Thermodynamic analysis for an inclined channel containing two immiscible couple stress fluids using HAM

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.In this paper, the flow of two immiscible couple stress fluids between two inclined parallel plates of a channel with constant wall temperatures is studied in terms of entropy generation rate. The flow is assumed to be governed by Stokes’s couple stress fluid flow equation. The flow region consists of two zones, the flow of the heavier fluid taking place in the lower zone. The governing non-linear differential equations are then solved using Homotopy Analysis Method (HAM). Profiles of dimensionless velocity, temperature, entropy generation number and Bejan number are shown graphically for various values of couple stress parameter, Brinkman number, Grashof number, Reynolds number and viscous dissipation parameter. It is observed that couple stress fluid decreases the frictional forces and hence increases exergy.cf201

Second law analysis of the flow of two immiscible couple stress fluids in four zones

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.This work investigates the entropy generation in a steady flow of two immiscible couple stress fluids in a horizontal channel bounded by two porous beds at the bottom and top. The flow is considered in FOUR zones: zone-IV contains the flow of viscous fluid in the large porous bed with low permeability at the bottom, zone-I and II contain free flow of two immiscible couple stress fluids and zone-III contains the flow of viscous fluid in the thin porous bed with high permeability at the top. The flow is assumed to be governed by Stokes’s couple stress fluid flow equations in the free channel. In zone-IV, Darcy’s law together with the Beavers-Joseph (B-J) slip condition at the interface is used whereas in zone-III Brinkman’s model is used for flow. The plates of the channel are maintained at constant temperatures higher than that of the fluid. The closed form expressions for entropy generation number and Bejan number are derived in dimensionless form by using the expressions of velocity and temperature. The effects of relevant parameters on velocity, temperature, entropy generation number and Bejan number are analyzed and presented through graphs.dc201

Couple on a rotating permeable sphere in a couple stress fluid

In this paper, the flow generated by the slow steady rotation of a permeable sphere with thin surface about its axis of symmetry in an incompressible couple stress fluid which is otherwise at rest is studied. Expressions for the velocity and couple stress tensor components are obtained in terms of modified Bessel functions and Gagenbauer’s polynomials. The couple experienced by the permeable sphere due to the internal and external flow is evaluated. The more is couple stress offered by the fluid (i.e. the lesser values of couple stress parameter), the more the fluid particles are thrown away from the sphere. It is noticed that the internal flow is similar to viscous flow and the couple acting on the sphere due to internal flow is zero. The problem differs from that of micro-polar fluids. Keywords: Permeable sphere, Couple stress fluid, Rotary flow, Modified Bessel functions, Gagenbauer function

Couple stress fluid flow due to slow steady oscillations of a permeable sphere

The study of oscillating flow of a Couple Stress fluid past a permeable sphere is considered. Analytical solution for the flow field in terms of stream function is obtained using modified Bessel functions. The formula for Drag acting on the sphere due external flow is evaluated. Pressure field for the flow region past and inside the sphere is obtained. Effects of physical parameters like couple stress parameter, permeability, frequency and geometric parameters on the drag due to internal and external flows are represented graphically. It is observed that the drag for viscous fluid flow will be less than the case of couple-stress fluid flow and hence couple stress fluids offer resistance for flow

Flow generated by slow steady rotation of a permeable sphere in a micro-polar fluid

The analytical study of the flow generated by the slow steady rotation of a permeable sphere in an incompressible micro-polar fluid is considered. Both the flows internal and external to the sphere are coupled. The result will degenerate to independent equations for the case of viscous fluids for the inner and external flows. The flow field in the form of velocity w and micro rotation function Ï are obtained in terms of modified Bessel functions and Gegenbauer polynomials. The flow pattern is shown in the form of graphs. It is interesting to note that the velocity and micro-rotation functions within the sphere are constant at distances from the axis of rotation since it represents a rigid body rotation. Effects of physical parameters on the Couple are also shown in the form of graphs. Keywords: Micro polar fluid, Steady rotation, Permeable sphere, Couple stress, Nonstick and hyper stick condition