Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation

In this paper an analysis has been made to study heat and mass transfer in two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in the presence of buoyancy force and thermal radiation. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations containing Prandtl number, Schmidt number and Sherwood number which are solved numerically with appropriate boundary conditions for various values of the dimensionless parameters. Comparison of the present numerical results are found to be in excellent with the earlier published results under limiting cases. The effects of various physical parameters on the boundary layer velocity, temperature and concentration profiles are discussed in detail for both the cases of assisting and opposing flows. The computed values of the skin friction coefficient, local Nusselt number and Sherwood number are discussed for various values of physical parameters. The tabulated results show that the effect of radiation is to increase skin friction coefficient, local Nusselt number and Sherwood number.     

The modified constrained volume model predictions in shearing flow at nonunity viscosity ratio values

In this paper, the modified constrained volume model, which describes the evolution of anisotropy of immiscible polymer blends, composed of Newtonian components, was examined during shearing motion (steady and oscillatory) at various viscosity ratio values. We found that the linear correction to the rate of deformation tensor causes the droplet to change its volume at viscosity ratio values lower than unity, and to cause premature tumbling at viscosity ratio values larger than unity, in a case where retraction, breakup, and coalescence modules of the model were turned off. The use of Eshelby tensor, together with a closure to relate anisotropy to the Eshelby concentration tensor, mostly solved the problem. The model’s predictions are then shown at various capillary number values and at various viscosity ratio values. Comparison of model predictions to single droplet data at nonunity viscosity ratio value showed good agreement. Finally, model predictions of first normal stress difference during startup of steady shear are compared to experimental rheological results for immiscible polymer blends that are available in literature. Good predictions can be achieved by the introduction of a new switch function that controls the retraction and breakup modules. The model’s predictions at large amplitude oscillatory shear were examined. It was found that linear corrections to the velocity gradient tensor can be used for strains up to 100 %. For larger strain values, the Eshelby concentration tensor must be used.     

Horizontal structure of atmospheric tidal oscillations

The horizontal structure of atmospheric tidal oscillations determined by the solutions of Laplace’s tidal equation for various values of the equivalent depths, including negative values, is considered. The eigenfrequencies and modes are obtained numerically over a wide equivalent depth range. The frequencies and modes are investigated for negative values of the equivalent depth. The negative equivalent depth modes are classified. The numerical results are compared with well-known asymptotic formulas.     

Chemical reaction effects on unsteady MHD flow past semi-infinite vertical porous plate with viscous dissipation

The chemical reaction effect on an unsteady magnetohydrodynamic (MHD) flow past a semi-infinite vertical porous plate with viscous dissipation is analyzed. The governing equations of motion, energy, and species are transformed into ordinary differential equations (ODEs) using the time dependent similarity parameter. The resultant ODEs are then solved numerically by a finite element method. The effects of various parameters on the velocity, temperature, and concentration profiles are presented graphically, and the values of the skin-friction, Nusselt number, and Sherwood number for various values of physical parameters are presented through tables.     

On the rotation of a rotlet or sphere in the presence of an interface

The flows produced by a rotlet and a sphere rotating perpendicular to an interface separating two immiscible fluids are studied, and exact solutions are constructed in terms of the stream function and velocity. A comprehensive set of values for the torque acting on a sphere for various values of the parameters defining the ratio of sphere radius to its distance from the interface and the ratio of viscosities is given.     

MHD forced convection boundary layer flow with a flat plate and porous substrate

The flow and heat transfer for an electrically conducting fluid with a porous substrate and a flat plate under the influence of magnetic field is considered. The magnetic field is assumed to be uniform and also along normal to the surface. The momentum and energy equations are transformed to ordinary differential equations by using suitable similarity transformation and are solved by standard techniques. But the energy equation is solved by considering two boundary layers, one in the porous substrate and the other above the porous substrate. Numerical results are presented through graphs with various values of magnetic parameter for both velocity and thermal boundary layers along with Nusselt number and for various values of Prandtl number and Eckert number in thermal boundary layer.     

Time-optimal swing-up feedback control of a pendulum

Time-optimal feedback control is obtained that brings a pendulum to the upper unstable equilibrium position. The solution is based on the maximum principle and involves analytical investigations combined with numerical computations. As a result, the switching and dispersal curves that bound the domains in the phase plane corresponding to different values of the optimal bang-bang control are constructed for various values of the maximal admissible control torque.     

Fluid Flows past Spheroids at Moderate Reynolds Numbers

Axisymmetric viscous fluid flows past spheroids are considered. The time-independent complete Navier-Stokes equations written in a spherical coordinate system are used for describing the flow. The problem is solved by the stabilization method on the basis of a variable direction scheme. The input coordinate system is transformed in order to construct a regular computational grid. As a result of the numerical investigation, the stream patterns of flow past elongated and oblate spheroids are obtained for various values of the determining parameters. Numerical values of the dimensions of the circulation zone and the drag coefficient are given for various values of the spheroid semi-axis ratio in the domain of moderate Reynolds numbers.     

Mathematical model of axisymmetric quasi-steady-state heat and mass transfer in a gas hydrate reservoir

Two problems of axisymmetric gas (gas and water) flow through a reservoir which contains a heterogeneous mixture, namely, gas hydrate, ice (water), and gas, are considered. The exact solutions to the corresponding steady-state and quasi-steady-state nonlinear problems are found. The critical diagrams are constructed for various flow regimes. The characteristic distributions of the gas hydrate, ice (water), and gas saturations are shown for various values of the parameters.     

Choice of optimal blunting radius of axisymmetric body with account for surface radiation

We consider the problem of determining the optimal blunting with respect to heat transfer of an axisymmetric body in supersonic gas flow at zero angle of attack with account for body surface radiation. Results are presented of a calculation of the optimal blunting radius of a cone with half-angle 10° for various values of the ratio of convective heat flux at the stagnation point to the radiative heat flux. It is shown that for small values of this ratio the small bluntings are optimal.     

The Stability in Two Measures of Axially Compressed Elastic Cylinders

Two nonnegative integral functionals are taken as measures of deviation of the basic solution from a perturbed one. Sufficient conditions of stability in selected measures are obtained for the zero solution of the linearized equation of motion for isotropic elastic bodies acted upon by "dead" surface forces. The method of integral estimates is used to determine the critical values of the loading parameters. Such values are found for an axially compressed cylindrical body made of a standard material of the second order under various end conditions     

Fluctuating flow of a second-order fluid near a stagnation point

Summary The boundary layer equations for axisymmetric flow of an incompressible second-order fluid have been deduced. The flow of such a fluid near a stagnation point when the main stream outside the boundary layer fluctuates in magnitude but not in direction has been discussed. The velocity distribution is found for various values of the steady mean in two limiting cases of small and large values of the frequency of the oscillation of the main stream. The frequency for which two approximate solutions overlap has been calculated in each case.     

Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

The nature of singularities at the vertex of conical notches and inclusions is found for problems of potential theory and for elastostatic problems of torsion and of axisymmetric stress. A solution in terms of spherical harmonics and a general numerical solution based upon the field equations are used to determine the power dependence of the field quantities upon the distance from the apex of the cone. Eigenvalues representing the exponent are computed for various values of cone angle and for various Poisson ratios.     

Criterion for establishing deviations from the local thermodynamic equilibrium in atmospheric pressure plasma jets

In this paper a dimensionless parameter is defined which allows the prediction of the thermodynamic state in the field-free plasma jet of D. C. operated plasma torches of various designs. This dimensionless parameterP is derived from the conservation equations applied to a two-step temperature and velocity model and contains only quantities which can be experimentally determined without using sophisticated equipment. Critical values ofP based on a critical electron density of 10¹⁶ cm^?3 have been calculated for argon, hydrogen, nitrogen, oxygen, and helium and corresponding values of P_crit have been determined experimentally for two different D. C. operated argon plasma torches using various diagnostic techniques. The experimental values corroborate the assumptions made for the calculation of P_crit. ForP < P_crit, substantial deviations from the local thermodynamic equilibrium (LTE) may occur.     

Time-dependent fiber spinning equations. 2. Analysis of the stability of numerical approximations

The truncated time-dependent one-dimensional fiber spinning equations for an Upper Convected Maxwell model, presented in the previous paper [1], are approximated using various numerical methods. The eigenvalues and eigenfunctions of the linearized problem around the steady-state solution are calculated and compared against the analytical results for various values of Deborah and Reynolds numbers.It is shown that upwind formulations of Finite-Difference and Finite-Element methods produce the most stable results. The most accurate eigenvalues and eigensolutions are those calculated by Pseudospectral methods. However, both Chebyshev and Legendre Pseudospectral methods become unstable at high values of De. Finally, it is shown that the boundary conditions have to be incorporated into the numerical scheme in a suitable way; spectacular instabilities might be generated otherwise.     

Temperature dependent mechanical behaviour of PVDF: Experiments and numerical modelling

The mechanical behaviour of Polyvinylidene Fluoride (PVDF) is analysed. To this end, tensile tests are performed on both smooth and notched specimens, for several values of the notch radius in order to set specific values of the stress triaxiality ratio in the net section. Tests were performed at various temperatures and at various strain rates. Experimental data together with fracture surface examinations by SEM allow the dependence of deformation and void growth processes on strain rate and temperature to be investigated. This experimental work was carried out in order to test the mechanics of porous media model. For each investigated temperature, constitutive relations take both porosity and strain rate sensitivity into account. The model is proposed for deformation leading to crazing. The material coefficients are optimised by imposing a continuous dependence on temperature.     

一种改进的位移反分析方法

为了发展可用于各种岩土工程及工程地质问题的一般的位移反分析系统方法, 本文在边界控制方法的基础上进行了改进。其目的是对于其各种复杂的系统问题确定最重要的力学参数。     

An optimal method for the design of a robotic tracked vehicle to operate over fresh concrete under steering motion

The objective of this paper is to find an optimal method for the design of tracked base travel systems for special purpose vehicles and robotic machines that may be required to steer over a light bonded terrain composed of fresh concrete. For the case of a vehicle traveling on a weak fresh concrete during construction, the paper presents detailed comparative studies of the steering performances of a small model tracked test vehicle with alternative amount of steering ratio for various concrete slump values. For these studies a detailed simulation analytical method has been developed. From this work it is proven, in comparison to experiment, that the simulation analytical method is useful for predicting various steering performances of a test tracked vehicle running upon soft fresh concrete of various consistencies.     

Free-convection flow about a wedge under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a wedge with mixed thermal boundary conditions. Boundary-layer velocity and temperature profiles were determined numerically for various values of the Prandtl number and the magnetic parameter. The results show that the magnetic field retards the velocity profiles and increases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in higher surface temperatures. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.     

Natural convection flow over a vertical frustum of a cone for constant wall heat flux

Laminar natural convection flow and heat transfer over a vertical frustum of a cone has been studied. The governing boundary layer equations are solved using local non-similarity method for constant wall heat flux. The local similarity and the local non-similarity two and three-equation models are constructed and the resulting equations are solved numerically. Results obtained from two and three-equation models are in good agreement. The numerical values of the flow and temperature functions required to calculate the surface skin friction and heat transfer rate are reported for various values of Prandtl numbers.