taken from the prevailing scheme ratifies magnificent conformity with the predecessors while comparing among investigations to the existing literature. The formulation for skin friction coefficient and Nusselt number are interpreted and displayed through graphs.

MHD Flow of Nanofluid with Homogeneous-Heterogeneous Reactions in a Porous Medium under the Influence of Second-Order Velocity Slip

The influence of second-order velocity slip on the MHD flow of nanofluid in a porous medium under the effects of homogeneous-heterogeneous reactions has been analyzed. The governing flow equation is exactly solved and compared with those in the literature for the skin friction coefficient in the absence of the second slip, where great differences have been observed. In addition, the effects of the permanent parameters on the skin friction coefficient, the velocity, and the concentration have been discussed in the presence of the second slip. As an important result, the behavior of the skin friction coefficient at various values of the porosity and volume fraction is changed from increasing (in the absence of the second slip) to decreasing (in the presence of the second slip), which confirms the importance of the second slip in modeling the boundary layer flow of nanofluids. In addition, five kinds of nanofluids have been investigated for the velocity profiles and it is found that the Ag-water nanofluid is the lowest. For only the heterogeneous reaction, the concentration equation has been exactly solved, while the numerical solution is applied in the general case. Accordingly, a reduction in the concentration occurs with the strengthening of the heterogenous reaction and also with the increase in the Schmidt parameter. Moreover, the Ag-water nanofluid is of lower concentration than the Cu-water nanofluid. This is also true for the general case, when both of the homogenous and heterogenous reactions take place.

Inflow performance relationship of vertical wells in fractured vuggy media during semi-steady state flow regime

The inflow performance relationship (IPR) is one of the essential key parameters that control the fluids production/injection rate from wells. The presence of the vugs in addition to fractures in carbonate reservoirs introduce many difficulties related the estimation of IPR of future wells. In this study, a novel analytical IPR of dual-permeability, triple porosity model is derived for the first time. The introduced IPR formula is derived for the standard scenario model of a vertical and fully penetrating well in a circular reservoir under single-phase flow of slightly compressible fluid. The three governing flow equations (matrix flow equation, fracture flow equation and interaction between vugs and other two continuum equation) are solved simultaneously as a system of differential equations for semi-steady state (SSS) flow regime. The generated SSS IPR is the same as Darcy's straight line IPR multiplied by an error parameter (E23) which is bounded between zero and one. A detailed investigation of the effect of the reservoir petro-physical parameters like storativities, inter-porosities and fracture to matrix permeability ratio are presented. The newly presented IPR of dual-permeability, triple porosity system can be reduced to sub-models IPRs by further modification of error parameter to fit sub-model as single permeability, triple porosity (E13) or dual permeability, dual porosity (E22). The presented IPR formula has the advantage of dividing the pressure drop of the fluid flow to two components, one for the internal resistance between different continuums (which is resented by E) and the other one is the radial flow in the same continuum toward/from well-bore. The generated IPR model is double verified using both cell pressure centred finite volume numerical simulation and conventional pressure transient analysis.

Chemically reactive species of time-dependent natural convection couple stress fluid flow past an isothermal vertical flat plate

The transient two-dimensional natural convective couple stress fluid flow past a semi-infinite vertical flat plate in the presence of first-order homogenous chemical reaction is investigated. The analysis has been carried out by considering the effects of skin-friction coefficient and Nusselt and Sherwood numbers. The unsteady coupled nonlinear governing flow equations have been solved by applying the Crank–Nicolson implicit finite difference scheme. For the different set physical parameters, graphs are shown and examined. A relevant study with existing results is made in a limiting sense. The transient and steady-state velocity profiles decrease as the chemical reaction parameter, Schmidt number, and couple stress parameter increase. The deviations of concentration, temperature, and velocity contours of the couple stress fluid flow are considerably varied in comparison with the Newtonian fluid flow.