Analytical approach to unidirectional flow of non-Newtonian fluids of differential type

This thesis is regarding the development of mathematical models and analytical techniques for non-Newtonian fluids of differential types on a vertical plate, horizontal channel, vertical channel, capillary tube and horizontal cylinder. For a vertical plate, a mathematical model of the unsteady flow of second-grade fluid generated by an oscillating wall with transpiration, and the problem of magnetohydrodynamic (MHD) flow of third-grade fluid in a porous medium, have been developed. General solutions for the second-grade fluid are derived using Laplace transform, perturbation and variable separation techniques, while for the third-grade fluid are derived using symmetry reduction and new modified homotopy perturbation method (HPM). For a horizontal channel, a new analytical algorithm to solve transient flow of third-grade fluid generated by an oscillating upper wall has been proposed. A new approach of the optimal homotopy asymptotic method (OHAM) have been proposed to solve steady mixed convection flows of fourth-grade fluid in a vertical channel. The accuracy of the approximate solution is achieved through the residual function. For a capillary tube, two flow problems of the second-grade fluid were developed. Firstly, oscillating flow and heat transfer driven by a sinusoidal pressure waveform, and secondly, free convection flow driven due to the reactive nature of the viscoelastic fluid. The solutions for the first problem were derived using Bessel transform technique while for the second problem by using a new modified homotopy perturbation transform method. For a horizontal cylinder, an unsteady third-grade fluid in a wire coating process inside a cylindrical die is developed. A special case of the problem is obtained for magnetohydrodynamic flow with heat transfer for second-grade fluid. Both of these two problems are solved using a new modified homotopy perturbation transform method. Data, graph and solutions obtained are shown and were found in good agreement with previous studies

Challenges and progress on the modelling of entropy generation in porous media: a review

Depending upon the ultimate design, the use of porous media in thermal and chemical systems can provide significant operational advantages, including helping to maintain a uniform temperature distribution, increasing the heat transfer rate, controlling reaction rates, and improving heat flux absorption. For this reason, numerous experimental and numerical investigations have been performed on thermal and chemical systems that utilize various types of porous materials. Recently, previous thermal analyses of porous materials embedded in channels or cavities have been re-evaluated using a local thermal non-equilibrium (LTNE) modelling technique. Consequently, the second law analyses of these systems using the LTNE method have been a point of focus in a number of more recent investigations. This has resulted in a series of investigations in various porous systems, and comparisons of the results obtained from traditional local thermal equilibrium (LTE) and the more recent LTNE modelling approach. Moreover, the rapid development and deployment of micro-manufacturing techniques have resulted in an increase in manufacturing flexibility that has made the use of these materials much easier for many micro-thermal and chemical system applications, including emerging energy-related fields such as micro-reactors, micro-combustors, solar thermal collectors and many others. The result is a renewed interest in the thermal performance and the exergetic analysis of these porous thermochemical systems. This current investigation reviews the recent developments of the second law investigations and analyses in thermal and chemical problems in porous media. The effects of various parameters on the entropy generation in these systems are discussed, with particular attention given to the influence of local thermodynamic equilibrium and non-equilibrium upon the second law performance of these systems. This discussion is then followed by a review of the mathematical methods that have been used for simulations. Finally, conclusions and recommendations regarding the unexplored systems and the areas in the greatest need of further investigations are summarized

ANALYSIS OF ENTROPY GENERATION DUE TO MAGNETOHYDRODYNAMIC COUPLE STRESS FLUID

We demonstrate the first reconfigurable photonic metamaterial controlled by electrical currents and magnetic fields, providing first practically useful solutions for sub-megahertz and high contrast modulation of metamaterial optical properties

Comments on: "Starting solutions for some unsteady unidirectional flows of a second grade fluid," [Int. J. Eng. Sci. 43 (2005) 781]

A significant mathematical error is identified and corrected in a recent highly-cited paper on oscillatory flows of second-grade fluids [Fetecau & Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are shown to agree identically with numerical ones generated by a finite-difference scheme, while the original ones of Fetecau & Fetecau do not. A list of other recent papers in the literature that commit the error corrected in this Comment is compiled. Finally, a summary of related erroneous papers in this journal is presented as an Appendix.Comment: 8 pages, 2 figures (4 images), elsarticle class; accepted for publication in International Journal of Engineering Scienc

Hall current and suction/injection effects on the entropy generation of third grade fluid

In this work, effects of Hall current and suction/injection on a steady, viscous, incompressible and electrically conducting third grade fluid past a semi-infinite plate with entropy generation is investigated. It is assumed that the fluid motion is induced by applied pressure gradient. Hot fluid is injected with a constant velocity at the injection wall while it is sucked off at the upper wall with the same velocity. The governing equations of Navier-Stoke, energy and entropy generation obtained are non-dimensionalised, the resulting dimensionless velocity and temperature profiles are solved by Adomian decomposition technique due to the nonlinearity of the coupled system of equations. The obtained solution for the velocity profile is validated by the exact solution and the existing one in literature at M = 0 and the analytical expressions for fluid velocity and temperature are utilized to calculate the entropy generation and irreversibility ratio. Various plots are presented and discussed. It is found that increasing Hall current parameter increases primary velocity, temperature, entropy generation and Bejan number while the reverse trend is observed when both suction/injection and magnetic field parameters are increased. It is also noticed that entropy production at the upper wall is due to heat transfer

MHD Mixed Convective Flow of Viscoelastic and Viscous Fluids in a Vertical Porous Channel

In this paper, we analyze the problem of steady, mixed convective, laminar flow of two incompressible, electrically conducting and heat absorbing immiscible fluids in a vertical porous channel filled with viscoelastic fluid in one region and viscous fluid in the other region. A uniform magnetic field is applied in the transverse direction, the fluids rise in the channel driven by thermal buoyancy forces associated with thermal radiation. The equations are modeled using the fully developed flow conditions. An exact solution is obtained for the velocity, temperature, skin friction and Nusselt number distributions. The physical interpretation to these expressions is examined through graphs and table for the shear stress and rate of heat transfer coefficients at the channel walls

Effect of temperature-dependent viscosity on entropy generation in transient viscoelastic polymeric fluid flow from an isothermal vertical plate

A numerical investigation of the viscosity variation effect upon entropy generation in time-dependent viscoelastic polymeric fluid flow and natural convection from a semi-infinite vertical plate is described. The Reiner-Rivlin second order differential model is utilized which can predict normal stress differences in dilute polymers. The conservation equations for heat, momentum and mass are normalized with appropriate transformations and the resulting unsteady nonlinear coupled partial differential equations are elucidated with the well-organized unconditionally stable implicit Crank-Nicolson finite difference method subject to suitable initial and boundary conditions. Average values of wall shear stress and Nusselt number, second-grade fluid flow variables conferred for distinct values of physical parameters. Numerical solutions are presented to examine the entropy generation and Bejan number along with their contours. The outcomes show that entropy generation parameter and Bejan number both increase with increasing values of group parameter and Grashof number. The present study finds applications in geothermal engineering, petroleum recovery, oil extraction and thermal insulation, etc