Influence Of Various Dimensionless Parameters Research Articles

Numerical study of the relative equilibrium of a droplet with a simply connected free surface on a rotating plane

The paper investigates the shapes of relative rest of limited layers of liquid on a rotating horizontal plane in the field of gravity in the presence of surface tension. The layers under consideration have a simply connected free surface and rotational symmetry with respect to the line of action of the angular velocity. The mathematical formulation of this problem is reduced to a system of first-order ordinary differential equations with boundary and integral closing conditions. A new algorithm for the numerical solution of the resulting system is proposed, the influence of various dimensionless parameters on the characteristics of equilibrium droplet shapes is studied, and criteria for the existence of such shapes are determined. The paper is of theoretical interest, since the problem under consideration is one of the fundamental ones in the research of capillary phenomena. The developed numerical scheme can also be applied in a wider class of differential equations. The results of the article can be used in practical tasks related to coating, fiber and powder production by the centrifugal-disk method.

Effects of Uniform and Non-Uniform Temperature Gradients on Marangoni Convection in a Composite Layer with Variable Heat Sources

An investigation is carried out to determine the effect of uniform and non-uniform temperature profiles on single component Darcy-Benard Marangoni (DBM) convection in a composite layer system consisting of an incompressible fluid saturated porous layer on top of which is a layer of the same fluid with variable heat sources in both layers. The upper surface of the fluid layer is free with surface tension effects depending on temperature and the lower surface of the porous layer is rigid. The eigen value, thermal Marangoni number (TMN) is solved exactly for linear, parabolic and inverted parabolic temperature profiles for the adiabatic thermal boundary conditions at the horizontal boundaries of the composite layer. The influence of various dimensionless parameters on the eigen value against depth ratio is discussed in detail.

Natural convection of a binary liquid in cylindrical porous annuli/rectangular porous enclosures with cross-diffusion effects under local thermal non-equilibrium state

The present article reports an analytical study of the double diffusive natural convection (DDNC) in cylindrical porous annuli (CPA) and rectangular porous enclosures (RPE), which are handled in a unified way using the curvature parameter, saturated by a binary liquid under the assumption of local thermal non-equilibrium (LTNE) state. The buoyancy forces (thermal and solutal) driving the flow are assumed to be induced by the maintenance of constant and uniform heat and mass fluxes applied along the vertical (radial) walls and insulation of both horizontal walls of the annuli/rectangular enclosures. The Darcy-Boussinesq equations with LTNE assumption between the fluid and solid phases are employed to model the problem of DDNC in a binary liquid-saturated porous medium with cross-diffusion effects. The analytical results are obtained by employing the Oseen-linearization transformation technique in the study. The influence of various dimensionless parameters on heat and mass transports of the system are depicted using the Nusselt and Sherwood numbers and isotherms plots, and the obtained results are analysed with the physical explanation. Special attention is given to understand the effect of LTNE parameter and cross-diffusion parameters on heat and mass transports of the system. Different aspect ratio values are chosen to obtain the results of three types of CPA/RPE (shallow, square and tall). Among these CPA/RPE, maximum and minimum heat and mass transports are achieved in the cases of shallow and tall CPA/RPE, respectively. The results of the pure thermal convection problem is obtained at the zero value of buoyancy ratio and solute Rayleigh number. The increasing value of N magnifies the heat and mass transports in the system due to the augmented buoyancy effect resulted from the thermal and solutal gradients. The increase of solid inner cylinder radius, by fixing its volume, makes the annulus slender which yields to decrease the heat and mass transports in the system. The effects of LTNE parameter and cross-diffusion parameters on heat and mass transports of the system are clearly brought out. The results of LTE model are obtained at the infinite value of ratio of porosity modified thermal conductivities, γ, as a particular case of the present model. From the study, we conclude that the shallow porous annulus and tall rectangular enclosure are best suited in the design of heat removal and heat storage systems, respectively.

RETRACTED: A study of a computational BVP for heat transfer and friction drag in magnetohydrodynamics viscous flow of a nanofluid subject to the curved surface

The ongoing work investigates the features of Joule heating and convective condition over a magnetohydrodynamic stagnation point flow of [Formula: see text] nanofluid moving across a curved surface. Moreover, mass suction is supposed through the stretching/shrinking surface. The initially developed model of partial differential equations is transformed into the ordinary ones assisted by suitable similarity variables. Subsequently, the ultimate nonlinear model of ordinary differential equations is solved with the help of a built-in function bvp4c package in MATLAB. Several graphical results are plotted to see the influence of various dimensionless parameters over the velocity, temperature, heat transfer, and friction drag. We found that there exists an escalation in temperature with increasing values of curvature, Eckert number, Hartmann number, and Biot number; however, the velocity profile declines with large curvature, ratio parameter, and high concentration of nanoparticles. It is also important to note that the friction drag rises with the mass suction, and reduces with vast curvature, whereas the rate of heat transfer improves with suction and Biot number but lowers with Eckert number and Hartmann number.

Analytical Study of the Solidification of a Phase Change Material in an Annular Space

In this study, the process of the solidification of a PCM (phase change material) liquid in an annular space was analytically investigated with the use of a simplified quasi-steady-state model. This model described the phase change phenomenon with the cylindrical solidification front and with the solidification liquid overheated above the solidification temperature. One of the important novelties of the applied model was the determination of the coefficient of the heat transfer between the liquid and the solidified layer on the solidification surface, which was calculated as a function of the location of the solidification front. A method for calculating the variable coefficient of heat transfer on the surface of the solidification front during the solidification process is presented. The contact layer between the cold wall and the solidified layer was incorporated into the model and played an important role. The theoretical analytical method describing the solidification process based on the quasi-steady model was used in the study. Moreover, the main problem considered in this work could be reduced to a conjugate system of differential equations, allowing it to be solved numerically. From this perspective, the influence of various dimensionless parameters on the solidification process could be clearly seen. The obtained numerical results are presented in graphical form. The results of the theoretical research were compared with the experimental research of one of the author’s earlier works and they showed a significant agreement. Finally, the simple analytical approach presented in this work can be used for designing annular heat accumulators.

Effect of thermal radiation on MHD Casson fluid flow over an exponentially stretching curved sheet

This paper presents the flow and heat transfer characteristics of an electrically conducting Casson fluid past an exponentially stretching curved surface with convective boundary condition. The fluid motion is assumed to be laminar and time dependent. The effects of temperature-dependent thermal conductivity, Joule heating, thermal radiation, and variable heat source/sink are deemed. Suitable transformations are considered to transform the governing partial differential equations as ordinary ones and then solved by the numerical procedures like shooting and Runge–Kutta method. Graphs are outlined to describe the influence of various dimensionless parameters on the fields of velocity and temperature and observe that there is an enhancement in the field of temperature with the radiation, temperature-dependent thermal conductivity, and irregular heat parameters. Also, the Casson parameter has a tendency to suppress the distribution of momentum but an inverse development is noticed for the curvature parameter. Attained outcomes are also compared with the existing literature in the limiting case, and good agreement is perceived.

An experimental and theoretical study of the solidification process of phase change materials in a horizontal annular enclosure

The main purpose of this paper is to examine experimentally and theoretically the process of heat accumulation and heat release for PCM (phase change materials) in an annular space.The theoretical part of this work provides a solution of the problem of liquid solidification in an annular space under the influence of free convection. Here a simplified quasi-steady-state model for solidification has been applied. The new simplified model describes the solidification phenomenon with an imposed boundary condition on the solidification interface by applying a heat transfer coefficient. From the developed model, the influence of various dimensionless parameters on the phase change problem can be seen clearly.Measurements and observation of the thickness of the solidified layer were performed in a newly built apparatus. In addition, this paper is also concerned with the role of the contact layer in the solidification process. Results are showing the thickness of the solidification layer depending on time and the distribution of the local heat transfer coefficient on the surface of the solidification front. The obtained experimental and numerical results show good agreement.The examined solidification process makes it possible to use the results obtained for the design of new heat accumulators. The presented method to analyse heat accumulation is important for power engineering. It opens up the possibility to reduce the size of heat accumulators, thus, possible leading to a reduction in their production costs.

Effects of MHD on the Unsteady Thin Flow of Non-Newtonian Oldroyd –B Fluid over an Oscillating Inclined Belt Through a Porous Medium

The unsteady (MHD) thin film flow of an incompressible Oldroyd -B fluid over an oscillating inclined belt making a certain angle with the horizontal through a porous mediumis analyzed .The analytical solution of velocity field is obtained by a semi-numerical technique optimal homotopy asymptotic method (OHAM) .Finally the influence of various dimensionless parameters emerging in the model on velocity field is analyzed by graphical illustrations. I. Introduction In everyday life and in engineering flow of non-Newtonian fluid are frequently occurred .It is ubiquitous in nature and technologies .Therefore ,to understand there mechanics is essential in most application .Most of it problems appeared in several examples are polymer solution ,paints ,certain oils ,exocitic lubricants ,colloidal and suspension solutions , clay coatings and cosmetic products .In non-Newtonian fluids Thin film flows have a large varying of practical applications in nonlinear science and engineering industries . For modeling of non-Newtonian Fluid flow problem we used several model like (second grade, third grade , Maxwell fluid ,Oldroyd-B ) ..ect fluid model by which we got linear or nonlinear ordinary differential equation or partial differential equations which may be solved exactly, analytically or numerically. For solution of these problems different varieties of methods are used, in which (ADM,VAM,HAM,HPM,OHAM) are frequently used. In this work we have modeled a partial differential equations by using oldroyd-B fluid model. Solution of the problem is obtained by using OHAM. Fetecau et al. (3) studied the exact solutions of an Oldroyd-B fluid over a flat plate on constantly accelerating flow. In the following year, Fetecau et al. (4) obtained the exact solutions of the transient oscillating motion of an Oldroyd-B fluids in cylindrical domains. Haitao and Mingyu (5) investigated the series solution of an Oldroyd-B fluid by using the sine and Laplace transformations for the plane Poiseuille flowand plane couette flow. Lie L. (7) studied the effect of MHD flow for an Oldroyd-B fluid between two oscillating cylinders .Khan et al. Burdujan (2) discussed the solution for the flow of an incompressible Oldroyd-B fluid between two cylinders . Shahid et al. (12) studied the solution of the steady and unsteady flow of Oldroyd-B fluid by using Laplace and Fourier series. Shah et al. (13) studied the solution by using OHAM of thin film flow of third grade fluid on moving inclined plane. Marinca et al. (11) studied the approximate solution of non-linear steady flow of fourth grade fluid by using OHAM. Marinca et al (10) discussed the approximate solution of the unsteady viscous flow over a shrinking cylinder by using OHAM method . Kashkari (6) studied the OHAM solution of nonlinear Kawahara equation. For comparison HPM, VHPM and VIM method is used but OHAM ismore successful method. . Anakira et al. (1) the analytical solution of delay differential equation by using OHAM. Mabood et al. (8,9) investigated the approximate solution of non-linear Riccati differential equation by using OHAM . Taza Gul (14) studied the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. In this paper , we study the unsteady (MHD) thin film flow of an incompressible Oldroyd -B fluid over an oscillating inclined belt making a certain angle with the horizontal in porous medium . the solution of velocity field is obtained by using a semi-numerical technique optimal homotopy asymptotic method (OHAM). Finally, we analyzed the influence of various dimensionless parameters emerging in the model on velocity field is analyzed by graphical illustrations.

Numerical study of MHD heat and mass transfer of a Jeffrey fluid over a stretching sheet with chemical reaction and thermal radiation

A numerical model is developed to study the effects of chemical reaction and heat source on MHD heat and mass transfer of an electrically conducting Jeffrey fluid over a stretching sheet in the presence of power law form of temperature and concentration. Similarity transformations are used to convert the governing partial differential equations to a set of coupled non-linear ordinary differential equations. The resulting equations are then solved numerically by shooting method with Runge–Kutta fourth order scheme. The influence of various dimensionless parameters on the velocity, temperature and concentration distributions are analyzed and discussed through graphs and tables. It is observed that the Deborah number (β) and ratio of relaxation and retardation times parameter (λ) have opposite effects on the skin friction coefficient. However, the effects of β and Pr on the Nusselt number profiles are similar. Subsequently the present results are in very good agreement with the results obtained for a viscous fluid.

Numerical investigation of thermosolutal natural convection in a rectangular enclosure of an aspect ratio four with heat and solute sources

A numerical study of double-diffusive natural convection in an enclosure with a partial vertical heat and mass sources for an aspect ratio Ar = 4 has been carried out. The influence of various dimensionless parameters (Rayleigh number, buoyancy ratio, source location, Lewis number, and source length) on the flow behavior are investigated. Correlations of average Nusselt and Sherwood numbers are obtained as function of two parameters (Ra, d) and (Le, d), respectively.

Analysis of a porous-inclined slider bearing lubricated with magnetic fluid considering thermal effects with slip velocity

A theoretical model of a porous-inclined slider bearing lubricated with magnetic fluid has been considered together with slip velocity boundary condition. Our aim is to study the influence of various dimensionless parameters arising out of the analysis of the model. By assuming the viscosity µ = µ0 exp [-β(tm - t0)] of magnetic fluid, the expressions for mean temperature and load capacity have been obtained. It has been observed that both mean temperature field and load capacity are the functions of slip parameter, magnetic parameter, thermal parameter and permeability parameter. The dependence of the mean temperature field as well as of load capacity on these parameters has been seen graphically.

Two-fluid modeling in analyzing the interfacial stability of liquid film flows

The area-averaged two-fluid model formulation of a separated two-phase flow system is used to investigate interfacial stability of liquid film flows. The analysis takes into account the effects of phase change at the interface as well as the dynamic effects of the adjacent vapor flow on the interfacial stability. Wave formation and instability criteria are established in terms of the generalized fluid and flow parameters. The criteria are applied to investigate the stability of laminar liquid film flow with interfacial shear and phase change. The influence of various dimensionless parameters characterizing film thickness, gravity, phase change and interfacial shear are studied with respect to the neutral stability, temporal growth factor and the wave propagation velocity. The results of the present study indicate that the interfacial stability analysis developed within the frame of the two-fluid model formulation proves to be quite accurate as judged by comparing its results with the available experimental data and with the results of much longer and more complex analytical investigations which are valid only for the liquid film free of interfacial shear.

Hall effects on convective hydromagnetic flow past a flat plate

Hydromagnetic free convective flow past an infinite vertical, porous plate in the presence of a uniform transverse magnetic field has been considered taking Hall effects into account. Approximate solutions for the mean velocity, mean temperature and their related quantities are obtained. The influence of various dimensionless parameters is discussed

Collection of aerosol particles by fabric filters in an electrostatic field

The deposition of uncharged aerosols on charged fibers perpendicular to the air stream in a homogeneous electrical field is analytically investigated. The simple theoretical model of a filter studied in this work consists of evenly arranged layers of equidistant parallel cylinders of infinite length normal to the flow direction. The critical trajectories of the particles are calculated by numerically solving the differential equation for the particle trajectories. The calculated values of the deposition coefficient are compared with the results of previous investigations. The influence of various dimensionless parameters on deposition is discussed.