Dispersion of a Solute in Hartmann Two-Fluid Flow between Two Parallel Plates

The paper presents an analytical solution for the dispersion of a solute in a conducting immiscible fluid flowing between two parallel plates in the presence of a transverse magnetic field. The fluids in both the regions are incompressible, electrically conducting and the transport properties are assumed to be constant. The channel walls are assumed to be electrically insulating. Separate solutions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The results are tabulated for various values of viscosity ratio, pressure gradient and Hartman number on the effective Taylor dispersion coefficient and volumetric flow rate in the absence and in the presence of chemical reactions. It is found that the solute is dispersed relative to a plane moving with the mean speed of flow with an effective Taylor diffusion coefficient which decreases with an increase in magnetic field with or without chemical reactions. The validity of the results obtained for conducting two fluid model is verified by comparison with the available one-fluid model and the values tally very well

Unsteady Oscillatory Flow and Heat Transfer in a Horizontal Composite Porous Medium Channel

The problem of unsteady oscillatory flow and heat transfer in a horizontal composite porous medium is performed. The flow is modeled using the Darcy-Brinkman equation. The viscous and Darcian dissipation terms are also included in the energy equation. The partial differential equations governing the flow and heat transfer are solved analytically using two-term harmonic and non-harmonic functions in both regions of the channel. Effect of the physical parameters such as the porous medium parameter, ratio of viscosity, oscillation amplitude, conductivity ratio, Prandtl number and the Eckert number on the velocity and/or temperature fields are shown graphically. It is observed that both the velocity and temperature fields in the channel decrease as either of the porous medium parameter or the viscosity ratio increases while they increase with increases in the oscillation amplitude. Also, increasing the thermal conductivity ratio is found to suppress the temperature in both regions of the channel. The effects of the Prandtl and Eckert numbers are found to decrease the thermal state in the channel as well

Free Convection Flow of an Electrically-Conducting Micropolar Fluid between Parallel Porous Vertical Plates Using Differential Transform

In the present study, the effect of temperature-dependent heat sources on the fully developed free convection flow of an electrically conducting micropolar fluid between two parallel porous vertical plates in the presence of a strong cross magnetic field is analyzed. The micropolar fluid fills the space inside the porous plates when the rate of suction at one boundary is equal to the rate of injection at the other boundary. The coupled nonlinear governing differential equations are solved using the differential transform method (DTM). Moreover, the Runge-Kutta shooting method (RKSM), which is a numerical method, is used for the validity of DTM method and an excellent agreement is observed between the solutions of DTM and RKSM. Trusting this validity, the effects of Hartmann number, Reynolds number, micropolar parameter, and applied electric field load parameter are discussed on the velocity, microrotation velocity, and temperature. The skin friction, the couple stress, and Nusselt numbers at the plates are shown in graphs. It is observed that the Hartmann number and the micropolar parameter decreases the skin friction and the couple stress at both plates for suction and injection

Two-Fluid Mixed Magnetoconvection Flow in a Vertical Enclosure

The problem of steady, laminar flow and heat transfer of an electrically conducting fluid through vertical channel in the presence of uniform transverse magnetic field is formulated using a two-fluid continuum model. Combined free and forced convection inside the channel is considered. The effects of viscous and ohmic dissipations are included in the energy equation. Both walls are kept either at the same or different temperatures such as isoflux-isothermal and isothermal-isoflux conditions. Governing equations in cartesian co-ordinates are solved analytically using regular perturbation technique to develop the expression for velocity and temperature. Velocity, temperature and Nusselt number are presented graphically. Effects of pertinent parameters, such as Hartmann number, electric field load parameter, viscosity ratio, width ratio and conductivity ratio are determined

Perturbation and numerical study of double-diffusive dissipative reactive convective flow in an open vertical duct containing a non-darcy porous medium with robin boundary conditions

A mathematical model for thermosolutal convection flow in an open two-dimensional vertical channel containing a porous medium saturated with reactive Newtonian fluid is developed and studied. Robin boundary conditions are prescribed, and a first-order homogenous chemical reaction is considered. The Darcy–Forchheimer model is used to simulate both the first- and second-order porous mediums’ drag effects. For the general non-Darcy-case, a numerical solution is presented using the Runge–Kutta quadrature and a shooting method. The influences of thermal (0≤λ1≤15) and solute Grashof numbers (0≤λ2≤20) , Biot numbers (1≤Bi1≤10,Bi2=10) , Brinkman number (0≤Br≤0.5) , first-order chemical reaction parameter (2≤α≤8) , porous medium parameter (2≤σ≤8) and Forchheimer (inertial drag) parameter (0≤I≤12) on the evolutions of velocity, temperature and concentration (species) distributions are visualized graphically. Nusselt number and skin friction at the walls are also computed for specific values of selected parameters. The study is relevant to the analysis of geothermal energy systems with chemical reaction

Laminar mixed convection of permeable fluid overlaying immiscible nanofluid

Immiscible flow has been extensively emerged in science and technology. Researchers and architects were delighted by the concept of multiple fluid transport by the means of shear pressure. The reliance of drag impact of the two immiscible liquids is very much aspired but yet challenging. A mathematical examination has been conveyed to understand the free convection inside a vertical vessel. There are two immiscible liquids filled in the enclosure which are synthesized as two discrete regions encompassing a nanofluid and permeable fluid. The Tiwari–Das model and Dupuit–Forchheimer is utilized to define the nanofluid and permeable fluid, respectively. Southwell over-relaxation technique subject to suitable interface and boundary conditions is bestowed to solve the conservation equations. Essential criteria defining the fluid flow and energy transfer are studied deliberately. The outcomes demonstrate that the Grashof, Brinkman and Darcy numbers augment the velocity, whereas inertial, solid volume fraction, viscosity and thermal conductivity ratios depletes the momentum. The temperature distributions are not much modulated with any of the controlling parameters. By sagging nanoparticles, the flow is not much reformed but reckoning copper nanoparticle as ethylene glycol–mineral oil base fluid regulates the supreme flow. Diamond nanoparticle dropped in water catalyzes the highest rate of heat transfer

Mixed convection flow of an electrically conducting fluid in a vertical channel using Robin boundary conditions with heat source/sink

A numerical study of steady, mixed convection of electrically conducting fluid in a vertical channel with heat source/sink is analyzed using Robin boundary conditions. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperature of the external fluid are considered. The governing equations are solved analytically using regular perturbation method and numerically by Runge–Kutta fourth order method with shooting technique. The graphs illustrating the effects of various parameters involved in the problem on the flow as well as average velocity and Nusselt number are presented and discussed. It is found that the effect of negative electric field load parameter is to aid the flow while the effect of positive electric field load parameter is to oppose the flow as compared to the case of short circuit. The analytical and numerical solutions agree very well for small values of perturbation parameter