Jai Prakash Narain

Combined forced and free-convection over thin needles

Abstract The problem of laminar combined forced and free-convection heat transfer from a vertical thin needle in a variable external stream is considered. The similarity solutions for needles with isothermal walls and needles with uniform wall heat fluxes have been obtained. For a given value of the needle size, the flow and heat transfer behaviours are similar to those encountered with flat plates. The Nusselt number and the skin-friction coefficients increase with decreasing needle sizes for assigned values of Prandtl number, local Reynolds number, and local Grashof number.

Combined Forced and Free-Convection Heat Transfer from Vertical Thin Needles in a Uniform Stream

The problem of laminar combined forced and free‐convection heat transfer from a thin needle in a uniform external stream is considered. The series and local similarity solutions have been discussed.

Stability of Coaxial Rotating Jet and Vortex of Different Densities

Stability of a rotating axisymmetric jet surrounded by a potential vortex to infinitesimal disturbances in the inviscid incompressible fluid approximation is considered. The jet and the vortex may have different densities. The dispersion relation for angular frequency covers a wide range of configurations. A rotating or nonrotating jet in a medium at rest is unstable for all density ratios. A vortex enclosing a stagnant core is stable for axisymmetric disturbances for all densities. A vortex with a rotating core without axial velocity is unstable if the jet fluid density is greater than the vortex fluid density. The jet vortex system is destabilized by the slightest amount of axial velocity; increasing jet fluid density has a destabilizing effect. A vortex around a rotating or nonrotating jet of any density suppresses some of the large scale instabilities. In general, axial velocity of the jet, its rotation, and increase in its density have a destabilizing effect. The surface tension between the two fluid...

Laminar Free Convection from Vertical Thin Needles

A similarity solution is obtained for the problem of free‐convection heat transfer over a thin vertical needle with uniform heat flux at the surface. A few errors in previous papers on “isothermal” needles have been modified.

Numerical prediction of confined swirling jets

Abstract The axisymmetric flow of a swirling viscous, incompressible fluid jet inside confining cylindrical boundaries has been numerically investigated using the well-known implicit finite-difference scheme. For a swirling jet confined by cylindrical tube, the vortex-breakdown or the formation of an axisymmetric isolated eddy occurs at high values of swirl ratios at a moderate flow rate or Reynolds number. With the introduction of artificial adverse pressure gradients, such as one studied in the case of a step-up cylindrical tube, the vortex-breakdown occurs at a relatively lower swirl ratio at a given flow rate. For a swirling jet discharging in a coaxial non-rotating surrounding stream enclosed by a cylindrical tube, the vortex-breakdown and its structure depend on various parameters such as the flow rate of the jet, surrounding stream velocity, the swirl of the jet and on the radius of the enclosing cylindrical tube. In general increasing Reynolds numbers, swirl ratio, decreasing surrounding stream velocity and increasing size of the cylindrical tube enhance the occurrence and size of the vortex-breakdown.

Magnetohydrodynamics of Conical Flows

The effect of diverging or converging electric currents on a stationary, viscous, incompressible, conducting body of fluid, confined in a cone of infinite extent, is investigated. The fluid moves down from upstream infinity near the walls and as it approaches the apex of the cone, it changes its direction in the core of the cone and moves toward upstream infinity near the axis. With increasing currents, the velocity near the axis rises very rapidly. Similar phenomenon have been observed in the laboratory electric arcs and in thermal plasmas of the solar atmosphere. Next, when a fixed amount of fluid is drained from the apex of the cone, the flow divides into two regions far from the apex. The drained fluid reaches the apex only through a narrow region near the walls whereas fluid in the core of the cone executes a secondary motion, similar to the first case of confined flow. There exists a stagnation point on the axis and its location is primarily controlled by current density, fluid drainage rate, and th...

The motion of a trailing vortex-wake in a stratified medium

Abstract An analytical study of a trailing vortex-wake in a uniform and a stratified environment is presented. A turbulent entrainment velocity is postulated based on the assumption of similarity of the wake surface and consistent with several averaged conservation equations. In a homogeneous density environment, the descending wake is brought to rest due to its buoyancy in the initial phase of wake motion. It is then accelerated upwards. The lifetimes of the wakes are found to be in excellent agreement with previous experimental results. In the absence of mutual interaction of vortices in the wake, the final ascending phase is a decelerating phase. The effect of weak linear stratification is to damp the movement of the vortex wake. The wake oscillates with decreasing amplitude and wavelengths with increasing magnitudes of linear stratification.

Nonlinear stability of cylindrical vortex enclosing a central jet of light or dense fluid

A nonlinear analysis of the inviscid stability of a cylindrical vortex enclosing a central jet of light or dense fluid is presented. A uniformly valid second‐order expansion is obtained using the method of multiple time scales. For a stagnant core surrounded by a potential vortex, the axisymmetric mode remains stable to various scales of disturbances independent of core density. For asymmetric modes, the nonlinear effects make the stagnant core vortex sheet more unstable in second order for a given value of the core density. A central jet of any finite density always has a destabilizing effect on the jet‐vortex system undergoing any mode of deformation. A jet of any velocity tends to increase the unstable growth rates with increasing order of perturbations. The surface tension has a stabilizing effect with increasing order of perturbations. The frequency of oscillation becomes amplitude dependent in various orders of perturbations. The cylindrical surface departs significantly from its initially perturbed...

Fluid motion caused by conical currents

Exact analytical solution for motion of an incompressible inviscid fluid and numerical solutions for viscous fluid flow caused by conical flow of current are given. Breakdown of viscous solutions at a critical value of current parameter depending on cone angle is discussed.

Heat transfer in cylindrical shrouded cavities

Abstract The flow field, temperature field and the heat transfer rates in cylindrical shrouded cavities with rotation, recirculation and coolant through-flow have been analyzed numerically. Two cavity configurations are considered. In the first configuration, a heated cylindrical shroud is enclosed by a stationary insulated stator disc and a rotating insulated rotor disc. The coolant air enters the cavity by a central opening in the rotor and exits through an annular gap at the rim of the rotor. The second configuration studies the heat transfer from an air cooled gas turbine disc using the model of a plane disc rotating close to an insulated shrouded stator. The coolant enters centrally through the stator disc and exits radially through a gap between the shroud and the rotor. The flow field and heat transfer rates are computed for several values of coolant flow rate, the rotor swirl speed, the cavity aspect ratio and the exit gap width in the two cavity configurations. The swirl of the rotor changes immensely the flow pattern, recirculating zones and isotherms inside such cavities. In general, increasing coolant flow rate, decreasing swirl and decreasing aspect ratio enhances the heat transfer from the shroud in the first cavity configuration. For the second cavity configuration, the heat transfer rates increase with increasing coolant flow rate, increasing swirl of the rotor, increasing size of the cavity and decreasing exit gap width between the stator and the rotor.