Soret Number Sr Research Articles

Effect of heat production on MHD natural convection transport of nanofluid flow via a vertical uniform perforated plate: An unsteady analysis

This article statistically investigates the impact of heat production on the unstable MHD natural convection transport of nanofluid flow via a perforated sheet. The ordinary differential equations (ODEs) are derived from the partial differential equations (PDEs) by using of the similarity transformation. The dimensionless ordinary differential equations (ODEs) may be numerically resolved with the help of the MATLAB ODE45 tool and the finite difference method (FDM) along with the shooting strategy. Four innovative water-based nanofluids such as TiO2, Cu, Al2O3, and Ag are considered nanoparticles. The numerical results have been explained for the role of numerous non-dimensional numbers or parameters such as heat generation or absorption (Q), nanoparticle volume fraction (φ), Dufour number (Df), Prandtl number (Pr), magnetic force parameter (M), Soret number (Sr), and Schmidt number (Sc) on the fluid flow, and heat and mass transfer rates. The fluid temperature drops but velocity is enhanced for higher amounts of Q. Copper nanoparticle volume fraction up to 4 % shows a rise in temperature, concentration, and velocity curves. Heat transfer rate ( − θ′(0)) diminishes by about 124 %, while the values of f′(0) promote by approximately 26 % owing to an increase in the values of Q (heat generation) from 1.0 to 2.0. The value of ( − θ′(0)) increases by 49 %, but f′0 decreases by 15 % due to a rise in Q (heat absorption) from -3.0 to -10.0. The local skin friction coefficient (f′(0)) diminishes by about 65.21 % due to an increase in the values of the magnetic force parameter (M) from 0.5 to 3.5 whereas the rate of heat and mass transfer remain unchanged. As φ increased from 0.01 to 0.04, the local skin friction coefficient (f′(0)) exhibited a 36 % increase, while the heat transport rate (θ′(0)) decreased around by 10 %. In conclusion, a comparison was made between our findings and those of the published research. The comparison indicates a high degree of consistency.

Optimizing heat transfer with electro-osmotic ciliated propulsion in a non-uniform canals with Cu-blood characteristics considering thermal casson nano fluid

Electroosmosis peristaltic flows find promising applications in electro-fluid thrusters in space propulsion, polymer injection systems, ion exchange membrane designs, microbe fuel cells, biochip fabrication and fossil fuel energy process. In light of this, the current work aims to investigate blood based electroosmotic peristaltic flow in a ciliated, non-uniform propagation channel when copper nanoparticles are present. For that purpose, mathematical modeling is done in two dimensional frame and then governing partial differential equations are simplified and converted in ordinary differential equations using dimensionless quantities and long wave length and low Reynolds number approximations. In result we got coupled nonlinear boundary value problem that is solved numerically using three-stage Lobatto IIIa formula known as bvp4c invoking shooting technique. Peristaltic ciliated waves are thought to pass along the channel wall. The properties of both fluid phase and particle phase flow are modeled and investigated. Plotting against various parameters, streamline contours, temperature contours, concentration and temperature profiles, and pressure rise graphs are examined in-depth from a physical perspective. The obtained results revealed that concentration profile α upsurges for rising values of Casson fluid parameter β, nanoparticle volume fraction ϕ and flow rate Q while it drops with an increase in particulate volumetric fraction C, Eckert number Ec, Soret number Sr, Schmidt number Sc and viscosity constant. A decrease in temperature is also caused by an increase in the volumetric percentage of nanoparticles. In the pumping portion, there is a decrease in pressure rise; however, this decrease changes to an increase in the increased pumping zone.

Employing ISPH simulations and artificial intelligence for enhanced heat and mass transfer in a core reactor with nano-enhanced phase change materials

This research investigates the heat and mass transfer characteristics of nano-enhanced phase change material (NEPCM) within a core reactor, employing both the incompressible smoothed particle hydrodynamics (ISPH) simulations and artificial intelligence (AI) analysis. NEPCM holds promise for enhancing thermal energy storage and transfer efficiency, with applications spanning various fields, including nuclear reactors. Through ISPH simulations, this study delves into the intricate fluid dynamics and phase change phenomena within the reactor, providing valuable insights into the thermal behavior of NEPCM. Eight embedded rods are initially settled inside a reactor with high temperature and concentration on four rods and the others are maintained at low temperature and concentration. The effects of various parameters including the Cattaneo–Christov heat parameter ( δ Heat ) , Cattaneo–Christov mass parameter ( δ Mass ) , Dufour number ( Du ) , Hartmann number ( Ha ) , Soret number ( Sr ) , and thermal radiation ( Rd ) are conducted in this work. δ Heat and δ Mass play critical roles in evaluating heat and mass transfer efficiencies. Raising the Dufour number improves temperature distribution while having a minimal impact on concentration. Additionally, increasing the Dufour number from 0 to 1.5 leads to a 30% increase in the velocity field. Elevating the Soret number significantly enhances velocity and concentration, while increasing the thermal radiation parameter improves temperature distribution. These findings are pertinent across multiple domains like combustion, chemical engineering, and geophysics, aiding in process optimization and system design. The ANN model exhibits high precision in predicting Nusselt and Sherwood numbers, highlighting its effectiveness in forecasting.

Influence of thermal radiation and shape factor on a hybrid nanofluid flow over a permeable flat plate with cross-diffusion effects: An irreversibility analysis

Understanding and controlling the shape factors of nanoparticles in fluid flow problems is crucial for optimizing heat transfer, fluid dynamics, and various applications such as nanofluids, drug delivery systems, catalysis, and nanocomposites. By tailoring the shape of nanoparticles, researchers can manipulate their behavior, dispersion, and interaction with the fluid, thereby optimizing the desired outcomes in various fluid flow problems. The meticulous investigation uncovers the integration of entropy analysis in the investigation of the flow of convective magnetohydrodynamic hybrid nanofluid via a permeable flat surface, by considering the effects of Dufour, viscous dissipation, Soret, and thermal radiation. The governing equations are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved using the bvp4c solver, a MATLAB in-built function. We display the outcomes for three different shape factors: platelet, cylinder, and brick. The skin friction coefficient increases at a rate of 1.5089 for the brick shape, 1.5163 for the cylindrical shape, and 1.5212 for the platelet shape when the mixed convection parameter lies between 1 and 5. In this regard, it is important to point out that there is a direct connection between the increase in temperature transmission rate and a decline in the Dufour number ( Du ). It has been found that when 1 ≤ Du ≤ 2.4 , the Nusselt number decreases by 0.4786, 0.4618, and 0.4512 for brick, cylinder, and platelet shapes, respectively. A decline in the Sherwood number is noticed with an upsurge in the Soret number ( Sr ). There is a noticeable increase of 0.0442 in the Sherwood number for brick shape, 0.0438 for cylinder form, and 0.0435 for platelet form when 1 ≤ Du ≤ 2.4 . Furthermore, we have detected that an increase in the radiation parameter amplifies both the Bejan number and the profiles of entropy formation.

MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: Electromagnetic therapy simulation

The ureter typically experiences a frequency of one to five peristaltic contractions per minute. However, it is important to note that these contractions can be disrupted by various physical and mechanical irritants. Ionic contents in the urine make it electrically conducting and responsive to electromagnetic body forces. MHD can be deployed in bio magnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system. This article therefore focuses on the hydromagnetic effects on flow patterns of urine with debris (monoliths). The mechanism of urine flow is largely coordinated by the kidneys. The flow inside the ureter is interrupted by microliths, which are generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted, comprising the electromagnetic urological viscous fluid phase and the particulate phase for solid grains. The peristaltic propulsion of two-phase liquid in the ureter is simulated as a sinusoidal wave propagation of incompressible non-Newtonian fluid. The Williamson viscoelastic model is deployed for the rheology. Heat transfer is also included with Soret thermo-diffusion and viscous heating effects. Long wave and low Reynolds number approximations are employed based on lubrication theory. The mass, momentum, energy and concentration conservation equations with associated boundary conditions are rendered non-dimensional via appropriate scaling transformations. A numerical solution is achieved via BVP4C MATLAB quadrature. Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter ( ζ ), Hartmann number (M), Prandtl number (Pr), Weissenburg number (We), particle volume fraction (C), Eckert number (Ec), Soret number (Sr), Schmidt number (Sc). The novelty of the present work is therefore the simultaneous consideration of a generalized two-phase model, wall slip, non-Newtonian characteristics, cross diffusion, viscous dissipation, mass diffusion, magnetic body force and curvature effects in peristaltic urological transport, which has not been undertaken previously. The detailed simulations reveal that the flow velocity is reduced due to the presence of solid particles and the channel curvature, in comparison to the flow in an unobstructed channel devoid of solid particles. Enhancing the hydrodynamic slip parameter speeds up the movement of particles and fluid near the channel walls, boosts wall skin friction, raises pressure difference in the pumping area, and amplifies bolus magnitudes.The rise in peristaltic pumping results in a reduction in solid particle concentration, which is significant phenomena.This theoretical approach may aid in treating conditions such as Urinary Tract Infections (UTIs). The computations effectively demonstrate that significant manipulation of urological pumping characteristics can be achieved with an electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted as relevant to magnetic therapy techniques, which may be beneficial to clinicians.

Electrohydrodynamic peristaltic microfluidic flow with thermal and molecular analysis featuring sloped configurations

This study examines the simultaneous impacts of thermal and molecular transfer of non-Newtonian fluid propelled by the collective impact of electroosmosis and peristaltic pumping via inclined channel. Internal frictional heating and heat generation are also taken into consideration. The electrohydrodynamic phenomenon is described by the nonlinear Poisson–Boltzmann equation. The problem is modulated mathematically through a system of coupled non-linear differential equations in wave frame of reference. Using the regular perturbation method around a small wave number δ, we obtain sequential solutions for stream function ψ, electric potential ϕ, velocity u, pressure gradient dpdx, temperature θ and concentration Ω distributions. The influences of newly arising parameters such as the electroosmotic parameter me, relaxation time parameter λ1, retardation time parameter λ2, wave number δ, Reynold’s number Re, heat generation parameter β, Prandtl number Pr, Schmidt number Sc, Froude number Fr and Soret number Sr on physical characteristics are analyzed graphically. There is an inverse correlation between the parameters of relaxation time and retardation time and their effects on axial velocity, concentration, and temperature distributions. In particular, the temperature of the fluid increases as the EDL parameter, relaxation time parameter, viscous dissipation parameter, and Reynolds number increase, but decreases as the retardation time parameter increases. Moreover, the axial pressure gradient increases as Reynolds number and inclination angle increase, while it decreases as Froude number increases. The current model has applicability in the chemical industry, reservoir engineering, micro-fabrication, and biomedical applications, where electroosmotic effects on heat and mass movement are crucial.

Heat and mass transfer analysis of nonmiscible couple stress fluid in a porous saturated channel

The present flow problem analyzes the impact of radiative heat and mass transfer with inclined magnetic field on thermal exchange and entropy production of two immiscible nature of electrically conducting couple stress fluid in a static porous saturated conduit. In this model, the lower and upper porous regions of the rectangular channel are occupied by two different types of couple stress fluids. The static horizontal parallel plates of the porous duct are completely isothermal and the flow of immiscible fluid through the porous duct develops because of a constant pressure gradient at the entry zone of the duct. The Brinkman model is utilized in the modeling of fluid flow through porous saturated domain and Rosseland’s approximation is utilized to compute the radiative thermal exchange effect on nonmiscible couple stress fluid. In this work, authors have analyzed the effect of various thermo-physical parameters such as the Hartmann number (Ha), permeability parameter (Da), Schmidt number (Sc), Soret number (Sr) and couple stress parameter ([Formula: see text]) on the entropy generation characteristics, Bejan number distribution, thermal behavior, concentration distribution and flow characteristics of immiscible couple stress fluid which passes through the porous channel. The parameters Ha, Da, [Formula: see text], Sc, Sr correspond to magnetic field effect, permeability of porous media, couple stress, mass diffusion and thermal diffusion, respectively. The most significant findings of this research work are as follows: • In a porous saturated channel, the immiscible couple stress fluid velocity, entropy production number and thermal profile get enhanced on increasing the couple stress parameter. • On increasing the Hartmann number and decreasing the permeability of porous region, the thermal properties and entropy production number both decrease. • The couple stress fluid’s concentration field and Bejan number distribution get decreased on enhancing Soret number Sr and Schmidt number Sc. • The entropy generation near the wall of the channel rapidly increases on increasing the Schmidt number and Soret number. The emerging finding of this research work exhibits excellent agreement with previously published work. This research work can be utilized in food processing, petroleum products and chemical process.

MHD mixed convection flow for Maxwell Hybrid nanofluid with Soret, Dufour and Morphology effects

We have investigated the two-dimensional mixed convective Maxwell hybrid nanofluid boundary layer mass and heat flows over a linearly stretching porous surface with the applied external magnetic flux. Thermal radiations along with the Dufour and Soret effects are also incorporated. The governing model of partial differential equations (PDE) is altered into ordinary differential equations (ODE) with an appropriate similarity transformation. The finite difference-based numerical method BVP4c is applied to solve the system of nonlinear ODEs. The flow features and the heat transfer characteristics have been illustrated with graphical representations and a numerical table. For varied values of the flow-related variables, organized and graphical data for the Nusselt number and skin friction coefficient are indicated. In most cases, spherical-shaped nanoparticles have a better influence on stream function, velocity and temperature distributions. This behavior is the opposite of the mass concentration profile. It has been observed that stream function decreases as increase the value of the magnetic field but opposite for mass concentration distribution and temperature profile. The temperature gradient is enhanced as a result of stronger convective flow when Soret number Sr values increase, which causes the boundary layer thickness to grow. A comparative study of hybrid nanofluid and nanofluid showed that the hybrid nanofluid has superior shear stress/skin friction and Sherwood number/surface mass flux than nanofluid flow.

Effect of Soret on MHD rotating fluid flow through a porous medium with heat and mass transfer

PurposeThe purpose of this paper to analyze the effect of Soret with heat and mass transfer on an unsteady two-dimensional Magnetohydrodynamics flow through a porous medium under the influence of the uniform transverse magnetic field in a rotating parallel plate is considered.Design/methodology/approachA mathematical model was developed using the slip conditions under unsteady state situations. Analytical expressions for the velocity, temperature and concentration profiles, wall shear stress, rates of heat and mass transfer and volumetric flow rate were obtained and computationally discussed with respect to the non-dimensional parameters. Further, the velocity reduces with increasing Hartmann number M and increases with Grashof number Gr and permeability parameter K.FindingsIt is observed that temperature reduces with an increase in Prandtl number Pr and ω. It is noted that the thermal radiation increases with increase in Soret number Sr, Schmidt number Sc, Prandtl number pr and ω.Originality/valueConcentration decreases with an increase in radiation parameter R and chemical reaction parameter Kc.

Double-diffusive convection flow with Soret and Dufour effects in an irregular geometry in the presence of thermal radiation

In this study, the effect of radiation on double-diffusive natural convection is investigated by considering the phenomena of Soret and Dufour in complex geometry, for the first time. The multi-time relaxation lattice Boltzmann method has been adopted to calculate the momentum, energy, and species equations. The radiative transfer equation has been solved using the finite volume method. Complex boundaries have been simulated by the sharp interface-immersed boundary method. The influences of effective parameters including the optical thickness (τ = 1 to 100), Rayleigh number (Ra = 104 and 105), Planck number (Pl = 0.01 to 1), Buoyancy ratio (Br = − 5 to 5), Soret number (Sr = − 1 to 1), and Dufour number (Df = − 1 to 1) have been analyzed on the flow field, heat, and mass transfer in a square cavity with an internal circular cylinder. Moreover, temporal variations of velocity and phase space trajectory have been used to study the effects of radiation on unsteady flow behavior. Results indicate that, the increment in optical thickness significantly reduces radiation, while a sweep behavior occurs in mass and heat transfer. Increasing the Dufour (Soret) parameter depending on the value of the Soret (Dufour) parameter can increase or decrease the mass (heat) transfer.

Bioconvection Unsteady Magnetized Flow in a Horizontal Channel with Dufour and Soret Effects

In the current decade, bioconvection phenomenon has received a lot of attention in research because of its applications in the biological polymer synthesis, biosensors and biotechnology, pharmaceutical industry, microbial enhanced oil recovery, environmentally friendly applications, and continuous refinements in mathematical modeling. Therefore, this article is prepared to address the unsteady mixed bioconvection in electrically conducting fluid flow between two infinite parallel plates with magnetic field and first-order chemical reaction impacts. Furthermore, the heat and mass transfer study has taken Dufour and Soret effects into account. The nonlinear coupled systems representing the continuity, momentum, energy, mass diffusion, and microorganisms’ equations are renewed into an ordinary differential equation (ODE) by employing the similarity renovation. The renovated ODEs are interpreted by the Homotopy Analysis Method (HAM). Impacts of the different emerging parameters, namely, magnetic field parameter ( M ), heat generation parameter ( Q ), Dufour number ( D u ), Soret number ( S r ), Schmidt number ( S c ), chemical reaction parameter ( K 0 ), Prandtl number ( P r ), squeezing parameter ( β ), Peclet number ( P e ), and Lewis number ( L e ) on the dimensionless velocity, temperature, concentration, and microorganism profiles as well as the frictional drag, Nusselt number, Sherwood number, and microorganisms mass flux are presented. The main outcomes of this investigation are that the velocity profile rises as the squeezing parameter is increased, and clear enhancement is noticed in the temperature profile for augmented estimations of chemical reaction, heat generation/absorption, and Dufour parameters. There is a significant downward trend in the concentration profile and microorganism density for elevated values of Dufour and Soret parameters.

Impact of Hall Current, Dufour and Soret on transient MHD flow past an inclined porous plate: Finite element method

The aim of the current article is, to explore the impact of Hall Current, Dufour Du and Soret Sr on Transient MHD flow past an inclined porous plate. The basic nonlinear partial differential equations (PDEs) are converted to dimensionless nonlinear PDEs with similar transformations. Non-dimensional governing equations for present investigation are solved numerically by the Finite Element Method (FEM) with appropriate initial conditions. Impacts of the different emerging parameters namely, Hall current m , Dufour number Du, Soret number Sr, magnetic field parameter M, heat generation parameter Q, Schmidt number Sc, chemical reaction parameter Kr, Prandtl number Pr, Viscous dissipation Ec on the velocity, temperature and concentration are evaluated and discussed computationally with the help of graphical profiles. For engineering interest, we obtained skin friction, Nusselt number and discussed numerically. Finally, a comparison has been made with published results in the absence of some non-dimensional parameters for a particular case found in good agreement.

Effects of Soret and Dufour numbers on MHD thermosolutal convection of a nanofluid in a finned cavity including rotating circular cylinder and cross shapes

This study considers a more complex problem by introducing magnetohydrodynamic (MHD) thermosolutal convection of a nanofluid in a square cavity including dual rotation amongst an outer circular cylinder and an inner cross shape. The influences of the length of a cross shape LCros, a dimensionless time parameter τ, Hartmann number Ha, Soret number Sr, Dufour number Du, solid volume fraction ϕ, an inclination angle of a magnetic field γ, and Rayleigh number Ra on the heat/mass transfer and nanofluid movements within a cavity are examined. Three different thermal/solutal boundary conditions of an outer circular cylinder carrying (Tc & Cc) (case 1), (Th & Ch) (case 2), and adiabatic conditions (case 3) are conducted. The inner cross shape is kept at Th and Ch. The obtained numerical simulations revealed that the changes in the thermal/solutal boundary conditions have a good role in controlling the thermosolutal convection and nanofluid speed within a cavity. Increasing the length of a cross shape LCros enhances the nanofluid speed and intensity of temperature and concentration within a cavity in cases 1 and 3. Case 2 gives the highest values of mean Nusselt number Nu¯ and Sherwood number Sh¯. The Rayleigh number is performing well in enhancing the nanofluid movements and heat/mass transfer within a cavity.

MHD double diffusion of a nanofluid within a porous annulus using a time fractional derivative of the ISPH method

Using an inner complex blockage within a square cavity is spreading massively for the cooling process. This study adopts the time-fractional derivative of the incompressible smoothed particle hydrodynamics (ISPH) method for studying the magnetic field, diffusion-thermo, and thermo-diffusion impacts on the double diffusion of a nanofluid in a porous annulus between a square cavity and an astroid shape. The alterations of the pertinent parameters, fractional derivative order [Formula: see text] between 0.9 and 1, dimensionless time parameter [Formula: see text] between 0 and 0.6, the radius of an astroid [Formula: see text] between 0.1 and 0.45, solid volume fraction [Formula: see text] between 0 and 0.06, Hartman parameter Ha between 0 and 100, Darcy parameter Da between [Formula: see text] and [Formula: see text], and Soret number Sr between 0.1 and 2 supplemented by Dufour number Du between 0.6 and 0.03 on the velocity field, temperature, concentration, and mean of Nusselt and Sherwood numbers are discussed. The main findings of the ISPH numerical simulations showed that a decrease in a fractional derivative order [Formula: see text] delivers the sooner steady-state of the double diffusion which suppresses the performed calculations. The velocity field’s maximum powers by 19.23% as [Formula: see text] increases from 0.1 to 0.45 and it decreases by 16.67%, 28.89%, and 97.99% as [Formula: see text] powers from 0 to 0.06, Ha powers from 0 to 100, and Da decreases from 10[Formula: see text] to 10[Formula: see text], respectively. The outlines of [Formula: see text] and [Formula: see text] are increasing as [Formula: see text] and [Formula: see text] are increased. A growth in Sr supplemented by a reduction in Du is diminishing the distributed concentration and nanofluid velocity within an annulus.

MHD free convective dissipative flow past a porous plate in a porous medium in the presence of radiation and thermal diffusion effects

AbstractThe problem of a hydromagnetic convective flow of an electrically incompressible viscous conducting fluid past a uniformly moving vertical porous plate is investigated analytically, taking into consideration radiation and thermal diffusion effects. A constant suction velocity is applied to the plate. A uniformly strong magnetic field is supposed to be applied normally to the plate and directed into the fluid region. To find a solution to the problem, an asymptotic series expansion method is used. The effects of thermal diffusion, magnetic field, porosity parameter, thermal radiation, and Grashof number are mainly focused on the discussion of the current problem. Increasing Soret number (Sr) hikes the velocity profile and skin friction but declines Sherwood number. Also, it has been found that, when the magnetic parameter (M) increased, the fluid velocity and the concentration profile decreased. The current results show a good deal of agreement with previously published work. The findings of this study could be relevant in a variety of applications, including diffusion processes involving molecular diffusion of species with molar concentration.

On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer

The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient (f′(η)) enhances with the higher values of the Hall and shrinking parameters (m,ϱ), while it reduces with magnetic parameter and Weissenberg number (M,We). The y-component of fluid velocity (g(η)) rises with the augmenting values of m and M, while it drops with the augmenting viscous nature of the Carreau fluid associated with the varying Weissenberg number. The fluid temperature θ(η) enhances with the increasing values of radiation parameter (Rd) and Dufour number (Du), while it drops with the rising Prandtl number (Pr). The concentration field (ϕ(η)) augments with the rising Soret number (Sr) while drops with the augmenting Schmidt number (Sc). The variation of the skin friction coefficients (Cfx and Cfz), Nusselt number (Nux) and Sherwood number (Shx) with changing values of these governing parameters are described through different tables. The present and previous published results agreement validates the applied analytical procedure.

MHD Mixed Convection Nanofluid Flow over Convectively Heated Nonlinear due to an Extending Surface with Soret Effect

The aim of this paper is to investigate the flow of MHD mixed convection nanofluid flow under nonlinear heated due to an extending surface. The transfer of heat in nanofluid subject to a magnetic field and boundary conditions of convective is studied to obtain the physical meaning of the convection phenomenon. The governing partial differential equations (PDEs) of the boundary layer are reduced to ordinary differential equations (ODEs) considering a technique of the transformation of similarity. The transformed equations are solved numerically considering the technique of an efficient numerical shooting applying the Runge–Kutta technique scheme from the fourth‐fifth order. The results corresponding to the dimensionless speed, temperature, concentration profiles, and the Nusselt number reduced, and the Sherwood numbers are presented by figures to display the physical meaning of the phenomena. A comparison has been made between the obtained results with the previous results obtained by others and agrees with them if the new parameters vanish. The results obtained indicate the impacts of the nondimensional governing parameters, namely, magnetic field parameter M, Soret number Sr, heat source λ, thermal buoyancy parameterλT , and solutal buoyancy parameterλC on the flow, temperature, and concentration profiles being discussed and presented graphically.

Heat and Mass Transfer Effects on MHD Flow Past an Inclined Porous Plate in the Presence of Chemical Reaction

The impact of heat and mass transfer effects on an MHD flow past an inclined porous plate in the presence of a chemical reaction is investigated in this study. An effort has been made to explain the Soret effect and the influence of an angle of inclination on the flow field, in the presence of the heat source, chemical reaction and thermal radiation. The momentum, energy and concentration equations are derived as coupled second order partial differential equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless partial differential equations can be solved by using a closed analytical method. Numerical results for pertaining parameters, such as the Soret number (Sr), Grashof number (Gr) for heat and mass transfer, the Schmidt number (Sc), Prandtl number (Pr), chemical reaction parameter (Kr), permeability parameter (K), magnetic parameter (M), skin friction (τ), Nusselt number (Nu) and Sherwood number (Sh) on the velocity, temperature and concentration profiles are presented graphically and discussed qualitatively.

Radiation absorption on MHD free convective laminar flow over a moving vertical porous plate, viscous dissipation and chemical reaction with suction under the influence of transverses magnetic field

Abstract The aim of the present chapter is to investigate the problem of Study on MHD boundary layer flow over a moving vertical porous plate with heat generation and chemical reaction in the presence of thermal absorption. The governing equations of the flow are transformed into nonlinear ordinary differential equations and then solved by using Runge-Kutta-fourth order along with shooting method. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The influence of the various parameters like Magnetic parameter (M), thermal Grashof number (Gr), mass Grashof number (Gc), permeability parameter (K), Prandtl number (Pr), Dufour number (Df), Soret number (Sr), Schmidt number (Sc), Heat generation (B), Radiation Parameter (Ra) and Chemical reaction (Ch) on the flow are analyzed and discussed through graphs in detail. The values of the skin friction coefficient, Nusselt number and the Sherwood number for different physical parameters are also tabulated.

Metachronal propulsion of a magnetised particle-fluid suspension in a ciliated channel with heat and mass transfer

Biologically-inspired pumping systems are of great interest in modern engineering since they achieve enhanced efficiency and circumvent the need for moving parts and maintenance. Industrial applications also often feature two-phase flows. In this article, motivated by these applications, the pumping of an electrically-conducting particle-fluid suspension due to metachronal wave propulsion of beating cilia in a two-dimensional channel with heat and mass transfer under a transverse magnetic field is investigated theoretically. The governing equations for mass and momentum conservation for fluid- and particle-phases are formulated by ignoring the inertial forces and invoking the long wavelength approximation. The Jeffrey viscoelastic model is employed to simulate non-Newtonian characteristics. The normalised resulting differential equations are solved analytically. Symbolic software is employed to evaluate the results and simulate the influence of different parameters on flow characteristics. Results are visualised graphically with carefully selected and viable data. With increasing wave number (β) fluid velocity is accelerated in the core region whereas it is decelerated near the channel wall, for the Newtonian case. With increasing eccentricity of cilia elliptic path (α), a similar response is computed as for the wave number. The size of the bolus is enhanced (and quantity of boluses is reduced) with increasing eccentricity of the cilia elliptic path (α) and Hartmann (magnetic) number (M) whereas bolus size is decreased (and quantity of boluses is increased) with increasing wave number (β) and particle volume fraction (C). It is also noted that increasing Schmidt number (Sc) and Soret number (Sr) diminish the concentration magnitudes. Furthermore, Brinkman number (which represents viscous heating effects) significantly boosts the temperature magnitudes. The current analysis provides a useful benchmark for more general computational simulations.