Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Free convection heat transfer from vertical cylinders part II: Exponential surface temperature variation

Investigation on laminar free convection heat transfer from vertical cylinders and wires having a surface temperature variation of the form TW - T∞ = M emx are presented. As in Part I for power law surface temperature variation, the axisymmetric boundary layer equations of mass, momentum and energy are transformed to more convenient forms and solved numerically. The second approximation refines the results of the first upto a maximum of only 2%. Analysis of the results indicates that cylinders can be classified into the same three categories as in Part I, namely, short cylinders, long cylinders, and wires, heat transfer and fluid flow correlations being developed for each case.

Estimation of the critical viscous sublayer in heat transfer problems

Imagining a disturbance made on a compressible boundary layer with the help of a heat source, the critical viscous sublayer, through which the skin friction at any point on a surface is connected with the heat transferred from a heated element embedded in it, has been estimated. Under similar conditions of external flow (Ray1)) the ratio of the critical viscous sublayer to the undisturbed boundary layer thickness is about one-tenth in the laminar case and one hundredth in the turbulent case. These results are similar to those (cf.1)) found in shock wave boundary layer interaction problems.

Transient MHD stagnation flow of a non-Newtonian fluid due to impulsive motion from rest

The transient boundary layer flow and heat transfer of a viscous incompressible electrically conducting non-Newtonian power-law fluid in a stagnation region of a two-dimensional body in the presence of an applied magnetic field have been studied when the motion is induced impulsively from rest. The nonlinear partial differential equations governing the flow and heat transfer have been solved by the homotopy analysis method and by an implicit finite-difference scheme. For some cases, analytical or approximate solutions have also been obtained. The special interest are the effects of the power-law index, magnetic parameter and the generalized Prandtl number on the surface shear stress and heat transfer rate. In all cases, there is a smooth transition from the transient state to steady state. The shear stress and heat transfer rate at the surface are found to be significantly influenced by the power-law index N except for large time and they show opposite behaviour for steady and unsteady flows. The magnetic field strongly affects the surface shear stress, but its effect on the surface heat transfer rate is comparatively weak except for large time. On the other hand, the generalized Prandtl number exerts strong influence on the surface heat transfer. The skin friction coefficient and the Nusselt number decrease rapidly in a small interval 0 < t* < 1 and reach the steady-state values for t* >= 4. (C) 2010 Published by Elsevier Ltd.

Parametric Analysis Of Turbulent Wall Jets

The concept of a fully-developed flow based on the hypothesis of selective memory is here applied to general wall-jet type flows. In the presence of a (constant) external stream, the free-stream velocity and the jet momentum flux are taken to be the chief quantities governing the development of the wall jet: two additional nondimensional parameters, representing a momentum flux Reynolds number and the relative momentum defect in the initial boundary layer, are shown to have only a secondary effect on the fully-developed flow. The standard correlations so determined are also found to predict quite well the flow development in Gartshore and Newman's experiments on wall jets in adverse pressure gradients; possible reasons for this somewhat surprising result are discussed. Finally it is shown, by application to the still-air case, that the parameters discovered in incompressible flow are, with appropriate but straightforward modification, successful in describing compressible wall jets also.

Localised instability in unsteady separation bubbles

We propose in experimental method to study the instability of thin unsteady separation bubbles, i.e. of unsteady boundary layers with reverse flow. The unsteady boundary layer is created by controlled temporal and spatial variations of the velocity external to the boundary layer. We present results of the evolution of instability in different temporally varying flows in a shallow angle diffuser. Depending on the extent of reverse flow in the boundary we observe that instability can be spatially localised.

Unsteady mixed convection flow of a thermomicropolar fluid on a long thin vertical cylinder

The unsteady laminar mixed convection boundary layer flow of a thermomicropolar fluid over a long thin vertical cylinder has been studied when the free stream velocity varies with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite difference scheme in combination with the quasilinearization technique. The results show that the buoyancy, curvature and suction parameters, in general, enhance the skin friction, heat transfer and gradient of microrotation, but the effect of injection is just opposite. The skin friction and heat transfer for the micropolar fluid are considerably less than those for the Newtonian fluids. The effect of microrotation parameter is appreciable only on the microrotation gradient. The effect of the Prandtl number is appreciable on the skin friction, heat transfer and gradient of microtation.

Generalised vortex motion of compressible fluid with and without magnetic field and suction

The laminar boundary layer over a stationary infinite disk induced by a rotating compressible fluid is considered. The free stream velocity has been taken as tangential and varies as a power of radius, i.e. v∞ ˜ r−n. The effect of the axial magnetic field and suction is also included in the analysis. An implicit finite difference scheme is employed to the governing similarity equations for numerical computations. Solutions are studied for various values of disk to fluid temperature ratio and for values of n between 1 and −1. In the absence of the magnetic field and suction, velocity profiles exhibit oscillations. It has been observed that for a hot disk in the presence of a magnetic field the boundary layer solutions decay algebraically instead of decaying exponentially. In the absence of the magnetic field and suction, the solution of the similarity equations exists only for a certain range of n.

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.

Unsteady MHD forced flow due to a point sink

An analysis is performed to study the unsteady laminar incompressible boundary-layer flow of an electrically conducting fluid in a cone due to a point sink with an applied magnetic field. The unsteadiness in the flow is considered for two types of motion, viz. the motion arising due to the free stream velocity varying continuously with time and the transient motion occurring due to an impulsive change either in the strength of the point sink or in the wall temperature. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The magnetic field increases the skin friction but reduces heat transfer. The heat transfer and temperature field are strongly influenced by the viscous dissipation and Prandtl number. The velocity field is more affected at the early stage of the transient motion, caused by an impulsive change in the strength of the point sink, as compared to the temperature field. When the transient motion is caused by a sudden change in the wall temperature, both skin friction and heat transfer take more time to reach a new steady state. The transient nature of the flow and heat transfer is active for a short time in the case of suction and for a long time in the case of injection. The viscous dissipation prolongs the transient behavior of the flow.

A numerical study of the role of the vertical structure of vorticity during tropical cyclone genesis

An eight-level axisymmetric model with simple parameterizations for clouds and the atmospheric boundary layer was developed to examine the evolution of vortices that are precursors to tropical cyclones. The effect of vertical distributions of vorticity, especially that arising from a merger of mid-level vortices, was studied by us to provide support for a new vortex-merger theory of tropical cyclone genesis. The basic model was validated with the analytical results available for the spin-down of axisymmetric vortices. With the inclusion of the cloud and boundary layer parameterizations, the evolution of deep vortices into hurricanes and the subsequent decay are simulated quite well. The effects of several parameters such as the initial vortex strength, radius of maximum winds, sea-surface temperature and latitude (Coriolis parameter) on the evolution were examined. A new finding is the manner in which mid-level vortices of the same strength decay and how, on simulated merger of these mid-level vortices, the resulting vortex amplifies to hurricane strength in a realistic time frame. The importance of sea-surface temperature on the evolution of full vortices was studied and explained. Also it was found that the strength of the surface vortex determines the time taken by the deep vortex to amplify to hurricane strength.

The hard-particle model for a dense granular flow down an inclined plane

Perfectly hard particles are those which experience an infinite repulsive force when they overlap, and no force when they do not overlap. In the hard-particle model, the only static state is the isostatic state where the forces between particles are statically determinate. In the flowing state, the interactions between particles are instantaneous because the time of contact approaches zero in the limit of infinite particle stiffness. Here, we discuss the development of a hard particle model for a realistic granular flow down an inclined plane, and examine its utility for predicting the salient features both qualitatively and quantitatively. We first discuss Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.58 are in the rapid flow regime, due to the very high particle stiffness. An important length scale in the shear flow of inelastic particles is the `conduction length' delta = (d/(1 - e(2))(1/2)), where d is the particle diameter and e is the coefficient of restitution. When the macroscopic scale h (height of the flowing layer) is larger than the conduction length, the rates of shear production and inelastic dissipation are nearly equal in the bulk of the flow, while the rate of conduction of energy is O((delta/h)(2)) smaller than the rate of dissipation of energy. Energy conduction is important in boundary layers of thickness delta at the top and bottom. The flow in the boundary layer at the top and bottom is examined using asymptotic analysis. We derive an exact relationship showing that the a boundary layer solution exists only if the volume fraction in the bulk decreases as the angle of inclination is increased. In the opposite case, where the volume fraction increases as the angle of inclination is increased, there is no boundary layer solution. The boundary layer theory also provides us with a way of understanding the cessation of flow when at a given angle of inclination when the height of the layer is decreased below a value h(stop), which is a function of the angle of inclination. There is dissipation of energy due to particle collisions in the flow as well as due to particle collisions with the base, and the fraction of energy dissipation in the base increases as the thickness decreases. When the shear production in the flow cannot compensate for the additional energy drawn out of the flow due to the wall collisions, the temperature decreases to zero and the flow stops. Scaling relations can be derived for h(stop) as a function of angle of inclination.

Combined free and forced convection along a rotating vertical cylinder

The steady incompressible laminar mixed convection boundary layer flow along a rotating slender vertical cylinder with an isothermal wall has been studied. The transformed coupled nonlinear partial differential equations have been solved numerically using the Keller box method. In general, the rotation of the cylinder, the buoyancy forces and the curvature parameter are found to significantly affect the skin friction, heat transfer, velocity and temperature profiles as well as the pressure distribution. The buoyancy forces cause an overshoot in the axial velocity profile but the rotation and curvature parameters reduce it.

Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface

A numerical solution of the unsteady boundary layer equations under similarity assumptions is obtained. The solution represents the three-dimensional unsteady fluid motion caused by the time-dependent stretching of a flat boundary. It has been shown that a self-similar solution exists when either the rate of stretching is decreasing with time or it is constant. Three different numerical techniques are applied and a comparison is made among them as well as with earlier results. Analysis is made for various situations like deceleration in stretching of the boundary, mass transfer at the surface, saddle and nodal point flows, and the effect of a magnetic field. Both the constant temperature and constant heat flux conditions at the wall have been studied.

Low-voltage varistors from ZnO+CaMnO3 ceramics

: Varistors prepared from ZnO with CaMnO3 perovskite as the only forming additive, exhibit voltage-limiting current-voltage characteristics with nonlinearity coefficient alpha up to 380 at low voltages of 1.8-12 V/mm. High nonlinearity is observed only with a suitable combination of processing parameters. The most crucial of them are (i) initial formulation of ceramics and (ii) the sintering temperature and conditions of post-sinter annealing. An electrically active intergranular phase is formed between ZnO grains with the composition ranging from Ca4Mn6Zn4O17 to Ca4Mn8Zn3O19, which creates the n-p-n heterojunctions. The low-voltage nonlinearity originates as a result of higher concentration of Mn(III)/Mn(IV) present at the grain boundary layer regions, being charge compensated by zinc vacancies. Under the external electric field, the barrier height is lowered due to the uphill diffusion of holes mediated by the acceptor states. Above the turn-on voltages, the unhindered transport of charge carriers between grains generates high current density associated with large nonlinearity.