This article analyzes the Darcy Forchheimer 2D thin film fluid of nanoliquid. Flow of nanoliquid is made due to a flat unsteady stretchable sheet. In nanoliquids, nanomaterial is in form of CNTs (carbon nanotubes). Also, in present analysis, single walled carbon nanotubes (SWCNTs) are accounted as nanoparticles. The classical liquid ‘water’ is treated as based liquid. The flow in permeable region is characterized by Darcy–Forchheimer relation. Heat transport phenomena are studied from convective point of view. The transformation of partial differential set of equations into strong ordinary differential frame is formed through appropriate variables. Homotopy Analysis Method (HAM) scheme is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like Pr (Prandtl number), λ (unsteadiness factor), k (porous medium factor), F (Darcy-porous medium factor) on liquid velocity and thermal field are scrutinized and studied through sketches. Certain physical factors like f″(0) (friction factor coefficient) and −θ′(0) (rate of heat transport) are first derived and then presented through tables.

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Darcy Forchheimer nanofluid thin film flow of SWCNTs and heat transfer analysis over an unsteady stretching sheet

The present investigation reveals the effect of variable thickness on the steady two-dimensional boundary layer flows of a TiO2-water and Ag-water nanofluid through a slendering stretching sheet. The whole analysis has been performed in the presence of variable magnetic field and variable surface temperature. Similarity transformation has been introduced to renovate the non-linear partial differential equations into ordinary ones and then they were solved using the innovative technique of Natural decomposition method (NDM). The influence of pertinent parameters on velocity and temperature distribution has been illustrated by means of graphs and tables approach. Our analysis conveys that the temperature of the nanofluid reduces due to enhancing of the variable thickness parameter. The rate of heat transfer is significantly reduced for the Ag-water nanofluid with the positive impact of nanoparticle volume fraction.

Ramification of variable thickness on MHD TiO2 and Ag nanofluid flow over a slendering stretching sheet using NDM

In this paper, the effects of viscous and Ohmic heating and heat genera-tion/absorption on magnetohydrodynamic flow of an electrically conducting Casson thin film fluid over an unsteady horizontal stretching sheet in a non-Darcy porous medium are investigated. The fluid is assumed to slip along the boundary of the sheet. Similar-ity transformation is used to translate the governing partial differential equations into ordinary differential equations. A shooting technique in conjunction with the 4th order Runge-Kutta method is used to solve the transformed equations. Computations are car-ried out for velocity and temperature of the fluid thin film along with local skin friction coefficient and local Nusselt number for a range of values of pertinent flow parameters. It is observed that the Casson parameter has the ability to enhance free surface velocity and film thickness, whereas the Forchheimer parameter, which is responsible for the inertial drag has an adverse effect on the fluid velocity inside the film. The velocity slip along the boundary tends to decrease the fluid velocity. This investigation has various applications in engineering and in practical problems such as very large scale integration (VLSI) of electronic chips and film coating.

Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier's partial slip

The development of new applications of nanofluids in chemical engineering and other technologies has stimulated significant interest in computational simulations. Motivated by coating applications of nanomaterials, we investigate the transient nanofluid flow from a time-dependent spinning sphere using laminar boundary layer theory. The free stream velocity varies continuously with time. The unsteady conservations equations are normalized with appropriate similarity transformations and rendered into a ninth-order system of nonlinear coupled, multidegree ordinary differential equations. The transformed nonlinear boundary value problem is solved using the homotopy analysis method (HAM), a semicomputational procedure achieving fast convergence. Computations are verified with an Adomian decomposition method (ADM). The influence of acceleration parameter, rotational body force parameter, Brownian motion number, thermophoresis number, Lewis number, and Prandtl number on surface shear stress, heat, and mass (nanoparticle volume fraction) transfer rates is evaluated. The influence on boundary layer behavior is also investigated. HAM demonstrates excellent stability and leads to highly accurate solutions.

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Homotopy Simulation of Nonlinear Unsteady Rotating Nanofluid Flow from a Spinning Body

This paper presents a theoretical study of a non-linear rheological fluid transport in an axisymmetric tube by cilia. However, an attempt has been made to explain the role of cilia motion on the transport of fluid through the ductus efferentes of the male reproductive tract. Ostwald-de Waele power-law viscous fluid has been considered to represent the rheological fluid. To analyze pumping by means of a sequence of beat of cilia from row-to-row of cilia in a given row of cells and from one row of cells to the next (metachronal wave movement), we consider the conditions that the corresponding Reynolds number is small enough for inertial effects to be negligible and the wavelength to diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Analyses and computations of the detailed fluid motion reveal that the time-averaged flow rate is dependent on $\epsilon$, a non-dimensional measure involving the mean radius $a$ of the tube and the cilia length. Thus, flow rate significantly varies with the cilia length. Moreover, the flow rate has been reported near to the estimated value $6\times 10^{-3}$$ml/h$ for human efferent ducts if $\epsilon$ is near by 0.4. The estimated value was suggested by Lardner and Shack [1] in human, based on the experimental observations for flow rates in efferent ducts of other animals, e.g., rat, ram and bull. In addition, the nature of the rheological fluid, i.e., the value of the fluid index $n$ strongly influences various flow-governed characteristics. The interesting feature of the paper is that the pumping improves with the thickening behavior for small values of $\epsilon$ or in free pumping ($\Delta P=0$) and pumping ($\Delta P>0$) regions.

Rheological fluid motion in tube by metachronal wave of cilia

The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method (ADM). The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile, and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.

On study of horizontal thin film flow of Sisko fluid due to surface tension gradient

This paper deals with the drainage of Sisko fluid film down a vertical belt. It provides an approximate solution of the resulting non-linear and inhomogeneous ordinary differential equation using perturbation method (PM) and Adomian decomposition method (ADM). Comparison of the results obtained by both methods demonstrate that these series solutions are strictly identical but ADM is easy to compute and can be extended to any higher order. The important physical quantities like velocity profile, volume flow rate, average film velocity, shear stress, force exerted by the fluid film and vorticity vector are derived. The effects of fluid behaviour index, Stokes number and Sisko fluid parameter on some of these physical quantities are observed. Furthermore, we also made a comparison between the Sisko fluid film and Newtonian fluid film.

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Analytic Solution for the Drainage of Sisko Fluid Film Down a Vertical Belt

In this paper, we investigate the time-dependent drainage of a thin film of Eyring fluid of variable thickness, flowing down a vertical plate. The exact solutions for the velocity distribution, flow rate, mean thickness, average velocity, vorticity vector, and stress are obtained. Graphical results are presented and discussed for various flow variables like the velocity profile and the variable thickness.

A. Walait

Papers

On study of horizontal thin film flow of Sisko fluid due to surface tension gradient

Analytic Solution for the Drainage of Sisko Fluid Film Down a Vertical Belt

Time-dependent drainage of an Eyring film of variable thickness adhering to a vertical plate