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

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

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

Numerical Analysis Of Natural Convective Flow And Heat Transfer Of Nanofluids In A Vertical Rectangular Duct Using Darcy-Forchheimer-Brinkman Model

In this paper, natural convective flow and heat transfer of nanofluids in a vertical rectangular duct filled with porous matrix is investigated. The Darcy-Forchheimer-Brinkman model is used to represent the fluid transport within the porous medium covering the parametric ranges of 1 ≤ Gr ≤ 25,0 ≤ Br ≤ 8, and 0.0001 ≤ Da≤ 100. Also, pure water and five different types of nanofluids (Cu, diamond, TiO2, Ag and SiO2) are used with a volume fraction range of 0% ≤ Ø ≤0.2%. The governing nonlinear, coupled partial differential equations for the two-dimensional laminar, steady flow and heat transfer are solved numerically by a finite difference method with second order accuracy. It is found that the heat transfer is enhanced due to the use of a nanofluid. Further, it is noticed that an increase in the Darcy or Grashof or Brinkman numbers, or the aspect ratio parameter increase the flow and heat transfer characteristics; whereas the inertial or the viscosity ratio parameters reduce the flow and heat transfer characteristics. It is observed from 2-D graphs that the fluid rise up from the middle portion of the vertical wall and flow down along the two horizontal walls forming symmetric rolls with clockwise and counter-clockwise rotation inside the cavity. The temperature contours in 2-D are smooth curves which span the entire enclosure, and they are generally symmetry with respect to the horizontal symmetric line. The results obtained reveal many interesting behaviors that warrant further study on the heat transfer enhancement due to the nanofluids