Governing Flow Problem Research Articles

Computational study of the aligned magnetic field in a plume generated by the energy line source

This present research concerns with the study of two-dimensional, steady, magnetohydrodynamic free convection flow in a plume generated due to horizontal line heat source. The aligned magnetic field is applied at the vertical component of plume. The mathematical model of the governing flow problem is based on coupled nonlinear partial differential equations. Later, the system of partial differential equations is transformed into system of ordinary differential equations by using appropriate form of stream function formulation. For computational results, a Shooting technique along with bvp4c algorithm for MATLAB is employed to estimate the missing conditions in flow model. The effects of variation in Prandtl number., magnetic force parameter S , and magnetic Prandtl number γ on the velocity, current density, and temperature profile are illustrated in graphical manner along with their physical impacts. The novelty of current work is that the magnetic field has its strong impact on the vertical component of plume generated due to heat source. It is observed that, with the increase in the parameter S , the missing conditions, the velocity, current density, and temperature decreased. Whereas, the specified conditions, the skin friction f ″ and magnetic flux ϕ ′ drop while heat transfer rate θ ′ enhanced with increment in parameter S .

Mixed convection of two layers with radiative electro-magnetohydrodynamics nanofluid flow in vertical enclosure

Mixed convection flow of two layers nanofluid in a vertical enclosure is studied. The channel consists of two regions. Region I is electrically conducting while Region II is electrically non-conducting. Region I is filled with base fluid water with copper oxides nanoparticles and Region II is filled with base fluid kerosene oil with iron oxides. The simultaneous effects of electro-magnetohydrodynamics and Grashof number are also taken into account. The governing flow problem consists of nonlinear coupled differential equations which is tackled using analytical technique. Analytical results have been obtained by the homotopy analysis method (HAM). The results for the leading parameters, such as the Hartmann numbers, Grashof numbers, ratio of viscosities, width ratio, volume fraction of nanoparticles, and the ratio of thermal conductivities for three different electric field scenarios under heat generation/absorption were examined. It is found that the effect of the negative electric load parameter assists the flow while the effect of the positive electric load parameter opposes the flow as compared to the case when the electric load parameter is zero. All outcomes for significant parameters on velocity and temperature are discussed graphically.

Investigation of dissipative heat transfer and peristaltic pumping on MHD Casson fluid flow in an inclined channel filled with porous medium

A theoretical investigation is performed for free convective peristaltic pumping of a Casson fluid through an inclined porous wavy channel. The flow is subjected to uniform magnetic field in the transverse direction. In addition, the energy equation contains porous and viscous dissipation effects. The governing flow problem is modeled for Casson fluid with the help of conservation laws of mass, momentum, and energy under the long wavelength assumption. Using a regular perturbation method, we obtained the analytical expressions for the axial velocity, temperature, pressure rise per one wavelength, and heat transfer rate. The consequences of various effects on the flow quantities are demonstrated in the form of graphical representations and discussed in detail. The findings reveal that the rise in the thermal Grashof number and permeability parameter leads to an increment in the velocity and thermal fields. The heat transfer rate strengthened when the Casson parameter and magnetic parameter were increased. The pressure rise exhibits an enhancing trend for the Brinkmann number and permeability parameter. Further, we observed a decreasing behavior on streamlines for increasing magnetic field strength. Moreover, the obtained findings are applicable to a variety of fields in the bioengineering and medical sciences, such as targeted drug delivery, heart-lung machines, MRI, cancer therapy, power conversion devices, and micromanufacturing processes.

Thermal transport through carbon nanotubes based nanofluid flow over a rotating cylinder with statistical analysis for heat transfer rate

This study investigates the impact of magnetohydrodynamic effects and thermal radiation on axisymmetric flow with carbon nanotubes over a rotating cylinder. The thermal energy behavior of the nanofluid is analyzed using the Xue model, with water as the base fluid and two different types of nanoparticles: single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). The governing flow problem is transformed through appropriate transformations, resulting in a system of ordinary differential equations. Numerical solutions are obtained using the bvp4c function in MATLAB. The results indicate that the thermal transport coefficient increases with the radiation number in both SWCNTs and MWCNTs cases. Further, the presence of nanoparticles in the nanofluid leads to an increase in the thermal transport coefficient due to the volume fraction of the nanoparticles. Moreover, the study reveals that water-based MWCNTs exhibit a higher heat transfer rate than water-based SWCNTs. These findings contribute to understanding thermal energy characteristics in nanofluids and have implications for applications such as heat exchangers, electronic cooling systems, and the thermal management of advanced materials.

Thermal stratification effect on gravity driven transport of hybrid CNTs down a stretched surface through porous medium

The purpose of the current article is to explore the impact of thermal stratification and medium porosity on gravity-coerced transport of hybrid carbon nanotubes down an upright extending sheet inspired by a constant applied magnetic field along with heat transfer investigation in existence of thermal radiation, viscous dispersal, and joule heating effect. Rectangular coordinates are chosen for the mathematical interpretation of the governing flow problem. Homothetic analysis is employed for the sake of simplification process. The reduced system of coupled nonlinear differential equations is dealt numerically by dint of computational software MATLAB inbuilt routine function Bvp4c. The numerical investigation is carried out for the distinct scenarios namely, (i) Presence of favorable buoyancy force, (ii) Case of purely forced convection and (iii) Presence of opposing buoyancy force. Significant Findings: The key findings include that the presence of hybrid carbon nanotubes and medium porosity contributes significantly to upsurging surface shear stress magnitude whereas, external magnetic field and velocity slip effects in an altered manner. The present study may be a benchmark in study of fueling process in space vehicles and space technology.

Mathematical Analysis of Peristaltic Pumps for Fene-P model subject to Hall and Joule impact

A mathematical model is developed to discuss the impact of the Hall current and the Joule heating on the peristaltic flux of finitely extensible nonlinear elastic Peterlin (FENE-P) fluid in a tapered tube with mild stenosis. The fluid movement along the wall surface resulted from the sinusoidal wave flowing with constant speed. Conditions of velocity and thermal slip are applied. Lubrication approximation is adopted to modify the governing flow problem. To discover the solution to a system of equations, the regular perturbation approach is used. The effects of the different physical parameters are debated and graphically shown in a set of figures. It is discovered that as the Hall current parameter is increased and the Hartman number is decreased, the fluid velocity increases. It is also worth noting that the Dufour number causes the fluid temperature to rise, whilst the Hall current parameter causes the temperature to fall. In the meantime, both the Hall current parameter and the Soret number have the opposite effect on concentration. The trapping phenomenon is thoroughly investigated.

Slanting transport of hybrid (MWCNTs-SWCNTs/H2O) nanofluid upon a Riga plate with temperature dependent viscosity and thermal jump condition

The present exploration communicates the oblique transport of hybrid nanofluid containing MWCNTs (Multi Walled Carbon Nanotubes) and SWCNTs (Single Walled Carbon Nanotubes) over a moving/ stationary Riga plate in presence of temperature dependent viscosity and thermal jump condition at the surface. Comparison of heat transfer characteristics of traditional nanofluid emerging hybrid nanofluid, containing carbon nanotubes upon a stationary or moving surface is made. Modified Brinkman's viscosity model is used to study viscosity variation in flow regime. Oblique flow of Hybrid CNTs based fluid with variable viscosity and thermal jump condition has never been investigated in the past. The governing flow problem is converted into ODEs using similarity variables which are subsequently solved numerically using Runge-Kutta Fehlberg integration through computational software Maple. The investigation deals with some key parameters such as viscosity variation parameter, thermal slip parameter, modified magnetic parameter, width parameter and stretching ratio parameter through graphical representations of velocity, temperature and concentration of fluid. It is perceived that rate of heat transfer declines with viscosity variation parameter but it is higher in magnitude for the case of moving Riga plate as compared with stationary Riga plate. Normal skin friction declines while tangential skin friction rises with variable viscosity parameter.

Bio-convective couple stress nanofluid behavior analysis with temperature-dependent viscosity and higher order slip encountered by a moving surface

In nanotechnology, the nanofluids are decomposition of base materials and nanoparticles where the nanoparticles are immersed in base liquid. The utilization of such nanoparticles into base liquids can significantly enhance the thermal features of resulting materials which involve applications in various industrial and technological processes. While studying the rheological features of non-Newtonian fluids, the constant viscosity assumptions are followed in many investigations. However, by considering the viscosity as a temperature-dependent is quite useful to improve the heating processes along with nanoparticles. Keeping such motivations in mind, this investigation reports the temperature-dependent viscosity and variable heat-dependent conductivity in bioconvection flow of couple stress nanoparticles encountered by a moving surface. The famous Reynolds exponential viscosity model is used to deploy the relations for temperature-dependent viscosity. Moreover, the activation energy and higher order slip (Wu’s slip) are also elaborated to make this investigation more novel and unique. The emerging flow equations for governing flow problem are formulated which are altered into non-dimensional forms. The numerical simulations with applications of Runge–Kutta fourth–order algorithm are focused to obtain the desired solution. Before analyzing the significant physical features of various parameters, the confirmation of solution is done by comparing the results with already reported investigations as limiting cases. The results are graphically elaborated with relevant physical consequences. Various plots for velocity, temperature, concentration, wall shear stress, local Nusselt number, local Sherwood number and motile density numbers are prepared.

Mathematical Modeling and MHD Flow of Micropolar Fluid Toward an Exponential Curved Surface: Heat Analysis via Ohmic Heating and Heat Source/Sink

The main goal of the current article analyzed the influence of MHD flow of micropolar fluid via exponentially curved stretching surface. Heat transfer analysis is discussed with the impact of thermal radiation and Joule heating. For mathematical model curvilinear (u, v, r and s) is taken for governing flow problem. Viscous dissipation is also considered. Exponential similarity variables are used to transform partial differential equations to ordinary differential system. (ODEs). Numerical techniques have been used to solve the nonlinear ODEs. Effect of various physical variables like material parameter $$(K_{1} = 0.1, 0.2, 0.3, 0.4, 0.5)$$ , radius of curvature ( $$\delta = 1,2,3,4,5$$ ), magnetic parameter ( $$M = 0,0.1, 0.2, 0.3, 0.4$$ ), radiative parameter ( $$R_{d} = 1.0,2.0,3.0,4.0,5.0$$ ), heat generation parameter (Q = 0, 0.1, 0.2, 0.3, 0.4), surface friction, couple stress and surface temperature on the flow of velocity, temperature field and microrotation velocity has been examined through graphs. A good agreement of the present work has been noticed with a previous published result.

Nonlinear nanofluid fluid flow under the consequences of Lorentz forces and Arrhenius kinetics through a permeable surface: A robust spectral approach

BackgroundEmerging applications in nanomaterials processing are increasingly featuring multiple physical phenomena including magnetic body forces, chemical reactions and high temperature behavior. Stimulated by developing a deeper insight of nanoscale fluid dynamics in such manufacturing systems, in the current article, we study the magnetic nanofluid dynamics along a nonlinear porous stretching sheet with Arrhenius chemical kinetics and wall transpiration. Appropriate similarity transformations are employed to simplify the governing flow problem. MethodsThe emerging momentum, thermal energy and nanoparticle concentration ordinary differential conservation equations are solved numerically with a hybrid technique combining Successive Linearization and Chebyshev Spectral Collocation. A parametric study of the impacts of magnetic parameter, porous media parameter, Brownian motion parameter, parameters for thermophoresis, radiation, Arrhenius function, suction/injection (transpiration) and nonlinear stretching in addition to Schmidt number on velocity, temperature and nanoparticle (concentration) distribution is conducted. A detail numerical comparison is presented with different numerical and analytical techniques as a specific case of the current investigation. FindingsIncreasing chemical reaction constant parameter significantly decreases nanoparticle concentration magnitudes and results in a thickening of the nanoparticle concentration boundary layer. Enhancing the values of activation energy parameter significantly increases the nanoparticle concentration magnitudes. Increasing thermophoresis parameter elevates both temperature and nanoparticle concentration. Increasing radiation parameter increases temperature and thermal boundary layer thickness. Enlarging Brownian motion parameter (smaller nanoparticles) and Schmidt number both depress the nanoparticle concentration.

An Exploratory Approach to Study Electro-Osmotic of Non-Newtonian Bio-Bi-Phase Flow Due to Peristaltic Transport of Particulate Fluid

The present article aims to probe the impacts of electro-magneto-hydrodynamics (EMHD) peristaltic flow of in-compressible, dusty, non-Newtonian fluid in a hose of predetermined dimension together with homogeneously scattered analogous rigid particles. In the presence of transversal static magnetic field, Navier-Stokes’s equations are employed to design a flow problem for the particulate phase. Governing flow problem is simplified by approximation of long wavelength and zero Reynolds number. The analytical solution for both velocities (solid-liquid) and pressure rise is computed by using well known computational software Mathematica. Perturbation method is employed to extract analytical solution of the resulting ordinary differential equations. Impacts of different physical parameters, expansion in trapped bolus for fluid and particulate velocity profile by increasing Hartmann number are displayed and explained through graphs. Furthermore, a rise in skin friction is noticed with the rise in particle effect and electro-osmotic parameter. This study may have greater significance and viable applications to improve the quality of micro-fluidic devices.

Numerical simulation of fractional Maxwell fluid flow through Forchheimer medium

In this article we have studied the unsteady oscillatory flow of incompressible fluid with heat transfer in a horizontal channel. Maxwell fluid is flowing through a space filled by Forchheimer medium. The Caputo time derivative has been used in the formulation of governing flow problem. A numerical solution has been obtained using Finite Element Method for space variables and Finite Difference Method for fractional time derivatives. A small increase in α gives increase in velocity gradient and also thickness of the momentum boundary layer increases with the increase of α values. For α = 1 velocity boundary layer has a maximum peak. It means fractional parameter controls momentum boundary layer. A smooth profile of temperature gradient decreases with rise of temperature distribution and thickness of the thermal boundary layer rises when increase β values. It observe that β play an important rule in thermal boundary layer. The effects of pertinent physical parameters like Forchheimer parameter, Grashof number and Reynolds number on velocity and temperature distribution are considered and demonstrated through graphs.

Temperature-Dependent Viscosity Effect on the Peristaltic Transport of (MHD) Blood Flow Ree-Eyring Fluid Through Porous Medium inAn Asymmetric Channel

In this article the peristaltic transport of blood flow Ree-Eyring electrically conducting fluid in a porous medium under the effect of magnetohydrodynamic and temperature dependent viscosity through asymmetric channel is examined. Governing flow problem based on momentum, and energy equations are mathematically modelled and investigated in a wave frame of reference moving with the velocity of the wave, by considering the assumption of long wavelength approximation compared to small Renold’s number they simplified and reduced into couple partial differential equations. Exact solution for the temperature profile has been obtained whereas perturbation method employed to find the approximate solution for the stream function. The impact of important physical pertinent parameters on flow phenomena are discussed graphically. The graphs depict that the dimensionless viscosity parameter has mixed effect on velocity profile moreover the two Ree-Eyring fluid parameters and has opposite influence on velocity profile.

Electro-osmotic flow of hydromagnetic dusty viscoelastic fluids in a microchannel propagated by peristalsis

A theoretical study is carried out to determine the electric and magnetohydrodynamics of a dusty Jeffrey fluid containing small particles propagating through a wavy asymmetric microchannel. A static transverse magnetic field is applied in the presence of an electric field. Slip effects are considered to examine the flow behavior. The dusty Jeffrey model is taken into account to review its response. The governing flow problem is modelled with the help of ionic Nernst Planck equation, Poisson–Boltzmann equation, and Debye length approximation. It is then transformed into a steady wave frame with the help of coordinate transformation. Using the lubrication approach (“long wavelength and zero's Reynolds number”) the normalized governing equations of fluid and particle-phase that corresponds to the second order coupled partial differential equations represents the contribution of Jeffrey fluid model. The linearized boundary value problem is solved analytically, and exact solutions are presented for axial velocity distribution, wall shear stress and pressure gradient. It is reported from the obtained results that the magnitude of the particle-phase is more as compared to fluid-phase for velocity field and shear stress however it is less for pressure gradient. The findings of the present model are applicable in designing the microfluidics devices for the use of various transport phenomena in micro level where particles as well as fluids are transported together. The present study can be further extended and applicable for three-dimensional profile with appropriate assumptions and modifications.

Significance of bioconvection in chemical reactive flow of magnetized Carreau–Yasuda nanofluid with thermal radiation and second-order slip

Several non-Newtonian fluids are of practical interest, and it is fascinating to examine the rheology of such fluids with various flow features. In this study, the flow of Carreau–Yasuda nanofluid has been analyzed in the presence of gyrotactic microorganisms. The impressive features of nanofluid are displayed by abiding the thermophoresis and Brownian motion aspects. The second-order velocity slip effects are decomposed in the mathematical simulations. Further, the governing flow problem governed the impact of thermal radiation, chemical reaction and convective Nield boundary conditions. Although some attempts are available in the literature which examines the rheological features of Carreau–Yasuda nanofluid, whereas the analysis for bioconvection of flow of this non-Newtonian fluid model in the presence of second-order slip features is not proposed yet. Further, it has been noticed that many investigators used first-order or partial slip effects associated with their flow problems. The flow problem becomes more realistic due to the interaction of second-order slip constrains and subsequently develops a more stable boundary layer. The governing equations for the formulated flow problem are partial differential equations. Standard dimensionless quantities are recommended to alter the flow equations in dimensionless forms. The solution of the locally similar problem has been computed numerically via shooting technique. All the computations are performed by using bvp4c with the help of MATLAB software. Following the iterative procedure, the solution is accurate up to convincing accuracy of $$ 10^{ - 4} . $$ The step size for the present simulation is taken as $$ \Delta \eta = 1 \times 10^{ - 4} . $$ The results are also verified by comparing with already reported numerical computation and found a convincible accuracy. The implication of each parameter is executed for velocity, temperature, concentration and microorganisms’ distributions. Moreover, the substantial quantities, namely skin friction coefficient, motile density number, local Nusselt number, and local Sherwood number numerically evaluated and are overviewed for various parameters. The study reveals that velocity distribution decays with the presence of first-order slip parameter and Rayleigh number, while an enhanced velocity profile has been noted for variation of Weissenberg number. An improved nanoparticle temperature and concentration distributions have been found with the utilization of the second-order slip factor and combine parameter. It is further observed that the density of motile microorganisms declined with Peclet number and bioconvection Lewis number. In recent days, a growing interest has been developed from scientists toward the significance of nanoparticles because of their diverse engineering, industrial and commercial applications. The proposed observations can be useful in extrusion systems applications, biomolecules, biomimetic systems, energy production improvement and enhancement of manufacturing processes.

Entropy generation on MHD peristaltic flow of Cu‐water nanofluid with slip conditions

AbstractThe current research explores entropy generation and effect of magnetic field on peristaltic flow of copper‐water nanofluid in an asymmetric configuration saturated with porous medium. Slip conditions are invoked for velocity and temperature. Governing flow problem is constructed under the long wave length assumption. Analytical result for the problem is computed by exploiting homotopy analysis methodology. The influences of involved physical parameters are investigated through plots.

Heat transfer enhancement in hydromagnetic alumina–copper/water hybrid nanofluid flow over a stretching cylinder

In the current study, heat transfer performances and flow characteristics of alumina–copper/water (Al2O3–Cu/H2O) hybrid nanofluid over a stretching cylinder are explored under the influence of Lorentz magnetic forces and thermal radiation. The Roseland’s flux model is employed for the impact of thermal radiations. The governing flow problem comprises of nonlinear ordinary differential equations, which are transformed into nondimensional form via suitable similarity transforms, Boussinesq and boundary layer approximations. Results of heat and fluid flow as well as convective heat transfer coefficient and skin friction coefficient under influence of embedding parameters are displayed and discussed through tables and graphs. To check its heat transfer performance, a comparison of hybrid nanofluid with base fluid and single material nanofluids is also made and found that hybrid nanofluids are more effective in heat transfer than conventional fluids or single nanoparticles-based nanofluids.

New Insight into AuNP Applications in Tumour Treatment and Cosmetics through Wavy Annuli at the Nanoscale

The purpose of this study is to probe the peristaltic propulsion of a non-Newtonian fluid model with suspended gold nanoparticles. The base fluid is considered to simulate blood using the Carreau fluid model. We model a small annulus as a tube with a peristaltic wave containing a clot propagating towards the tube wall. An external variable magnetic field is also considered in the governing flow. An approximation for long wavelengths and small Reynolds numbers is employed to formulate the governing flow problem. The resulting nonlinear equations are solved using a perturbation scheme. Series solutions are obtained for the velocity profile, temperature profile, pressure rise and streamlines. The results indicate an enhancement in the temperature profile that can be utilized in eradicating tumour cells.

Heat transfer analysis in magnetohydrodynamic flow of solid particles in non-Newtonian Ree-Eyring fluid due to peristaltic wave in a channel

In this article, the influence of heat transfer on solid particle motion in MHD Ree-Eyring fluid due to peristaltic wave has been investigated. The governing flow problem is modelled for fluid phase and particle phase with the help of continuity, momentum, and energy equations under the assumption of long wave-length and creeping flow regime. The obtained coupled ODE have been solved analytically and exact solutions have been presented. The influence of all the physical parameters are discussed for Newtonian and non-Newtonian fluid with the help of graphs. In the present analysis, it is observed that due to influence of Hartmann number, the magnitude of the velocity diminishes.

Application of modified Fourier law in von Kármán swirling flow of Maxwell fluid with chemically reactive species

We develop a mathematical model for non-Newtonian Maxwell fluid over a rotating disk by extending the idea of classical von Karman swirling flow. The impact of modified Fourier’s law of heat conduction in flow of Maxwell fluid swirling due to a rotating disk subject to the magnetic field is considered in this study. Additionally, the influence of temperature-dependent thermal conductivity along with the application of first-order chemical reaction is utilized in heat and mass transfer phenomena. The disturbance of fluid in this problem is due to the uniform rotation and radial stretching of the disk. The nonlinear governing flow problem is considered for analysis with a numerical technique, namely Runge–Kutta–Fehlberg (RKF45) method, while using Maple software. The effects of governing physical parameters are demonstrated through graphs. All results related to this illustration are displayed in the form of the velocity, temperature and concentration profiles. The solutions predict that the influence of Lorentz force is to reduce the velocity components and enhance the fluid temperature. A significant decline in fluid temperature is observed for high values of thermal relaxation parameter. It is further noticed that the concentration field trend decelerates with Schmidt number and chemical reaction parameters.