Set Of Dimensionless Variables Research Articles

Combined effects of nonlinear thermal radiation and suction/injection on bioconvective boundary layer of Maxwell nanofluid over a porous movable surface

The nanofluids exclusively enhance the thermal significance of many engineering and industrial processes including the manufacturing processes, chemical reactions, polymers, thermal devices, heating systems, solar energy etc. The presence of porous medium and suction/injection phenomenon incorporates key importance in the petroleum engineering and plasma physics. The objective of current work is to present a theoretical analysis for investigating the bioconvective flow of Maxwell nanofluid with applications of suction/injection effects. The flow is causing by porous moving surface. The radiative phenomenon with nonlinear expressions is adopted. The chemical reaction features are used for analysis of concentration phenomenon. Modified Cattaneo–Christov approach is followed to model the problem. A set of dimensionless variables are used for simplifying the modeled equations. The solution procedure is subject to implementation of shooting scheme. Graphical explanation of problems is presented in order to evaluates the role of different parameters. Physical behavior of problem is focused and justified in details. It is noted that heat and mass transfer enhances due to suction/injection parameter. The temperature profile reduces due to thermal relaxation parameter. Current results reveal significance in the ehat exchangers, improving the sustainability of thermal systems, controlling the cooling processes, fertilizes, biofuels etc.

EFFECTS OF HOMOGENEOUS AND HETEROGENEOUS REACTIONS ON THE THERMALLY STRATIFIED WATER-BASED NANOFLUID STREAMING ABOVE AN EXTENDING SURFACE

The effect of homogeneous and heterogeneous reactions, as well as second-order velocity slip, on the magnetic influenced flow of nanofluid (Cu-water and MgO-water) passes above an extending surface has been examined. To alter the nature of leading equations of this problem, a new set of dimensionless variables have been employed. The resulting equations with the corresponding surface restrictions are solved using the Runge-Kutta-Fehlberg technique (RKF45) by developing a code in Maple-18. The outcomes of this investigation are presented in terms of pictorial mode with the effects of different novel flow parameters. Also, numerical values of physical quantities that are associated with this problem are set in terms of tabular mode. It is perceived that increasing the number of solid particles, the thermal and mass fractions of the nanofluid behave as an enhancing function, whereas the motion of the nanofluid is a decreasing function.

Dynamics of classes of barotropic fluids in spatially curved FRW spacetimes

In this article we perform dynamical analysis of a broad class of barotropic fluids in the spatially curved Friedmann-Robertson-Walker (FRW) spacetime background without considering the cosmological constant. The first part of our study concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS) having as the only assumption the non-negativity of the fluid's energy density. After defining a new set of dimensionless variables and a new evolution parameter, we introduce the function $\Gamma$ that encodes the EoS. In this general setup several features of the system are identified: critical points, invariant subsets and the characteristics of the function $\Gamma$, along with their cosmological interpretations. The second part of our work provides two examples with specific $\Gamma$ functions. In the first example we provide a $\Gamma$ function and then we exhibit how it can be trimmed down to a specific class of EoS through physical arguments, while in the second example we discuss the quadratic EoS studied in Phys.Rev. D {\bf 74}, 023523 (2006) by comparing our approach with their analysis.

Thermal analysis of an Eyring-Powell fluid flow-through a constricted channel

This paper is aimed to investigate the entropy generation in a MHD convective flow of Eyring-Powell fluid through a mildly constricted channel. The constriction is assumed to be of regular or irregular shape and is presented inside the channel wall. Mathematical model is developed using the basic laws of conservation of mass, momentum, and energy. The governing equations are normalized using appropriate set of dimensionless variables and solutions are obtained by regular perturbation technique. The solutions are further used to calculate the entropy expression associated with the Second law of thermodynamics. The heat transfer characteristics, like, temperature, isotherms, entropy generation number entropy lines and the Bejan number are analyzed for the variation in magnetic field, shape parameter, and material constants. It is observed that entropy production is maximum in the narrow part of the channel. Moreover, entropy generation rate is higher for the regular parabolic shape as compared to irregular shapes of constriction.

Combined effects of variable viscosity and thermophoretic transportation on mixed convection flow around the surface of a sphere

The physical behavior of the combined effect of temperature dependent viscosity and thermophoretic motion on mixed convection flow around the surface of a sphere is investigated. The set of non-linear coupled PDE is formulated and then non-dimensionalized by using an appropriate set of dimensionless variables. The dimensionless model is then transformed to convenient form for integration by employing a suitable set of primitive variables formulation and then discretized by using an efficient implicate finite difference scheme for numerical simulation. The effect of controlling parameters on velocity profile, temperature profile, and mass concentration as well as skin friction, rate of heat transfer, and mass transfer rate are analyzed. The obtained numerical results for different values of controlling parameters indicate that, velocity profile gains its largest magnitude at position X = 1.5 radian and slows down at postion X = ? radian. It is also predicted that the temperature distribution and mass concentration are diluted at position X = 1.5 radian due to rapid motion of fluid. The numerical results are highlighted in graphical as well as in tabular form.

Steady-State Approximate Freshwater–Saltwater Interface in a Two-Horizontal-Well Scavenging System

In this study, an approximate mathematical formulation is derived to delineate a steady-state freshwater–saltwater interface by a horizontal scavenger well system in a confined aquifer that consists of two horizontal pumping wells. One horizontal well is above the freshwater–saltwater interface to recover freshwater. The other horizontal well is below the interface to extract saltwater. A set of dimensionless variables are introduced to facilitate solution derivations. Critical pumping rates that correspond to critical upconing and downconing interfaces are then derived for two different interface extents. Finally, the horizontal scavenger well system is applied to a real-world case, the 1,500-foot sand in Baton Rouge, Louisiana, and is compared to the current vertical scavenger well system, where the Field-Critchley analytical solution is adopted. The real-world case study demonstrates that among many advantages, the horizontal scavenger well system can recover more freshwater and extract less saltwater than the vertical scavenger well system. The study also indicates that the current freshwater and saltwater pumping rates are far below the safe zone and that freshwater is pulled into the saltwater well.

Classes of nonminimally coupled scalar fields in spatially curved FRW spacetimes

In this work we perform a dynamical analysis of a broad class of non-minimally coupled real scalar fields in the Friedmann-Robertson-Walker (FRW) spacetime framework. The first part of our study concerns the dynamics of an unspecified positive potential in a spatially curved FRW spacetime, for which we define a new set of dimensionless variables and a new evolution parameter. In the framework of this general setup we have recognized several general features of the system, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation. The second part of our work focuses on flat FRW cases for which the tracker parameter is constant, i.e. we examine specific classes of potentials. After analyzing these cases dynamically, we discuss their physical interpretation.

Mixed convection flow of couple stress nanofluid over oscillatory stretching sheet with heat absorption/generation effects

Abstract The aim of this article is to highlight the unsteady mixed convective couple stress nanoliquid flow passed through stretching surface. The flow is generated due to periodic oscillations of sheet. An appropriate set of dimensionless variables are used to reduce the independent variables in governing equations arising from mathematical modeling. An analytical solution has been computed by employing the technique of homotopy method. The outcomes of various sundry parameters like couple stress parameter, the ratio of angular velocity to stretching rate, thermophoresis parameter, Hartmann number, Prandtl number, heat source/sink parameter, Schmidt number described graphically and in tabular form. It is observed that the velocity profile increases by increasing mixed convection parameter and concentration buoyancy parameter. The temperature enhances for larger values of Hartmann number and Brownian. The concentration profile increases by increasing thermophoresis parameter. Results show that wall shear stress increases by increasing couple stress parameter and ratio of oscillating frequency to stretching rate.

Natural Convection Flow of a Nanofluid along a Vertical Plate with Streamwise Temperature Variations

This work is devoted to study the natural convection boundary‐layer flow of nanofluids along a vertical flat plate with the effect of sinusoidal surface temperature variations. The model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. An appropriate set of dimensionless variables is used to transform the governing equations of the problem into a nonsimilar form. The obtained nonsimilar equations have the property that they reduce to various special cases previously considered in the open literature. An adequate and efficient implicit, tri‐diagonal finite difference method is employed for the numerical solution of the obtained equations. Comparison with previously published work is performed and the results are found to be in excellent agreement. A representative set of numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction, as well as the surface shear stress, rates of heat and nanoparticle volume fraction have been presented graphically and discussed to show interesting features of the solutions.

Impulse excitation of piezoelectric bimorphs for energy harvesting: a dimensionless model

Energy harvesting (EH) is a multidisciplinary research area, involving physics, materials science and engineering, with the objective of providing renewable sources of power sufficient to operate targeted low-power applications. Piezoelectric transducers are often used for inertial vibrational as well as direct excitation EH. However, due to the stiffness of the most common material (PZT), compact and light-weight harvesters have high resonant frequencies, making them inefficient at extracting low-frequency power from the environment. The technique of frequency up-conversion, in the form of either plucking or impulse excitation, aims to bridge this frequency gap. In this paper, the technique is modelled analytically with focus on impulse excitation via impact or shock. An analytical model is developed in a standard way starting from the Euler–Bernoulli beam equations adapted to a piezoelectric bimorph. A set of dimensionless variables and parameters is defined and a system of differential equations derived. Here the system is solved numerically for a wide range of the two group parameters present, covering piezoelectric coupling strength between PVDF and PMN-PT. One major result is that the strength of the coupling strongly affects the timescale of the process, but has only a minor effect on the total energy converted. The model can be readily adapted to different excitation profiles.

MHD-Conjugate Free Convection from an Isothermal Horizontal Circular Cylinder with Joule Heating and Heat Generation

The present work is devoted to the numerical study of laminar magnetohydrodynamic (MHD) conjugate natural convection flow from a horizontal circular cylinder taking into account Joule heating and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made nondimensional forms using a set of dimensionless variables. Thus, the nondimensional governing equations are solved numerically using finite difference method with Keller box scheme. Numerical outcomes are found for different values of the magnetic parameter, conjugate conduction parameter, Prandtl number, Joule heating parameter, and heat generation parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat transfer along the surface. It is found that the skin friction increases, and heat transfer rate decreases for escalating value of Joule heating parameter and heat generation parameter. Results are presented graphically with detailed discussion.

The Study of Heat Generation and Viscous Dissipation on Mhd Heat And Mass Diffusion Flow Past A Surface

The present work is devoted to the numerical study of magneto hydrodynamic (MHD) natural convection flow of heat and mass transfer past a plate taking into account viscous dissipation and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made non dimensional forms using a set of dimensionless variables. Thus, the non dimensional governing equations are solved numerically using finite difference method Crank-Nicolson's scheme. Numerical outcomes are found for different values of the magnetic parameter, Modified Grashof number, Prandtl number, Eckert number, heat generation parameter and Schmidt number for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat and mass transfer along the surface. Results are presented graphically with detailed discussion.

Viscous and Joule heating effects on forced convection flow from radiate isothermal porous surfaces

Purpose – To highlight the effect of viscous and Joule heating on different ionized gases in the presence of magneto and thermal radiation effects.Design/methodology/approach – The conservation equations are written for the MHD forced convection in the presence of thermal radiation. The governing equations are transformed into non‐similar form using a set of dimensionless variables and then solved numerically using Keller box method.Findings – The increasing of fluid suction parameter enhances local Nusselt numbers, while the increasing of injection parameter decreases local Nusselt numbers. The inclusion of thermal radiation increases the heat transfer rate for both ionized gases suction or injection. The presence of magnetic field decreases the heat transfer rate for the suction case and increases it for the injection case. Finally, the heat transfer rate is decreased due to viscous dissipation.Research limitations/implications – The combined effects of both viscous and Joule heating on the forced conve...

Practical Procedure To Predict Cresting Behavior of Horizontal Wells

Summary Water and gas cresting in horizontal wells are important phenomena in reservoirs that have an aquifer or a gas cap. In practical situations, many reservoirs are produced under supercritical rates, and a breakthrough of the displacing phase becomes inevitable. At the beginning of a reservoir simulation study, it is desirable to make an estimate of the breakthrough time and the post-breakthrough behavior. Grid sensitivity runs are also required to obtain the appropriate gridblock sizes. An accurate representation of cresting behavior requires a very fine grid, which is not always practical. In this work, a procedure was developed to obtain accurate breakthrough times by use of just coarse grid simulations. The flow equations were written in dimensionless form, and important parameters affecting multiphase flow were identified. Simple correlations for a quick estimate of breakthrough time, maximum oil rate, and post-breakthrough behavior were derived on the basis of an appropriate set of dimensionless variables and an extensive number of simulation runs. The effects of gridblock size and grid pattern were investigated in detail. Effects of rate, mobility ratio, well drainage area, well height, and endpoints and shapes of relative permeability curves were also included. A procedure to derive pseudofunctions, either by numerical correlations or coarse grid simulations, is also presented. These pseudofunctions can be used to improve the performance of coarse grid simulations. An optimum grid pattern to start a reservoir simulation study is proposed. An application with real data shows that the correlations and procedures derived are reliable and accurate and can be used for quick estimates before starting a reservoir simulation study.

Flight with lift modulation inside a planetary atmosphere

A set of dimensionless variables is introduced to derive the equations for flight with lift and bank modulation inside a planetary atmosphere in a Newtonian gravitational field. Flight subject to constraints on state variables is discussed and a general approach is presented. Two examples are analyzed in detail: flight at constant speed, and flight at constant sinking speed.

Optimum three-dimensional atmospheric entry

This paper presents the general solution for the optimal three dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere. A set of dimensionless variables is introduced, and the resulting exact equations of motion have the distinctive advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a general lift-drag polar is used to define the aerodynamic control. Hence, the results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary polar and entering any planetary atmosphere.

Presentation of Elastohydrodynamic Film-Thickness Results

Yet another set of dimensionless variables is offered. These have the advantage of the Blok groups, that all results can be plotted on a single graph, but in addition one group is of secondary importance, so that all results lie in a narrow band. Thus, film thickness is shown to depend primarily on a single parameter.It is deduced that the extrapolated rigid cylinder theories give a very good estimate of the film thickness under elastohydrodynamic conditions.