Taza Gul

MHD Thin Film Flows of a Third Grade Fluid on a Vertical Belt with Slip Boundary Conditions

The problem of heat transfer analysis is considered in electrically conducting thin film flows with slip boundary conditions. The flow is assumed to be obeying the nonlinear rheological constitutive equation of a third grade fluid. We have solved the governing nonlinear equations of present problems using the traditional Adomian decomposition method (ADM). Particular attention is given to the combined effect of heat and MHD on the velocity field. The results include the profile of velocity, volume flux, skin friction, average velocity, and the temperature distribution across the film. The effects of model parameters on velocity, skin friction and temperature variation have been studied. Optimal homotopy asymptotic method (OHAM) is also used for comparison. The numerical results and absolute errors are derived in tables.

Heat Transfer Analysis of MHD Thin Film Flow of an Unsteady Second Grade Fluid Past a Vertical Oscillating Belt

This article aims to study the thin film layer flowing on a vertical oscillating belt. The flow is considered to satisfy the constitutive equation of unsteady second grade fluid. The governing equation for velocity and temperature fields with subjected initial and boundary conditions are solved by two analytical techniques namely Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The comparisons of ADM and OHAM solutions for velocity and temperature fields are shown numerically and graphically for both the lift and drainage problems. It is found that both these solutions are identical. In order to understand the physical behavior of the embedded parameters such as Stock number, frequency parameter, magnetic parameter, Brinkman number and Prandtl number, the analytical results are plotted graphically and discussed.

Thin Film Flow in MHD Third Grade Fluid on a Vertical Belt with Temperature Dependent Viscosity

In this work, we have carried out the influence of temperature dependent viscosity on thin film flow of a magnetohydrodynamic (MHD) third grade fluid past a vertical belt. The governing coupled non-linear differential equations with appropriate boundary conditions are solved analytically by using Adomian Decomposition Method (ADM). In order to make comparison, the governing problem has also been solved by using Optimal Homotopy Asymptotic Method (OHAM). The physical characteristics of the problem have been well discussed in graphs for several parameter of interest.

Unsteady MHD Thin Film Flow of an Oldroyd-B Fluid over an Oscillating Inclined Belt.

This paper studies 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. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically.

Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables

Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method.

SCATTERING OF A THIN LAYER OVER A NONLINEAR RADIALLY EXTENDING SURFACE WITH MAGNETO HYDRODYNAMIC AND THERMAL DISSIPATION

The recent research is allied with the analysis of a thin layer, spreading over the nonlinear surface of a radially extended sheet. The temperature field has been taken with the accumulation of dissipation term. The similarity variables have been used to transform the basic flow equations into a set of nonlinear differential equations. The thickness of the spreading phenomenon has been taken as a variable. The approximate outcomes of the problem have been achieved using the optimal approach of the homotopy analysis method (HAM). The convergence of the HAM has been computed with numerical method. The impact of the variable thickness parameter β, generalized magnetic parameter M, Eckert number Ec and Pr on the spreading pattern and temperature field has been calculated and discussed. The attention has been paid to the important physical quantities of interest like the skin friction and Nusselt number under the effect of various embedded parameters.

Three-dimensional rotating flow of MHD single wall carbon nanotubes over a stretching sheet in presence of thermal radiation

In this article the modeling and computations are exposed to introduce the new idea of MHD three-dimensional rotating flow of nanofluid through a stretching sheet. Single wall carbon nanotubes (SWCNTs) are utilized as a nano-sized materials while water is used as a base liquid. Single-wall carbon nanotubes (SWNTs) parade sole assets due to their rare structure. Such structure has significant optical and electronics features, wonderful strength and elasticity, and high thermal and chemical permanence. The heat exchange phenomena are deliberated subject to thermal radiation and moreover the impact of nanoparticles Brownian motion and thermophoresis are involved in the present investigation. For the nanofluid transport mechanism, we implemented the Xue model (Xue, Phys B Condens Matter 368:302–307, 2005). The governing nonlinear formulation based upon the law of conservation of mass, quantity of motion, thermal field and nanoparticles concentrations is first modeled and then solved by homotopy analysis method (HAM). Moreover, the graphical result has been exposed to investigate that in what manner the velocities, heat and nanomaterial concentration distributions effected through influential parameters. The mathematical facts of skin friction, Nusselt number and Sherwood number are presented through numerical data for SWCNTs.

Analytical and numerical solutions of Oldroyd 8-constant fluid in double-layer optical fiber coating

Polymer flow during wire coating in a pressure-type casting die has been simulated under non-isothermal conditions. The flow is dependent on the wire velocity, geometry of the die, and the viscosity of the polymer. In the present study, the constitutive equation of an Oldroyd 8-constant fluid is used to characterize the rheology of the polymer melt. The equation describing the flow of polymer melt inside the die is solved (1) analytically by applying optimal homotopy asymptotic method (OHAM) and (2) numerically by the shooting method with Runge–Kutta–Fehlberg algorithm. The convergence of the series solution is established. The effect of physical characteristics of the problem has been discussed in detail through graphs by assigning numerical values for several parameters of interest. At the end, the present study is also compared with published work as a particular case and good agreement is found.

The experimental study to examine the stable dispersion of the graphene nanoparticles and to look at the GO–H2O nanofluid flow between two rotating disks

The nanofluid analysis has been carried out as a function of temperature and this idea is utilized to study the graphene oxide (GO) water-based nanofluid from both experimental and numerical perspectives. Various spectral investigations were used to endorse the successful synthesis of graphene oxide. The obtained GO exhibits large size platelet morphology with stable dispersion in water. The experimental procedure of the preparation of nanofluid and its outputs has been analyzed with numerical data. The obtained results from the Chebyshev spectral scheme were transformed into a mathematical model considering the 3D flow of the dispersed GO nanofluid between two parallel rotating disks using the governing Navier–Stokes equations and energy equation with the utilization of Von Karman similarity transformations. The obtained nonlinear differential equations have been examined through a recently fashionable analytic approximation method called the Optimal Homotopy Analysis Method (OHAM). Opposite and same direction rotational effects have been conferred on the flow characteristics. To analyze how the velocities, pressure and temperature fields are affected by various parameters, plots have been displayed. Convergence of the obtained results has been authenticated with residual errors physically and numerically. Moreover, the physical parameters impact, such as local Nusselt number and skin friction coefficients are obtained through numerical data and inspect.

A simple algorithm for exact solutions of systems of linear and nonlinear integro-differential equations

A Simple algorithm is used to achieve exact solutions of systems of linear and nonlinear integro- differential equations arising in many scientific and engineering applications. The algorithm does not need to find the Adomain Polynomials to overcome the nonlinear terms in Adomain Decomposition Method (ADM). It does not need to create a homotopy with an embedding parameter as in Homotopy Perturbation Method (HPM) and Optimal Homotopy Asymptotic Method (OHAM). Unlike VIM, it does not need to find Lagrange Multiplier. In this manuscript no restrictive assumptions are taken for nonlinear terms. The applied algorithm consists of a single series in which the unknown constants are determined by the simple means described in the manuscript. The outcomes gained by this algorithm are in excellent concurrence with the exact solution and hence proved that this algorithm is effective and easy. Four systems of linear and nonlinear integro-differential equations are solved to prove the above claims and the outcomes are compared with the exact solutions as well as with the outcomes gained by already existing methods.