Unsteady mixed convection with double diffusion over a horizontal cylinder and a sphere within a porous medium

The combined effects of the permeability of the medium, magnetic field, buoyancy forces and dissipation on the unsteady mixed convection flow over a horizontal cylinder and a sphere embedded in a porous medium have been studied. The nonlinear coupled partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The skin friction, heat transfer and mass transfer increase with the permeability of the medium, magnetic field and buoyancy parameter. The heat and mass transfer continuously decrease with the stream-wise distance, whereas the skin friction increases from zero, attains a maximum and then decreases to zero. The skin friction, heat transfer and mass transfer are significantly affected by the free stream velocity distribution. The effect of dissipation parameter is found to be more pronounced on the heat transfer than on the skin friction and mass transfer

Second-order boundary-layer effects for the unsteady laminar incompressible three-dimensional stagnation-point flow

All the second-order boundary-layer effects on the unsteady laminar incompressible flow at the stagnation-point of a three-dimensional body for both nodal and saddle point regions have been studied. It has been assumed that the free-stream velocity, wall temperature and mass transfer vary arbitrarily with time. The effect of the Prandtl number has been taken into account. The partial differential equations governing the flow have been derived for the first time and then solved numerically unsteady free-stream velocity distributions, the nature of the using an implicit finite-difference scheme. It is found that the stagnation point and the mass transfer strongly affect the skin friction and heat transfer whereas the effects of the Prandtl number and the variation of the wall temperature with time are only on the heat transfer. The skin friction due to the combined effects of first- and second-order boundary layers is less than the skin friction due to, the first-order boundary layers whereas the heat transfer has the opposite behaviour. Suction increases the skin friction and heat transfer but injection does the opposite

Natural Convection on a Horizontal Cone in a Porous Medium with Non-Uniform Wall Temperature/Concentration or Heat/Mass Flux and Suction/Injection

The steady natural convection flow on a horizontal cone embedded in a saturated porous medium with non-uniform wall temperature/concentration or heat/mass flux and suction/injection has been investigated. Non-similar solutions have been obtained. The nonlinear couple differential equations under boundary layer approximations governing the flow have been numerically solved. The Nusselt and Sherwood numbers are found to depend on the buoyancy forces, suction/injection rates, variation of wall temperature/concentration or heat/mass flux, Lewis number and the non-Darcy parameter.

Compressible Boundary-Layer Swirling Flow in a Nozzle and a Diffuser With Highly Cooled Wall

The steady laminar compressible boundary-layer swirling flow with variable gas properties and mass transfer through a conical nozzle, and a diffuser with a highly cooled wall has been studied. The partial differential equations governing the nonsimilar flow have been transformed to a system of coordinates using modified Lees transformation. The resulting equations are transformed into coordinates having finite ranges by means of a transformation which maps an infinite region into a finite region. The ensuing equations are then solved numerically using an implicit finite-difference scheme. The results indicate that the variation of the density-viscosity product across the boundary layer and mass transfer have strong effect on the skin friction and heat transfer. Separationless flow along the entire length of the diffuser can be obtained by applying suction. The results are found to be in good agreement with those of the local nonsimilarity method but they differ appreciably from those of the local similarity method.

Investigation of the effect of nonlocal scale on ultrasonic wave dispersion characteristics of a monolayer graphene

In this article, an ultrasonic wave propagation in graphene sheet is studied using nonlocal elasticity theory incorporating small scale effects. The graphene sheet is modeled as an isotropic plate of one-atom thick. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of wave propagation model is also derived for the graphene sheet. The nonlocal scale parameter introduces certain band gap region in in-plane and flexural wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. The explicit expressions for cutoff frequencies and escape frequencies are derived. The escape frequencies are mainly introduced because of the nonlocal elasticity. Obviously these frequencies are function of nonlocal scaling parameter. It has also been obtained that these frequencies are independent of y-directional wavenumber. It means that for any type of nanostructure, the escape frequencies are purely a function of nonlocal scaling parameter only. It is also independent of the geometry of the structure. It has been found that the cutoff frequencies are function of nonlocal scaling parameter (e(0)a) and the y-directional wavenumber (k(y)). For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(o)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this paper. (C) 2010 Elsevier B.V. All rights reserved.

Flow and heat transfer in steady laminar compressible boundary layer swirling flow in a nozzle

The axisymmetric steady laminar compressible boundary layer swirling flow of a gas with variable properties in a nozzle has been investigated. The partial differential equations governing the non-similar flow have been transformed into new co-ordinates having finite ranges by means of a transformation which maps an infinite range into a finite one. The resulting equations have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for compressible swirling flow through a convergent conical nozzle. The results indicate that the swirl exerts a strong influence on the longitudinal skin friction, but its effect on the tangential skin friction and heat transfer is comparatively small. The effect of the variation of the density-viscosity product across the boundary layer is appreciable only at low-wall temperature. The results are in good agreement with those of the local-similarity method for small values of the longitudinal distance.

Free vibration of circular plates of arbitrary thickness

Free vibration of circular plates of arbitrary thickness is investigated using the method of initial functions. State-space approach is used to derive the governing equations of the above method. The formulation is such that theories of any desired order can be obtained by deleting higher terms in the infinite-order differential equations. Numerical results are obtained for flexural and extensional vibration of circular plates. Results are also computed using Mindlin's theory and they are in agreement with the present analysis.

Unsteady three-dimensional boundary layer flow over a flat plate with attached cylinder

The unsteady laminar incompressible three-dimensional boundary layer flow and heat transfer on a flat plate with an attached cylinder have been studied when the free stream velocity components and wall temperature vary inversely as linear and quadratic functions of time, respectively. The governing semisimilar partial differential equations with three independent variables have been solved numerically using a quasilinear finite-difference scheme. The results indicate that the skin friction increases with parameter ? which characterizes the unsteadiness in the free stream velocity and the streamwise distance Image , but the heat transfer decreases. However, the skin friction and heat transfer are found to change little along Image . The effect of the Prandtl number on the heat transfer is found to be more pronounced when ? is small, whereas the effect of the dissipation parameter is more pronounced when ? is comparatively large.

Unsteady mixed convection over two-dimensional and axisymmetric bodies

The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The 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 indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows.

Unsteady boundary layer flow on a cylinder in a channel

The unsteady laminar incompressible nonsimilar boundary layer flow over a circular cylinder placed symmetrically inside a channel has been studied when the unsteadiness and nonsimilarity are due to the free stream velocity. The nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference in combination with the quasilinearization technique. It is found that the channel blockage parameter controls the transfer of heat from the cylinder and delays separation. The skin friction and heat transfer are significantly affected by the free stream velocity distributions.

Unsteady laminar compressible boundary-layer flow at a three-dimensional stagnation point

Unsteady laminar compressible boundary-layer flow with variable properties at a three-dimensional stagnation point for both cold and hot walls has been studied for the case when the velocity of the incident stream varies arbitrarily with time. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for two particular unsteady free-stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. The results indicate that the variation of the density-viscosity product across the boundary layer, the wall temperature and the nature of stagnation point significantly affect the skin friction and heat transfer.

An Experimental and Numerical Study of Calliphora Wing Structure

Experiments are performed to determine the mass and stiffness variations along the wing of the blowfly Calliphora. The results are obtained for a pairs of wings of 10 male flies and fresh wings are used. The wing is divided into nine locations along the span and seven locations along the chord based on venation patterns. The length and mass of the sections is measured and the mass per unit length is calculated. The bending stiffness measurements are taken at three locations, basal (near root), medial and distal (near tip) of the fly wing. Torsional stiffness measurements are also made and the elastic axis of the wing is approximately located. The experimental data is then used for structural modeling of the wing as a stepped cantilever beam with nine spanwise sections of varying mass per unit lengths, flexural rigidity (EI) and torsional rigidity (GJ) values. Inertial values of nine sections are found to approximately vary according to an exponentially decreasing law over the nine sections from root to tip and it is used to calculate an approximate value of Young's modulus of the wing biomaterial. Shear modulus is obtained assuming the wing biomaterial to be isotropic. Natural frequencies, both in bending and torsion, are obtained by solving the homogeneous part of the respective governing differential equations using the finite element method. The results provide a complete analysis of Calliphora wing structure and also provide guidelines for the biomimetic structural design of insect-scale flapping wings.

Propagation of quasi-simple waves in a compressible rotating atmosphere

A class of self-propagating linear and nonlinear travelling wave solutions for compressible rotating fluid is studied using both numerical and analytical techiques. It is shown that, in general, a three dimensional linear wave is not periodic. However, for some range of wave numbers depending on rotation, horizontally propagating waves are periodic. When the rotation ohgr is equal to $$\sqrt {(\gamma - 1)/(4\gamma )}$$ , all horizontal waves are periodic. Here, gamma is the ratio of specific heats. The analytical study is based on phase space analysis. It reveals that the quasi-simple waves are periodic only in some plane, even when the propagation is horizontal, in contrast to the case of non-rotating flows for which there is a single parameter family of periodic solutions provided the waves propagate horizontally. A classification of the singular points of the governing differential equations for quasi-simple waves is also appended.

A mathematical analysis of nonlinear waves in a fluid filled visco-elastic tube

Our investigations in this paper are centred around the mathematical analysis of a ldquomodal waverdquo problem. We have considered the axisymmetric flow of an inviscid liquid in a thinwalled viscoelastic tube under certain simplifying assumptions. We have first derived the propagation space equations in the long wave limit and also given a general procedure to derive these equations for arbitrary wave length, when the flow is irrotational. We have used the method of operators of multiple scales to derive the nonlinear Schrödinger equation governing the modulation of periodic waves and we have elaborated on the ldquolong modulated wavesrdquo and the ldquomodulated long wavesrdquo. We have also examined the existence and stability of Stokes waves in this system. This is followed by a discussion of the progressive wave solutions of the long wave equations. One of the most important results of our paper is that the propagation space equations are no longer partial differential equations but they are in terms of pseudo-differential operators.Die vorliegenden Untersuchungen beziehen sich auf die mathematische Behandlung des ldquorModalwellenrdquo-Problems. Die achsensymmetrische Strömung einer nichtviskosen Flüssigkeit in einem dünnwandigen viskoelastischen Rohr, unter bestimmten vereinfachenden Annahmen, wird betrachtet. Zuerst werden die Gleichungen des Ausbreitungsraumes im Langwellenbereich abgeleitet und eine allgemeine Methode zur Herleitung dieser Gleichungen für beliebige Wellenlängen bei nichtrotierender Strömung angegeben. Eine Operatorenmethode mit multiplem Maßstab wird verwendet zur Herleitung der nichtlinearen Schrödinger-Gleichung für die Modulation der periodischen Wellen, und die ldquorlangmodulierten Wellenrdquo sowie die ldquormodulierten Langwellenrdquo werden aufgezeigt. Weiters wird die Existenz und die Stabilität der Stokes-Wellen im System untersucht. Anschließend werden die progressiven Wellenlösungen der Langwellengleichungen diskutiert. Eines der wichtigsten Ergebnisse dieser Arbeit ist, daß die Gleichungen des Ausbreitungsraumes keine partiellen Differentialgleichungen mehr sind, sondern Ausdrücke von Pseudo-Differentialoperatoren.

Heat conduction with a phase change in a cylindrical mould

Analytical short time solution of moving boundary in heat conduction in a cylindrical mould under prescribed flux boundary condition has been studied in this paper. Partial differential equations are converted to integro-differential equations. These integro-differential equations which are coupled have been solved analytically for short time by choosing suitable series expansions for the unknown quantitities.