Several mechanisms in industrial use have significant applications in thermal transportation. The inclusion of hybrid nanoparticles in different mixtures has been studied extensively by researchers due to their wide applications. This report discusses the flow of Powell–Eyring fluid mixed with hybrid nanoparticles over a melting parabolic stretched surface. Flow rheology expressions have been derived under boundary layer theory. Afterwards, similarity transformation has been applied to convert PDEs into associated ODEs. These transformed ODEs have been solved the using finite element procedure (FEP) in the symbolic computational package MAPLE 18.0. The applicability and effectiveness of FEM are presented by addressing grid independent analysis. The reliability of FEM is presented by computing the surface drag force and heat transportation coefficient. The used methodology is highly effective and it can be easily implemented in MAPLE 18.0 for other highly nonlinear problems. It is observed that the thermal profile varies directly with the magnetic parameter, and the opposite trend is recorded for the Prandtl number.

Enhancement in Thermal Energy and Solute Particles Using Hybrid Nanoparticles by Engaging Activation Energy and Chemical Reaction over a Parabolic Surface via Finite Element Approach

This paper reports the heat and mass transfer characteristics in a viscous fluid which is squeezed between parallel plates. The governing partial differential equations for unsteady two-dimensional flow with heat and mass transfer of a viscous fluid are reduced to ordinary differential equations by similarity transformations. Homotopy analysis method (HAM) is employed to construct the series solution of the problem. Physical interpretation to various embedding parameters is assigned through graphs for temperature and concentration profiles and tables for skin friction coefficient, local Nusselt number and local Sherwood number.

On heat and mass transfer in the unsteady squeezing flow between parallel plates

An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM) and compared with the direct numerical solution (NS). Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its simplicity, versatility and high accuracy, the method can be applied to study linear and nonlinear boundary value problems arising in other engineering applications.

https://downloads.hindawi.com/journals/mpe/2009/603916.pdf

Approximate Analysis of MHD Squeeze Flow between Two Parallel Disks with Suction or Injection by Homotopy Perturbation Method

Meta-analysis on thermo-migration of tiny/nano-sized particles in the motion of various fluids

The effects of variable viscosity and thermal conductivity on the flow and heat transfer in a laminar liquid film on a horizontal shrinking/stretching sheet are analyzed. The similarity transformation reduces the time independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The resulting five-parameter problem is solved by the homotopy perturbation method. The results are presented graphically to interpret various physical parameters appearing in the problem.

The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet

The present paper analyses the unsteady 2‐dimensional flow of a viscous MHD fluid between two parallel infinite plates. The two infinite plates are considered to be approaching each other symmetrically, causing the squeezing flow. A similarity transformation is used to reduce the partial differential equations modeling the flow, to a single fourth‐order non‐linear differential equation containing the Reynolds number and the magnetic field strength as parameters. The velocity functions are obtained for a range of values of both parameters by using the homotopy perturbation method. The total resistance to the upper plate is presented.

Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method

Hydromagnetic couple-stress nanofluid flow over a moving convective wall: OHAM analysis

Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane An upper convected Maxwell model (UCM) has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot Behavior of the relaxations phenomenon has been presented in terms of Deborah number Transport phenomenon with convective cooling process has been analyzed Brownian motion “Db” and thermophoresis effects “Dt” occur in the transport equations The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number Both numerical and analytic solutions are presented and found in nice agreement Comparison with the published data is also made to ensure the validity Stream lines for Maxwell and Newtonian fluid models are presented in the analysis

/pdf/heat-generation-absorption-effects-in-a-boundary-layer-lpycqp4b8a.pdf

Heat Generation/Absorption Effects in a Boundary Layer Stretched Flow of Maxwell Nanofluid: Analytic and Numeric Solutions

This article examines the magneto-hydrodynamic (MHD) flow of nanofluid bounded by a stretching surface. The slip conditions are utilized in the present analysis. The involved differential systems are solved for the velocity, temperature and mass fraction. Graphical and numerical results are reported for the analysis of various parameters of interest entering into the modeled problems. Combined effects of thermal and concentration jump are analyzed. Various tables are constructed to show the rheological effects of different physical parameters. Streamlines are plotted showing the rheology for the slip and no slip flow regime. Plots of skin friction are also prepared for the slip and magnetic field effects.

Velocity, thermal and concentration slip effects on a magneto-hydrodynamic nanofluid flow

This paper considers the steady flow of an incompressible third grade fluid between two vertical concentric rotating cylinders of infinite lengths. Modified Homotopy perturbation method is used to reduce the volume of tedious calculations involved to solve second order nonlinear differential equation. Special cases with one cylinder, inner or outer at rest (bounded domain case), and fluid flow at a rotating cylinder (unbounded domain case) are obtained. The effect of @b, the non-dimensional number related to the material constants, @w, rotation of the cylinder and R, the ratio between radii of outer and inner cylinders, on the velocity profile are discussed and are shown graphically.

S. Irum

Papers

Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method

Hydromagnetic couple-stress nanofluid flow over a moving convective wall: OHAM analysis

Heat Generation/Absorption Effects in a Boundary Layer Stretched Flow of Maxwell Nanofluid: Analytic and Numeric Solutions

Velocity, thermal and concentration slip effects on a magneto-hydrodynamic nanofluid flow

Torsional flow of third grade fluid using modified homotopy perturbation method