NUMERICAL MODELING OF MHD CONVECTIVE HEAT AND MASS TRANSFER IN PRESENCE OF FIRST-ORDER CHEMICAL REACTION AND THERMAL RADIATION

An analysis was carried out numerically to study unsteady heat and mass transfer by free convection flow of a viscous, incompressible, electrically conducting Newtonian fluid along a vertical permeable plate under the action of transverse magnetic field taking into account thermal radiation as well as homogeneous chemical reaction of first order. The fluid considered here is an optically thin gray gas, absorbing-emitting radiation, but a non-scattering medium. The porous plate was subjected to a constant suction velocity with variable surface temperature and concentration. The dimensionless governing coupled, nonlinear boundary layer partial differential equations were solved by an efficient, accurate, extensively validated, and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature, and concentration fields were studied for the effects of Hartmann number (M), radiation parameter (R), chemical reaction (K), and Schmidt number (Sc). The local skin friction, Nusselt number, and Sherwood number are also presented and analyzed graphically. It is found that velocity is reduced considerably with a rise in the magnetic body parameter (M), whereas the temperature and concentration are found to be markedly boosted with an increase in the magnetic body parameter (M). An increase in the conduction-radiation parameter (R) is found to escalate the local skin friction (τ), Nusselt number, and concentration, whereas an increase in the conduction-radiation parameter (R) is shown to exert the opposite effect on either velocity or temperature field. Similarly, the local skin friction and the Sherwood number are both considerably increased with an increase in the chemical reaction parameter. Possible applications of the present study include laminar magneto-aerodynamics, materials processing, and MHD propulsion thermo-fluid dynamics.     

MHD Flow Through Porous Medium in Presence of Heat and Mass Transfer With Heat Source

Unsteady free convection and mass transfer flow past an accelerated infinite nonconducting vertical plate through a porous medium have been analyzed in the presence of a uniform magnetic field and constant heat source. Expressions for the velocity field for two different cases are obtained by the Laplace-transform technique. The influence of the various parameters entering into the problem on the velocity field is extensively discussed.     

Thermal Diffusion and MHD Effects on Combined Free‐Forced Convection and Mass Transfer of a Viscous Fluid Flow Through a Porous Medium with Heat Generation

The problem of thermal diffusion and magnetic field effects on combined free‐forced convection and mass transfer flow past a vertical porous flat plate, in the presence of heat generation is studied numerically. The governing momentum, energy and concentration equations are converted into a system of nonlinear ordinary differential equations by means of similarity transformations. The resulting system of coupled nonlinear ordinary differential equations is solved numerically by using the Shooting method. Numerical results are presented for velocity, temperature and concentration profiles within the boundary layer for different parameters of the problem including suction parameter, heat generation parameter, Soret number, Dufour number, magnetic parameter, etc. In addition, the effects of the pertinent parameters on the skin friction and the rates of heat and mass transfer are discussed numerically and illustrated graphically.     

Characteristics of the boundary layer with hydrogen combustion with variations of thermal conditions on a permeable wall

The paper describes a numerical study of the influence of thermal and boundary conditions on the structure of laminar and turbulent diffusion flames in the cases with hydrogen injection through a porous surface and with hydrogen combustion in an air flow. Two types of boundary conditions are compared: with a given constant temperature T _w = const over the length of the porous surface for arbitrary intensities of fuel injection and with a constant temperature T′ = const of the fuel injected through the porous wall. The first case occurs during combustion of a liquid fuel whose burning surface temperature remains unchanged. Injection of gaseous fuel usually leads to the second case with T′ = const. Despite significant differences in velocity and temperature profiles, the skin friction coefficients in the laminar flow are close to each other in these two regimes. In the turbulent regime, the effect of the thermal boundary conditions on friction and heat transfer is more pronounced. Moreover, the heat flux to the wall as a function of fuel-injection intensity is characterized by a clearly expressed maximum. A principal difference of the effect of combustion on friction and heat transfer in the laminar and turbulent flow regimes is demonstrated. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 3, pp. 3–11, May–June, 2009.     

FURTHER RESULTS ON HYDROMAGNETIC BOUNDARY-LAYER FLOW OF A NON-NEWTONIAN POWER-LAW FLUID OVER A CONTINUOUSLY MOVING SURFACE WITH SUCTION

The flow of a non-Newtonian, power-law conducting fluid under the effect of a constant transverse magnetic field is considered. The flow is produced by a plate moving with constant velocity in a calm fluid. The plate is porous and fluid can either be sucked or injected through it. The boundary layer equations are transformed into a nondimensional form and are solved with a finite difference method. Part of this problem has been investigated in the past but only for suction and pseudo-plastic fluids. However, all flows of the present work reach an asymptotic state and exact analytical solutions exist for Newtonian fluids. In the present work we extend the investigation to both pseudo-plastic Newtonian and dilatant fluids in both suction and injection cases.     

UNSTEADY HYDROMAGNETIC NATURAL CONVECTION OF A SHORT-MEMORY VISCOELASTIC FLUID IN A NON-DARCIAN REGIME: NETWORK SIMULATION

A mathematical model for the unsteady magnetohydrodynamic (MHD) laminar natural convection flow of a viscoelastic fluid from an infinite vertical porous plate to an isotropic, homogeneous, non-Darcian porous regime, with time-dependent suction, in the presence of a uniform transverse magnetic field, is studied. The generalized Beard-Walters rheological model is employed, which introduces a mixed third-order derivative into the momentum conservation equation. The transformed conservation equations are solved using the robust, well-tested computational procedure known as network simulation method (NSM). The NSM computations have shown that with an increase in viscoelasticity parameter (S) the flow accelerates considerably with time. Increasing magnetic field (M), however, retards the flow strongly with time. An increase in the Darcy number (Da) serves to augment the velocity (w) profiles, i.e., accelerate the flow in both the conducting (M ≠ 0) and nonconducting (M = 0) cases. Velocities also increase in value over time (τ). A velocity overshoot is identified close to the plate. A rise in the Forchheimer number (Fs), corresponding to an accentuation in the quadratic porous drag effect, induces a strong deceleration in the flow, in particular near the plate surface, for both conducting and nonconducting cases. Increasing buoyancy effects, as simulated via a rise in the thermal Grashof number (Gr), leads to a substantial retardation in the flow; this effect is enhanced with Lorentzian magnetic drag force. An increase in the suction parameter (A) causes a stronger adherence of the hydrodynamic boundary layer to the plate and leads to a reduction in velocities along the entire plate regime. A similar decrease in temperature (θ) is caused with increasing suction parameter (A). The results are of relevance in, for example, magneto-rheological materials processing operations and advanced hybrid magnetohydrodynamic energy systems exploiting non-Newtonian fluids.     

A NEW CLASS OF SIMILARITY SOLUTIONS OF AN UNSTEADY ELECTRICALLY CONDUCTING FREE-FORCED CONVECTIVE FLOW IN A VERTICAL POROUS SURFACE WITH DUFOUR AND SORET EFFECTS

The 2-D unsteady magnetohydrodynamic free-forced convective boundary layer flow of a viscous incompressible fluid is studied numerically taking into account heat and mass transfer. The fluid is subjected to uniform heat and mass fluxes embedded in a porous medium by the presence of coupled Dufour and Soret effects. A new class of similarity equations has been obtained by introducing a time-dependent length scale and a corresponding similarity variable. The resulting equations are then integrated numerically using the Nachtsheim-Swigert shooting iteration technique along with the sixth-order Runge-Kutta integration scheme. By developing locally similar solutions of the fluid flow, the behavior of the velocity, temperature, and concentration fields as well as the rate of heat transfer, wall temperature gradient, rate of mass transfer, and skin friction coefficient have been investigated. The effects of Grashof number (Gr), modified Grashof number (Gm), combined effects of the porous and magnetic parameter (S), suction/injection parameter Fw, Brinkman number (Br), Soret number (Sr), and Dufour number (D_f) have been observed on the flow field and discussed.     

THE EFFECT OF THERMAL RADIATION ON THE HEAT AND MASS TRANSFER FLOW OF A VARIABLE VISCOSITY FLUID PAST A VERTICAL POROUS PLATE PERMEATED BY A TRANSVERSE MAGNETIC FIELD

The effect of temperature-dependent viscosity on free convective flow past a vertical porous plate is studied in the presence of a magnetic field, thermal radiation, and a first-order homogeneous chemical reaction. Boundary layer equations are derived and the resulting approximate nonlinear ordinary differential equations are solved numerically by the shooting method. A parametric study of all parameters involved is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the skin-friction parameter and the Nusselt and Sherwood numbers is illustrated graphically to show typical trends of the solutions. The dynamic viscosity in this study is taken as a function of the temperature although the Prandtl number is considered constant.     

BOUNDARY LAYER FLOW AND DOUBLE DIFFUSION OVER AN UNSTEADY STRETCHING SURFACE WITH HALL EFFECT

The present investigation is concerned with the effect of Hall currents on boundary layer flow, and heat and mass transfer of an electrically conducting fluid over an unsteady stretching sheet in the presence of a strong magnetic field. The electron-atom collision frequency is assumed to be relatively high, so that the Hall effect is assumed to exist, while the induced magnetic field is neglected. The governing time-dependent boundary layer equations for momentum, thermal energy, and concentration are reduced using a similarity transformation to a set of coupled ordinary differential equations. The similarity ordinary differential equations are then solved numerically by the successive linearization method together with the Chebyshev pseudo-spectral collocation method. Effects of the Prandtl number, Pr, Schmidt number, Sc, magnetic field, M, Hall parameter, m, and the unsteadiness parameter, A, on the velocity, temperature, and concentration profiles as well as the local skin friction coefficient and the heat and mass transfer rates are depicted graphically and/or in tabular form. Favorable comparisons with previously published work on various special cases of the problem are also obtained.     

THE EFFECT OF VARIABLE THERMAL CONDUCTIVITY ON MICRO-POLAR FLUID FLOW BY CHEBYSHEV COLLOCATION METHOD

In this article, the authors analyzed the effect of thermal conductivity on unsteady magnetohydrodynamic (MHD) free convection in a micro-polar fluid past a semi-infinite vertical porous plate. The fluid thermal conductivity is assumed to vary as a linear function of temperature. By using the Chebyshev collocation method in the spatial direction and the Crank-Nicolson method in the time direction, the boundary layer equations are transformed into a linear algebraic system. There are several material parameters whose affect on the flow have been studied, for instance, thermal conductivity, radiation, magnetic, micro-polar, suction (or injection) parameters, and Prandtl number. Boundary layer and Boussineq approximations have been introduced together to describe the flow field. The domain of the problem is discretized according to the Chebyshev collocation scheme. The numerical results show that, the values of velocity, angular velocity and temperature profiles approach to the steady state when the time reach to infinity. However, the friction factor has been found to increase as micro-polar and thermal conductivity parameters increase. But it decreases as magnetic parameter increases. Meanwhile, Nusselt number increases as thermal conductivity parameter increases, and vice versa with the micro-polar parameter. Moreover, the local couple stress has been found to decrease as micro-polar and thermal conductivity parameters increase. On the other hand, it increases as magnetic parameter increases.     

Radiation-absorption,chemical reaction,Hall and ion slip impacts on magnetohydrodynamic free convective flow over semi-infinite moving absorbent surface

The investigation of radiation-absorption,chemical reaction,Hall and ion-slip impacts on unsteady MHD free convective laminar flow of an incompressible viscous,electrically conducting and heat generation/absorbing fluid enclosed with a semi-infinite porous plate within a rotating frame has been premeditated.The plate is assumed to be moving with a constant velocity in the direction of fluid movement.A uniform transverse magnetic field is applied at right angles to the porous surface,which is absorbing the fluid with a suction velocity changing with time.The non-dimensional governing equations for present inves-tigation are solved analytically making use of two term harmonic and non-harmonic functions.The graphical results of velocity,temperature and concentration distributions on the analytical solutions are displayed and discussed with reference to pertinent parameters.It is found that the velocity profiles decreased with an increasing in Hartmann number,rotation parameter,the Schmidt number,heat source parameter,while it increased due to an increase in permeability parameter,radiation-absorption param-eter,Hall and ion slip parameters.However,the temperature profile is an increasing function of radiation-absorption parameter,whereas an increase in chemical reaction parameter,the Schmidt num-ber Sc or frequency of oscillations decrease the temperature profile on cooling.Also,it is found that the concentration profile is decreased with an escalating in the Schmidt number or the chemical reaction parameter.     

EXTENDED KALMAN FILTER CONTROLLER: FIRST PRINCIPLES MODELS TO NEURAL NETWORKS

In this study we have obtained an exact solution to the problem of heat and mass transfer in a rotating vertical porous channel taking into account the effects of Hall current. A strong magnetic field of uniform strength is applied along the axis of rotation. The entire system rotates about the axis normal to the plates with a uniform angular velocity. The porous channel is subjected to a constant suction/injection velocity as well as uniform free stream velocity. The nonlinear and coupled governing equations are solved by perturbation technique. The analytical expressions for primary and secondary velocity components, temperature and concentration fields, and shear stresses are obtained. The effects of the magnetic field, rotation of the channel, buoyancy force, Hall current, injection-suction parameter, and the temperature oscillation frequency are described during the course of discussion. The results are presented graphically and discussed.     

MATHEMATICAL MODELING OF OSCILLATORY MHD COUETTE FLOW IN A ROTATING HIGHLY PERMEABLE MEDIUM PERMEATED BY AN OBLIQUE MAGNETIC FIELD

We study theoretically the incompressible, viscous, oscillatory hydromagnetic Couette flow in a horizontal fluid-saturated highly permeable porous medium parallel-plate channel rotating about an axis perpendicular to the plane of the plates under the action of a uniform magnetic field, B₀, inclined at an angle θ to the axis of rotation. The flow is generated by the non-torsional oscillation of the lower plate of the channel. The reduced unsteady momentum equations are nondimensionalized with appropriate variables. Exact solutions under specified boundary conditions are obtained using the Laplace transform method (LTM). The flow regime is found to be controlled by a rotational parameter (K²), which is the reciprocal of the Ekman number (Ek), the square of the Hartmann magnetohydrodynamic number (M²), a porous medium permeability parameter (K_p), which is the inverse of the Darcy number (Da), oscillation frequency (ω), dimensionless time (T), and magnetic field inclination (θ). The influence of these parameters on the primary (u₁) and secondary (v₁) velocity field is presented graphically and studied in detail. Asymptotic behavior of the solutions is also examined for several cases of the square of the Hartmann number, rotation parameter, and oscillation angular frequency. The existence of modified Hartmann boundary layers is also identified. The present study has important applications in MHD (magnetohydrodynamic) energy generator flows, chemical engineering magnetic materials processing, conducting blood flows, and process fluid dynamics.     

FLOW IN A RESERVOIR FILLED WITH A NON-NEWTONIAN FLUID INDUCED BY A MOVING PLATE

This paper presents a theoretical solution for the flow field in a reservoir filled with a non-Newtonian (power law) fluid, induced by a moving plate. The flow field consists of a boundary layer in the vicinity of the moving plate, a core “invicid” region in which the flow is driven by the suction effect at the edge of the boundary layer and a second boundary layer in the vicinity of the vertical wall of the reservoir. In addition to the velocity field, results for the friction coefficients at the moving plate and at the vertical wall of the reservoir are reported.     

Cu and Cu-SWCNT Nanoparticles’ Suspension in Pulsatile Casson Fluid Flow via Darcy–Forchheimer Porous Channel with Compliant Walls: A Prospective Model for Blood Flow in Stenosed Arteries

The use of experimental relations to approximate the efficient thermophysical properties of a nanofluid (NF) with Cu nanoparticles (NPs) and hybrid nanofluid (HNF) with Cu-SWCNT NPs and subsequently model the two-dimensional pulsatile Casson fluid flow under the impact of the magnetic field and thermal radiation is a novelty of the current study. Heat and mass transfer analysis of the pulsatile flow of non-Newtonian Casson HNF via a Darcy–Forchheimer porous channel with compliant walls is presented. Such a problem offers a prospective model to study the blood flow via stenosed arteries. A finite-difference flow solver is used to numerically solve the system obtained using the vorticity stream function formulation on the time-dependent governing equations. The behavior of Cu-based NF and Cu-SWCNT-based HNF on the wall shear stress (WSS), velocity, temperature, and concentration profiles are analyzed graphically. The influence of the Casson parameter, radiation parameter, Hartmann number, Darcy number, Soret number, Reynolds number, Strouhal number, and Peclet number on the flow profiles are analyzed. Furthermore, the influence of the flow parameters on the non-dimensional numbers such as the skin friction coefficient, Nusselt number, and Sherwood number is also discussed. These quantities escalate as the Reynolds number is enhanced and reduce by escalating the porosity parameter. The Peclet number shows a high impact on the microorganism’s density in a blood NF. The HNF has been shown to have superior thermal properties to the traditional one. These results could help in devising hydraulic treatments for blood flow in highly stenosed arteries, biomechanical system design, and industrial plants in which flow pulsation is essential.     

Friction properties of new porous carbon materials: Woodceramics

Woodceramics are new porous carbon materials obtained from wood or woody materials impregnated with phenol resin, and carbonized in a vacuum furnace at high temperature. Woodceramics have several superior characteristics from the viewpoints of engineering materials and ecological materials: they are hard and strong, have porous structure and low density, are made from natural resources, do not cause environmental pollution, and are cheap to manufacture. This paper describes the fundamental friction properties of Woodceramics in sliding contact with several materials. Woodceramics made of medium density fiberboard (MDF) and beech impregnated with phenol resin and carbonized in a vacuum furnace at 800°C and 2000°C were rubbed against alumina, silicon nitride, bearing steel and diamond by using a reciprocating friction apparatus. Experiments were carried out unlubricated in air, impregnated with base oil and in water, at several normal loads and sliding velocities. The following principal results were obtained: (1) The friction coefficient is around 0.15, under all three lubrication conditions; (2) The friction coefficient slightly decreases and then stays constant with increasing normal load; (3) The friction coefficient is not affected by sliding velocity; (4) Woodceramics have a good self-lubricity.     

Darcy's law for two‐dimensional flows: Singularities at corners and a new class of models

As is known, Darcy's model for fluid flows in isotropic homogeneous porous media gives rise to singularities in the velocity field for essentially two‐dimensional flow configuration, like flows over corners. Considering this problem from the modeling viewpoint, this study aims at removing this singularity, which cannot be regularized via conventional generalizations of the Darcy model, like Brinkman's equation, without sacrificing Darcy's law itself for unidirectional flows where its validity is well established experimentally. The key idea is that as confirmed by a simple analogy, the permeability of a porous matrix with respect to flow is not a constant independent of the flow but a function of the flow field (its scalar invariants), decreasing as the curvature of the streamlines increases. This introduces a completely new class of models where the flow field and the permeability field are linked and, in particular problems, have to be found simultaneously. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

考虑局部非热平衡的流体层流横掠多孔介质中恒热流平板的传热分析

对流体层流横掠多孔介质中恒热流加热的平板,应用Brinkman-Forchheime-extended Darcy流动模型和流体与多孔介质之间局部非热平衡理论建立守恒方程组,应用数量级分析和积分法,得出了速度边界层厚度、热边界层厚度、壁面黏性摩擦系数和对流传热系数、流体与多孔介质之间局部温差的计算公式。结果表明,速度边界层与光板时明显不同,其在平板前端迅速增长,之后越来越平坦,趋于一个恒定值;而热边界层则沿着流动方向不断增长,类似于光板时的情况;局部的表面对流传热系数在平板前端达最大值,之后逐渐减小,也类似于光板时的情况;多孔介质与流体间的局部温差在平板前端达最大值,之后呈现沿着流动方向逐渐减小的变化趋势。     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.