Study Of Free Convective Flow Research Articles

MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium

This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.

Numerical Study of Free Convective Flow of a Nanofluid over a Chemically Reactive Porous Flat Vertical Plate with a Second-Order Slip Model

AbstractA mathematical model for free convective boundary-layer flow of a nanofluid with second-order velocity slip over a permeable vertical flat plate has been presented. The system of governing equations is first nondimensionalized, and then similarity transformations are used to convert the governing partial differential equations into a set of coupled ordinary differential equations. A numerical algorithm is applied to this boundary value problem (BVP) of coupled ordinary differential equations. Collocation method is used for the solution of the nonlinear ordinary BVP. The dimensionless analysis revealed that the dimensionless field variables (velocity, temperature, and nanoparticle volume fraction), and the flow characteristics (skin friction factor, heat transfer, and nanoparticle volume fraction transfer) in the respective boundary layers depend on the Prandtl number (Pr), the Lewis numbers (Le), the thermophoresis parameter (Nt), the Brownian motion parameter (Nb), the buoyancy ratio parameter (N...

Effects of parabolic motion on an isothermal vertical plate with constant mass flux

An analytical study of free convection flow near a parabolic started infinite vertical plate with isothermal in the presence of uniform mass flux was considered. The mathematical model is reduced to a system of linear partial differential equations for the velocity, the concentration and the temperature; the closed form exact solutions were obtained by the Laplace transform technique. The velocity, temperature and concentration profiles for the different parameters as thermal Grashof number Gr, mass Grashof number Gc, Prandtl number Pr, Schmidt number Sc and time t were graphed and the numerical values for the skin friction were as tabulated. It is observed that the velocity is enhanced as the time increased and the velocity is decreased as the Prandtl number increased.

Numerical Study of Free Convection Flow past a Vertical Cone with Variable Heat and Mass Flux

ABSTRACT A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power-law according to () m q x x w  and * () n q x x w  respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then non-dimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter and semi-vertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published work nonand are found to be in excellent agreement. The local skin friction, Nusselt number and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes and hybrid solar energy systems.

Preface: Saltwater and freshwater interactions in coastal aquifers

The study of coastal aquifers, i.e., aquifers that have a hydraulic connection with a saline surface-water body, forms a somewhat separate discipline in groundwater science. This type of aquifer is typically characterized by variations of groundwater salinity in space and time, which warrants special treatment of groundwater flow, groundwater chemistry and water resource management problems. The interest in the study of this type of aquifer arose both from its strategic importance for the water supply of highly populated coastal areas and its susceptibility to salinization problems. Saltwater intrusion, i.e., the displacement of fresh groundwater by groundwater with a higher salinity, has become an accepted scientific term in the research field. Coastal aquifers and the interactions between fresh and saline groundwaters are the topic of this theme issue of Hydrogeology Journal. We decided to give this issue a twofold objective. On one hand, it is meant to present a series of papers that together demonstrate the state of the art of the research in coastal hydrogeology. On the other hand, the aim is to present a review of the extent of saltwater-intrusion problems around the world. The study of groundwater flow in coastal areas can not be considered separately from the transport of dissolved salts. This is because spatiotemporal changes in salinity give rise to density differences that control flow patterns. Consequently, equations of flow and solute transport must be solved simultaneously. The development of models that simulate flow and solute transport under variable-density conditions has been an enormous achievement. Although, by now, many sophisticated codes have become generally available, research in this field is still ongoing, which is reflected by a number of contributions to this theme issue. Voss et al. present a methodology to benchmark threedimensional (3D) variable-density flow and transport simulators. A benchmark is a test to confirm that the simulation results are correct and that the governing equations of flow and transport are correctly solved. Previously, unambiguous 3D benchmarks for unstable systems (i.e., a system in which, in some part or everywhere, the density decreases with depth) were lacking. The benchmark is based on analytically derived stability criteria for steady-state convection in a 3D box in an unstable system. Different modes of convection develop depending on the inclination of the box and the Rayleigh number. By comparing the results of the variable-density code with the analytically derived stability criteria, it can be ascertained that the code correctly simulates the physics of the flow system. An application of a model of coupled density-dependent groundwater flow, and solute and heat transport of an unstable system is presented by Hughes et al. They present a first assessment of the aquifer salinization process occurring beneath an engineered, hypersaline cooling-canal system. Their simulations show the development of salt fingers which can reach the bottom of the aquifer in times that range between a few days and 5 years, depending on the hydraulic conductivity configuration. They conclude that the temperature gradient, in this case, has a mitigating effect on the rate of aquifer salinization. Downwards unstable salinization is also studied by Post and Simmons, who show the results of a combined laboratory tank experiment and numerical modeling study of free convective flow at the scale of individual lowpermeability structures. Their results provide insight into the flow patterns that evolve in both the aquifer material surrounding the lens and within the lens itself. In the system studied, upward vertical-flow components are Received: 9 November 2009 /Accepted: 17 November 2009 Published online: 1 December 2009

Non-Darcy Natural Convection in a Saturated Horizontal Porous Annulus

A computational study of free convective flow and heat transfer in a saturated porous horizontal annulus is reported. Both isothermal and constant heat flux boundary conditions have been considered on the inner walls while the outer wall is held at a constant temperature. The calculation of the flow field involves consideration of non-Darcy effects, such as inertial and viscous forces, and also the variation of porosity near the walls. While the literature shows that Darcy flow model is inadequate in predicting average Nusselt numbers, the present study examines whether non-Darcy effects, and in particular the presence of the boundary, could play a significant role in explaining this discrepancy. Average Nusselt numbers have been obtained for Rayleigh–Darcy numbers from 20 to 4000 for the case of isothermal boundaries, and 20 to 20,000 for the case of constant heat flux on the inner wall. Radius ratio has been varied from 1.1 to 3. Over this range of parameters, inertia and viscous friction in the fluid phase have been found to produce a small effect on the Darcy flow. The effect of including variable porosity near a boundary is seen to produce channeling near the wall which in turn substantially increases the heat transfer coefficient.

Natural Convection in a Horizontal Porous Annulus With a Step Distribution in Permeability

A numerical and experimental study of free convective flow and heat transfer in a horizontal annulus containing saturated porous material is reported in the present study. The special case of a step distribution in permeability, resulting in a two-layer system, has been considered. Both isothermal and constant heat flux boundary conditions have been imposed on the inner wall, while the outer wall is kept at a constant temperature. For the case of isothermal boundaries, a simple resistance law gives rise to a model of permeability which collapses the average Nusselt numbers of the variable permeability problem to that of the uniform case. Generally, agreement between experiments and calculation is satisfactory, although under certain circumstances, a systematic divergence of the data is observed. It is deduced in the present work that this is strictly related to non-Darcy effects.

The Natural Convection of Air Over a Heated Plate With Forward-Facing Step

An experimental study of free convection flow of air over a vertically oriented, isothermal, heated plate with a forward-facing step was done. The step height was varied from 0.3175 to 0.9525 cm, and the distance of the step from the leading edge was varied from 7.62 to 15.24 cm. Temperature profiles were measured with a thermocouple probe, and velocity profiles were measured by photographing the trajectories of small dust particles carried along with the flow. For comparison purposes the same measurements were made for a flat plate. The results are nondimensionalized for comparison with the theoretical velocity and temperature profiles for a flat plate. A discussion of how the temperature and velocity profiles deform as the fluid passes over the step and the effect of step size and location on profile shape is included. The experimentally obtained temperature profiles are used to calculate the dimensionless heat-transfer coefficient. This coefficient is characterized in terms of the size and location of the step.

A Numerical Study of Laminar Free Convective Heat Transfer from Vertical Cones

A numerical study of free convective flow over vertical cones is described. The study is based on the use of the constant fluid properties boundary layer equations. Solutions have been obtained for...