Rehan Ali Shah

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.

Exact solution of a differential equation arising in the wire coating analysis of an unsteady second grade fluid

In this work, the mathematical modeling of unsteady second grade fluid in a wire coating process inside a straight annular die is developed in the form of a partial differential equation with non-homogenous boundary conditions. An exact solution is obtained for the governing equation by using the method of separation of variables.

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.

Steady flow and heat transfer analysis of Phan-Thein-Tanner fluid in double-layer optical fiber coating analysis with Slip Conditions

Modern optical fibers require double-layer coating on the glass fiber to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride (PVC) and low-high density polyethylene (LDPE/HDPE), nylon and Polysulfone. In this paper, double-layer optical fiber coating is performed using melt polymer satisfying PTT fluid model in a pressure type die using wet-on-wet coating process. The assumption of fully developed flow of Phan-Thien-Tanner (PTT) fluid model, two-layer liquid flows of an immiscible fluid is modeled in an annular die, where the fiber is dragged at a higher speed. The equations characterizing the flow and heat transfer phenomena are solved exactly and the effects of emerging parameters (Deborah and slip parameters, characteristic velocity, radii ratio and Brinkman numbers on the axial velocity, flow rate, thickness of coated fiber optics, and temperature distribution) are reported in graphs. It is shown that an increase in the non-Newtonian parameters increase the velocity in the absence or presence of slip parameters which coincides with related work. The comparison is done with experimental work by taking λ → 0 (non-Newtonian parameter).

Two-Phase Flow in Wire Coating with Heat Transfer Analysis of an Elastic-Viscous Fluid

This work considers two-phase flow of an elastic-viscous fluid for double-layer coating of wire. The wet-on-wet (WOW) coating process is used in this study. The analytical solution of the theoretical model is obtained by Optimal Homotopy Asymptotic Method (OHAM). The expression for the velocity field and temperature distribution for both layers is obtained. The convergence of the obtained series solution is established. The analytical results are verified by Adomian Decomposition Method (ADM). The obtained velocity field is compared with the existing exact solution of the same flow problem of second-grade fluid and with analytical solution of a third-grade fluid. Also, emerging parameters on the solutions are discussed and appropriate conclusions are drawn.

Double-layer optical fiber coating analysis using viscoelastic Sisko fluid as a coating material in a pressure-type coating die

Abstract. Double-layer optical fiber coating is performed using a melt polymer satisfying a Sisko fluid model in a pressure-type die. For this purpose, wet-on-wet coating process is applied. The assumption of fully developed flow of a Sisko fluid model, two-layer liquid flows of an immiscible fluid is modeled in an annular die of length L, where the bare glass fiber is dragged at a higher speed. The nonlinear governing equations are modeled and then solved by utilizing optimal homotopy asymptotic method (OHAM). The convergence of series solution is established. The convergence of OHAM is also verified by the Adomian decomposition method. In addition, the shear-thinning and shear-thickening characteristics of the non-Newtonian Sisko fluid are examined, and a comparison is made with the Newtonian fluid. At the end, the present work is also compared with the experimental results already available in the literature by taking the non-Newtonian parameter that tends to zero.

Steady flow and heat transfer analysis of MHD flow of Phan-Thien-Tanner fluid in double-layer optical fiber coating analysis with slip conditions

Abstract Modern optical fibers require a double-layer coating on the glass fiber in order to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride, low- and high-density polyethylene, nylon, and polysulfone. One of the most important things that affect the final product after processing is the design of the coating die. In the present study, double-layer optical fiber coating is performed using melt polymer satisfying the Phan-Thien-Tanner (PTT) fluid model in a pressure-type die. The fluid is electrically conducted in the presence of applied magnetic field. Wet-on-wet coating process is applied for double-layer optical fiber coating. The assumption of fully developed flow of PTT fluid model, two-layer liquid flows of an immiscible fluid, is modeled in an annular die of length L, where the fiber is dragged at a higher speed. The equations characterizing the flow ad heat transfer phenomena are solved exactly and the effects of emerging parameters are shown with the help of graphs. It is interesting to remark that an increase in the non-Newtonian parameters increases the velocity in the absence or presence of slip parameters, which coincides with the results reported earlier. Also, the effect of important parameters such as Deborah numbers, slip parameters, magnetic parameter, characteristic velocity, radii ratio, and Brinkman numbers on the axial velocity, flow rate, thickness of coated fiber optics, and temperature distribution are investigated. Furthermore, the results were compared with the experimental results already published. To the best of our knowledge, no such analysis of the double-layer coating flows of PTT fluid using slip conditions is available in the literature. At the end, the result of the present work is also compared with the experimental results already published by taking λ → 0 (non-Newtonian parameter).

Temperature Dependent Viscosity of a Third Order Thin Film Fluid Layer on a Lubricating Vertical Belt

This paper aims to study the influence of heat transfer on thin film flow of a reactive third order fluid with variable viscosity and slip boundary condition. The problem is formulated in the form of coupled nonlinear equations governing the flow together with appropriate boundary conditions. Approximate analytical solutions for velocity and temperature are obtained using Adomian Decomposition Method (ADM). Such solutions are also obtained by using Optimal Homotopy Asymptotic Method (OHAM) and are compared with ADM solutions. Both of these solutions are found identical as shown in graphs and tables. The graphical results for embedded flow parameters are also shown.