Fluid Flow in Composite Regions Past a Solid Sphere

A steady, 2-D, incompressible, viscous fluid flow past a stationary solid sphere of radius 'a' has been considered. The flow of fluid occurs in 3 regions, namely fluid, porous and fluid regions. The governing equations for fluid flow in the clear and porous regions are Stokes and Brinkman equations, respectively. These governing equations are written in terms of stream function in the spherical coordinate system and solved using the similarity transformation method. The variation in flow patterns by means of streamlines has been analyzed for the obtained exact solution. The nature of the streamlines and the corresponding tangential and normal velocity profiles are observed graphically for the different values of porous parameter 'σ'. From the obtained results, it is noticed that an increase in porous parameters suppresses the fluid flow in the porous region due to less permeability; as a result, the fluid moves away from the solid sphere. It also decreases the velocity of the fluid in the porous region due to the suppression of the fluid as 'σ' increases. Hence the parabolic velocity profile is noticed near the solid sphere.

Energy and Entropy Production of Nanofluid within an Annulus Partly Saturated by a Porous Region

The flow and heat transfer fields from a nanofluid within a horizontal annulus partly saturated with a porous region are examined by the Galerkin weighted residual finite element technique scheme. The inner and the outer circular boundaries have hot and cold temperatures, respectively. Impacts of the wide ranges of the Darcy number, porosity, dimensionless length of the porous layer, and nanoparticle volume fractions on the streamlines, isotherms, and isentropic distributions are investigated. The primary outcomes revealed that the stream function value is powered by increasing the Darcy parameter and porosity and reduced by growing the porous region’s area. The Bejan number and the average temperature are reduced by the increase in Da, porosity ε, and nanoparticles volume fractions ϕ. The heat transfer through the nanofluid-porous layer was determined to be the best toward high rates of Darcy number, porosity, and volume fraction of nanofluid. Further, the local velocity and local temperature in the interface surface between nanofluid-porous layers obtain high values at the smallest area from the porous region (D=0.4), and in contrast, the local heat transfer takes the lower value.

Influence of Heat Source/Sink on Free Convection in Annular Porous Region

The significant interpretation of this model is to explore the influence of temperature-dependent heat source/sink on laminar free-convective flow in an annular porous region such as petroleum engineering, thermal technique and groundwater hydrology. For a unified solution of the Brinkman-Darcy model, the regulatory equations solved analytically by applying the variation of parameter technique in terms of Bessel's functions for the heat source and sink. Moreover, we have investigated the Variations of Darcy number, Heat source/sink and viscosity ratio in the presence of isothermal and constant heat flux sequentially. As a result, we received the critical value of the velocity for the radii ratio (R = 2.05 and 2.92) in both the cases of source and sink (S = 1.0 and Si = 0.1) respectively which is exhibited through the graphs. Further, the numerical outcomes present of the skin friction including volume flow with annular gap by the graphs as well as tables.

Numerical investigation of simultaneous effects of nanofluid flow and porous baffle on thermal energy transfer and flow features in a circular channel

In the present work, the forced-convection heat transfer features of different nanofluids in a circular channel with porous baffles are numerically investigated. Nanofluid flow in the porous area is simulated by the simultaneous use of Darcy-Brinkman-Forchheimer and two-phase mixture models. The flow is considered to be laminar, two-dimensionall, steady, axially symmetric, and incompressible. The simulations are conducted in Fluent software and by using the finite volume method and SIMPLE algorithm. The influences of various parameters, including Reynolds number, volume fractions of nanoparticles, Darcy number, porous region height, and various nanofluid types on the nanofluid flows and their thermal energy transfer features, are investigated. Results show that porous blocks significantly change the flow characteristics and thermal energy transfer features. For instance, at low Darcy numbers, the permeability of the porous region decreases, and the porous baffles have greater resistance against the nanofluid flow. As a result, the vortex area becomes stronger and taller, and streamlines near obstacles are tighter. However, in high Darcy numbers, due to the high permeability of the porous medium, the flow will be the same as the flow in the channel without barriers, and the porous baffles will not have much influence on the flow. For example, at Darcy number Da = 10-4 the vortex area almost disappears. The growth of conductivity ratio increases the local Nu in the vicinity of the barriers. Properties of the porous medium and nanofluid flow affect the thermal energy transfer rate, and it can be improved by making appropriate changes to these features.