nan Pratibha

Two Perturbation Calculations in Fluid Mechanics using Large-expression Management

Two fluid-flow problems are solved using perturbation expansions, with special emphasis on the reduction of intermediate expression swell. This is done by developing tools in Maple that contribute to the efficient representation and manipulation of large expressions. The tools share a common basis, which is the creation of a hierarchy of representation levels such that expressions located at higher levels are expressed using entries from lower levels. The evaluation of higher-level expressions by the algebra system does not proceed recursively to the lowest level, as would ordinarily be the case, but instead can be directly controlled by the user.The first fluid-flow problem, arising in lubrication theory, is solved by implementing a technique of switch-controlled evaluation. The processes of simplification and evaluation are controlled at each level by user-manipulated switches. A perturbation solution is derived semi-interactively with the switch-controlled evaluation being used to reduce the size of intermediate expressions. The second fluid problem, in convection, is solved by extending a perturbation series in several variables to high order by implementing techniques for the automatic generation of hierarchical expression sequences.

REGULAR AND WELL-BEHAVED RELATIVISTIC CHARGED SUPERDENSE STAR MODELS

A new class of charged superdense star models is obtained by using an electric intensity, which involves two parameters, K and n. The metric describing the model shares its metric potential g44 with that of Durgapals fourth solution.1 The pressure-free surface is kept at the density 2 × 1014g/cm3and joins smoothly the Reissner–Nordstrom solution. The neutral solution is well-behaved for 0 < Ca2 ≤ 0.2645, while its charge analogs are well-behaved for a wide range, 0 < K < 32, i.e. the pressure, density, pressure–density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.1826 MΘ and 19.7120 km, respectively for Ca2 = 0.2645, while the redshift at the center and at the surface are given by Z0 = 1.6444 and Za = 0.6538, respectively. For the charged solution, the maximum mass and radius are 6.3811MΘ and 19.1609 km, respectively for K = 1.4, n = 1 and Ca2 = 0.5016, with the redshift at the center Z0 = 3.7437 and at the surface Za = 1.1038.

Invariant solutions of Einstein field equation for nonconformally flat fluid spheres of embedding class one

In the present paper, nonconformal spherical symmetric perfect fluid solutions to Einstein field equations are obtained by using the invariance of the equations under the Lie group of transformations and some new solutions of this category are obtained satisfying the reality conditions like ρ ≥ p ≥ 0, ρr < 0, pr < 0 (p and ρ being pressure and energy-density respectively) in the region 0 < r < a. Such fluids do not represent isolated fluid spheres as pressure free interface is not possible for nonconformally perfect fluids of class one.

SOME NONCONFORMAL ACCELERATING PERFECT FLUID PLATES OF EMBEDDING CLASS 1 USING SIMILARITY TRANSFORMATIONS

In view of renewed interest in the space–time embedded in higher-dimensional flat space which are useful in extrinsic gravity, string and brane theory, a set of six explicit solutions to Einsteins field equations for nonconformally flat accelerating and shearing perfect fluid plates is obtained using similarity transformations method by considering a five-dimensional flat metric. All the solutions thus obtained are analyzed physically. All the solutions are new in their respective category as far as authors are aware.

Effects of first-order chemical reactions on the dispersion coefficient associated with laminar flow through the lungs

This paper aims to look into the determination of effective area-average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute undergoes first-order chemical reaction both within the fluid and at the boundary. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. To understand the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Finite Difference Method. The resultant equation shows how the dispersion coefficient is influenced by the first-order chemical reaction. The effects of various dimensionless parameters e.g. Da (the Damkohler number), α (phase partitioning number) and Γ (dimensionless absorption number) on dispersion are discussed. One of the results exposes that the dispersion coefficient may approach its steady-state limit in a short time at a high value of Damkohler number (say Da ≥ 10) and a small but nonzero value of absorption rate (say Γ ≤ 0.5).

Using fast Hartley transform to study the free oscillations of the earth

In recent years, Hartley Transform (HT) as a substitute of much widely used Fourier Transform (FT) has been practised in science and industries. The advantage of faster computation of HT is enormous when one is dealing with very long data sets. One such application arises in computation of parameters of Free Oscillations of the Earth (FOE), where one needs to study very long period vibrations of the earth, excited after a large earthquake. We demonstrate here an application of HT to determine the parameters of these normal modes of the earth after the Minahasa Peninsula earthquake of 18 April 1990 (Ms = 7.5).

Stokes-Flow problem solved using maple

An unusual boundary-value problem that arises in a fluid-mechanical application is solved to high precision, as a challenge problem in scientific computation. A second-order differential equation must be solved on (0,∞ ), subject to boundary conditions that specify only the asymptotic behaviour of the solution at the two ends of the solution domain. In addition, the solution is required to high accuracy to settle a conjecture made by previous authors. The solution is obtained by computing multiple series solutions using Maple.

An Efficient Hybrid Approach for Simulating MHD Nanofluid Flow over a Permeable Stretching Sheet

The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a nanofluid under the effect of heat generation and partial slip is simulated using numeric symbolic approach. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDEs are transformed into a set of ODEs with the help of transformations. The differential equations are solved by variational finite element method as well as hybrid approach. The results obtained by the two approaches match well. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The comparison confirms excellent agreement. The efficiency of the hybrid approach is demonstrated through a table. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.

Effect of speed fluctuations due to driving imperfections on road traffic noise emission

Propagation of traffic noise in metro cities is a complex phenomenon. Since fluctuations in traffic flow are basic nature of a traffic stream, it can be studied by using Cellular Automata (CA). Braking tendencies among vehicles which reflect the driving imperfections affect the overall traffic flow. CA traffic flow model gives the wide description of stochastic nature of traffic flow. The present study reveals the influence of stochastic nature of traffic flow over traffic noise emission. Vehicles are classified into 7 types. To simulate traffic flow CA is used with simple updated rules for movement of vehicles. Stochastic CA is used for calculating flow, average speed and equivalent Sound Pressure Level (SPL) of traffic stream for various densities. Influence of speed fluctuations in continuous traffic streams over the noise emission level of different types of vehicles has been studied in conditions in India. A value of braking parameter p has been estimated for road conditions in India which is found suitable when compared with real observed data.

Numerical Study of Blood Partial Pressure of the Human Respiratory System

The study of blood partial pressure of human respiratory system is an important subject of human health. Respiration is the process of breathing in and out through the respiratory system. Lungs, Airways, Diaphragm, windpipe, Throat, Mouth, and Nasal passage are all parts of the respiratory system. People in certain jobs are more likely to have respiratory problems. The construction of a model and its analysis are actually linked with understanding the nature of the mechanism, including physiological mechanisms that satisfy the need of living organism. In the present paper we study the blood partial pressure of the human respiratory system numerically. Blood pressure depends on the heart rate and ventilation, since heart rate and ventilation are playing the important role in controlling the blood pressure. Jean Marie et al (2007) developed a mathematical model for blood partial pressure of the human respiratory system and discussed about the heart rate and ventilation functions. They have used two non linear coupled ordinary differential equations associated to blood pressure in arterial and in venous system. We are using the functions of heart rate and ventilation for determining the blood partial pressure in arterial and venous system. The solution of the system of nonlinear coupled ordinary differential equations is obtained numerically by using Runge Kutta Fourth Order method and the code of this problem in C++ language is also developed.