Mixed convective flow of immiscible fluids in a vertical corrugated channel with traveling thermal waves

AbstractFully developed laminar mixed convection in a corrugated vertical channel filled with two immiscible viscous fluids has been investigated. By using a perturbation technique, the coupled nonlinear equations governing the flow and heat transfer are solved. The fluids are assumed to have different viscosities and thermal conductivities. Separate solutions are matched at the interface using suitable matching conditions. The velocity, the temperature, the Nusselt number and the shear stress are analyzed for variations of the governing parameters such as Grashof number, viscosity ratio, width ratio, conductivity ratio, frequency parameter, traveling thermal temperature and are shown graphically. It is found that the Grashof number, viscosity ratio, width ratio and conductivity ratio enhance the velocity parallel to the flow direction and reduce the velocity perpendicular to the flow direction

Effects of Homogeneous and Heterogeneous Reactions on the Dispersion of a Solute for Immiscible Viscous Fluids between Two Plates

The paper presents an analytical solution for the dispersion of a solute of two immiscible viscous fluids in the presence of an irreversible first-order chemical reaction. The effects of both homogeneous and heterogeneous reactions on the dispersion are studied. The results are presented graphically and in tabular form for various values of viscosity ratio and pressure gradients on the volumetric flow rate and effective Taylor dispersion coefficient. It is found that for homogeneous chemical reaction, the effective Taylor dispersion coefficient decreases as reaction rate parameter increases. The validity of the results obtained from an analytical method for two fluid models is verified by comparison with the available one fluid model results, and good agreement is found

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

Convective transport in a porous medium layer saturated with a Maxwell nanofluid

A linear and weakly non-linear stability analys is has been carried out to study the onset of convection in a horizontal layer of a porous medium saturated with a Maxwell nanofluid. To simulate the momentum equation in porous media, a modified Darcy–Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. A Galerkin method has been employed to investigate the stationary and oscillatory convections; the stability boundaries for these cases are approximated by simple and useful analytical expressions. The stability of the system is investigated by varying various parameters viz., nanoparticle concentration Rayleigh number, Lewis number, modified diffusivity ratio, porosity, thermal capacity ratio, viscosity ratio, conductivity ratio, Vadász number and relaxation parameter. A representation of Fourier series method has been used to study the heat and mass transport on the non-linear stability analysis. The effect of transient heat and mass transport on various parameters is also studied. It is found that for stationary convection Lewis number, viscosity ratio and conductivity ratio have a stabilizing effect while nanoparticle concentration Rayleigh number Rn destabilizes the system. For oscillatory convection we observe that the conductivity ratio stabilizes the system whereas nanoparticle concentration Rayleigh number, Lewis number, Vadász number and relaxation parameter destabilize the system. The viscosity ratio increases the thermal Rayleigh number for oscillatory convection initially thus delaying the onset of convection and later decreases thus advancing the onset of convection hence showing a dual effect. For steady finite amplitude motions, the heat and mass transport decreases with an increase in the values of nanoparticle concentration Rayleigh number, Lewis number, viscosity ratio and conductivity ratio. The mass transport increases with an increase in Vadász number and relaxation parameter. We also study the effect of time on transient Nusselt number and Sherwood number which are found to be oscillatory when time is small. However, when time becomes very large both the transient Nusselt and Sherwood values approach to their steady state values