Search results

The purpose of this paper is to study the effect of non‐uniform double slot suction (injection) into a steady laminar boundary layer flow over a yawed cylinder when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Non‐similar solutions have been obtained from the starting point of the streamwise co‐ordinate to the exact point of separation.

The governing equations are tackled by the implicit finite difference scheme in combination with the quasi‐linearization technique. Quasi‐linear technique can be viewed as a generalization of the Newton‐Raphson approximation technique in functional space. An iterative sequence of linear equations is carefully constructed to approximate the nonlinear equations for achieving quadratic convergence and monotonicity. The quadratic convergence and monotonicity are unique characteristics of the quasilinear implicit finite difference scheme, which makes this scheme superior to built‐in iteration of upwind or finite amplitude techniques.

The results indicate that the separation can be delayed by non‐uniform double slot suction and also by moving the slot downstream. However, the effect of non‐uniform double slot injection is just the opposite. Yaw angle has very little affect on the location of the point of separation.

This analysis is useful in understanding many boundary layer problems of practical importance for undersea applications, for example, in suppressing recirculating bubbles and controlling transition and/or separation of the boundary layer over submerged bodies.

The purpose of this paper is to investigate the problem of the initial attitude detumbling and acquisition for micro‐satellite using geomagnetism with the aid of the pitch momentum bias, and the application of the feedback linearization method, H_∞ and μ‐synthesize control theory in the robust attitude acquisition controller design.

The pitch flywheels establish the momentum bias state in the beginning of the detumbling stage and keep the momentum bias state thereafter. The geomagnetic change rate feedback detumbling controller is used to detumble the micro‐satellite and the gyroscope rigidity is utilized to capture orbital negative normal orientation in the detumbling and attitude acquisition phase. Feedback linearization method is adopted to obtain the linear attitude dynamics. Based on the feedback linearization model, a quasi proportion differential (PD) controller is designed, meanwhile H_∞ and μ‐synthesis control theories are adopted to synthesis the robust attitude acquisition controllers.

The pitch momentum bias‐aided attitude detumbling and acquisition method make the capture of the orbital negative normal orientation faster and more accurate than the classical initial operation process. Quasi PD and H_∞ have greater robustness than the classical PD attitude acquisition controller in normal geomagnetic case; quasi PD and μ‐synthesis have greater robustness than the classical PD attitude acquisition controller in magnetic storm case.

Provides pitch momentum bias‐aided attitude detumbling and acquisition method for the micro‐satellite and the robust attitude acquisition controller design technology.

The purpose of this paper is to propose a numerical scheme based on forward finite difference, quasi-linearisation process and polynomial differential quadrature method to find the numerical solutions of nonlinear Klein-Gordon equation with Dirichlet and Neumann boundary condition.

In first step, time derivative is discretised by forward difference method. Then, quasi-linearisation process is used to tackle the non-linearity in the equation. Finally, fully discretisation by differential quadrature method (DQM) leads to a system of linear equations which is solved by Gauss-elimination method.

The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions and the numerical solutions exist in literature. The proposed scheme can be expended for multidimensional problems.

The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points. Secondly, the scheme gives better accuracy than (Dehghan and Shokri, 2009; Pekmen and Tezer-Sezgin, 2012) by choosing less number of grid points and big time step length. Also, the scheme can be extended for multidimensional problems.

The focus of the paper is only on the contributions toward the use of entropy generation of non-Newtonian Casson fluid over an exponential stretching sheet. The purpose of this paper is to investigate the entropy generation and homogeneous–heterogeneous reaction. Velocity and thermal slips are considered instead of no-slip conditions at the boundary.

Basic equations in form of partial differential equations are converted into a system of ordinary differential equations and then solved using the spectral quasi-linearization method (SQLM).

The validity of the model is established using error analysis. Variation of the velocity, temperature, concentration profiles and entropy generation against some of the governing parameters are presented graphically. It is to be noted that the increase in entropy generation due to increase in heterogeneous reaction parameter is due to the increase in heat transfer irreversibility. It is further noted that the Bejan number decreases with Brinkman number because increase in Brinkman number reduces the total entropy generation.

This paper acquires realistic numerical explanations for rapidly convergent temperature and concentration profiles using the SQLM. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The resulting equations are then integrated using the SQLM. The influence of emergent flow, heat and mass transfer parameters effects are shown graphically.

The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement.

The nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water.

The effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr.

The present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.

The purpose of this paper is to present a computational technique based on Newton–Cotes quadrature rule for solving fractional order differential equation.

The numerical method reduces initial value problem into a system of algebraic equations. The method presented here is also applicable to non-linear differential equations. To deal with non-linear equations, a recursive sequence of approximations is developed using quasi-linearization technique.

The method is tested on several benchmark problems from the literature. Comparison shows the supremacy of proposed method in terms of robust accuracy and swift convergence. Method can work on several similar types of problems.

It has been demonstrated that many physical systems are modelled more accurately by fractional differential equations rather than classical differential equations. Therefore, it is vital to propose some efficient numerical method. The computational technique presented in this paper is based on Newton–Cotes quadrature rule and quasi-linearization. The key feature of the method is that it works efficiently for non-linear problems.

The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects. Effects of various fluid parameters such as suction/injection, viscous dissipation, magnetic parameter and heat source/sink on velocity and temperature profiles are numerically analyzed. Moreover, numerically investigated on skin-friction and heat transfer coefficients when suction/injection occur.

The governing coupled partial differential equations are transformed to dimensionless form using non-similarity transformations. The non-dimensional partial differential equations are linearized by quasi-linearization technique and solved by varga's algorithm with numerical finite difference scheme on a non-uniform mesh.

The computation results are presented in terms of temperature, heat transfer and skin friction coefficients; these are useful for determining surface heat requirements. It was found that, in finite difference scheme for non-uniform mesh with quasi-linearization technique method gives smoothness of solution compared to finite difference scheme for uniform mesh, and this evidence is graphically represented in Figure 2.

The impacts of viscous dissipation (Ec) and magnetic parameter (Ha) on temperature profiles, skin friction and heat transfer are analyzed, which determine the heat generation/absorption to ensure the MHD flow of the laminar boundary layer on irregular boundary over a diverging channel.

This article offered two meshfree algorithms, namely the local radial basis functions-finite difference (LRBF-FD) approximation and local radial basis functions-differential quadrature method (LRBF-DQM) to simulate the multidimensional hyperbolic wave models and work is an extension of Jiwari (2015).

In the evolvement of the first algorithm, the time derivative is discretized by the forward FD scheme and the Crank-Nicolson scheme is used for the rest of the terms. After that, the LRBF-FD approximation is used for spatial discretization and quasi-linearization process for linearization of the problem. Finally, the obtained linear system is solved by the LU decomposition method. In the development of the second algorithm, semi-discretization in space is done via LRBF-DQM and then an explicit RK4 is used for fully discretization in time.

For simulation purposes, some 1D and 2D wave models are pondered to instigate the chastity and competence of the developed algorithms.

The developed algorithms are novel for the multidimensional hyperbolic wave models. Also, the stability analysis of the second algorithm is a new work for these types of model.

The purpose of this paper is to investigate the magnetohydrodynamics mixed convection flow over an exponentially stretching surface in the presence of non-uniform heat source/sink and cross-diffusion. Adequate non-similar transformations are used to transform governing mixed convection boundary layer equations to dimensionless form.

These dimensionless partial differential equations are solved by using implicit finite difference scheme in conjunction with Quasi-linearization technique.

The effects of admissible parameters such as Eckert number (Ec), the ratio of buoyancy forces parameter (N), non-uniform heat source/sink, Soret and Dufour numbers on flow, temperature and concentration distributions are discussed and analysed through graphs. In addition, the results for skin friction coefficient, Sherwood number and Nusselt number are presented and discussed graphically.

In literature, no research work has been found in similar to this research paper.

The purpose of this paper is to study the influence of thermally stratified medium on a free convection flow from a sphere, which is rotating about the vertical axis, immersed in a stably thermally stratified medium.

An implicit finite‐difference scheme in combination with the quasi‐linearization technique is applied to obtain the steady state non‐similar solutions of the governing boundary layer equations for flow and temperature fields.

The numerical results indicate that the heat transfer rate at the wall decreases significantly with an increasing thermal stratification parameter, but its effect on the skin friction coefficients is rather minimum. In fact, the presence of thermal stratification of the medium influences the heat transfer at wall to be in opposite direction, that is, from fluids to the wall above a certain height. The heat transfer rate increases but the skin frictions decrease with the increase of Prandtl number. In particular, the effect of buoyancy force is much more sensitive for low Prandtl number fluids (Pr = 0.7, air) than that of high Prandtl number fluids (Pr = 7, water). Also the skin friction in rotating direction is less sensitive to the buoyancy force as the buoyancy force acts in the streamwise direction for the present study of thermally stratified medium.

The ambient temperature T_∞∞ is assumed to increase linearly with height $h$. The viscous dissipation term, which is usually small for natural convection flows, has been neglected in the energy equation. The flow is assumed to be axi‐symmetric. The Boussinesq approximation is invoked for the fluid properties to relate density changes to temperature changes, and to couple in this way the temperature field to the flow field.

Free convection in a thermally stratified medium occurs in many environmental processes with temperature stratification, and in industrial applications within a closed chamber with heated walls. Also, free convections associated with heat rejection systems for long‐duration deep ocean powder modules where ocean environment is stratified are examples of such type.

The research presented in this paper investigates the free convection flow on a sphere, which is rotating with a constant angular velocity along its vertical axis in a stably thermally stratified fluid.