O. Anwar Bég

A STUDY OF NON-NEWTONIAN FLOW AND HEAT TRANSFER OVER A NON-ISOTHERMAL WEDGE USING THE HOMOTOPY ANALYSIS METHOD

The thermoconvective boundary layer flow of a generalized third-grade viscoelastic power-law non-Newtonian fluid over a porous wedge is studied theoretically. The free stream velocity, the surface temperature variations, and the injection velocity at the surface are assumed variables. A similarity transformation is applied to reduce the governing partial differential equations for mass, momentum, and energy conservation to dimensionless, nonlinear, coupled, ordinary differential equations. The homotopy analysis method (HAM) is employed to generate approximate analytical solutions for the transformed nonlinear equations under the prescribed boundary conditions. The HAM solutions, in comparison with numerical solutions (fourth-order Runge-Kutta shooting quadrature), admit excellent accuracy. The residual errors for dimensionless velocity and dimensionless temperature are also computed. The influence of the “power-law” index on flow characteristics is also studied. The mathematical model finds important applications in polymeric processing and biotechnological manufacture. HAM holds significant promise as an analytical tool for chemical engineering fluid dynamics researchers, providing a robust benchmark for conventional numerical methods.

Semi-computational simulation of magneto-hemodynamic flow in a semi-porous channel using optimal homotopy and differential transform methods

In this paper, the semi-numerical techniques known as the optimal homotopy analysis method (HAM) and Differential Transform Method (DTM) are applied to study the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field. The two-dimensional momentum conservation partial differential equations are reduced to ordinary form incorporating Lorentizian magnetohydrodynamic body force terms. These ordinary differential equations are solved by the homotopy analysis method, the differential transform method and also a numerical method (fourth-order Runge-Kutta quadrature with a shooting method), under physically realistic boundary conditions. The homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. The differential transform method (DTM) does not require an auxiliary parameter and is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The influence of Hartmann number (Ha) and transpiration Reynolds number (mass transfer parameter, Re) on the velocity profiles in the channel are studied in detail. Interesting fluid dynamic characteristics are revealed and addressed. The HAM and DTM solutions are shown to both correlate well with numerical quadrature solutions, testifying to the accuracy of both HAM and DTM in nonlinear magneto-hemodynamics problems. Both these semi-numerical techniques hold excellent potential in modeling nonlinear viscous flows in biological systems.

HOMOTOPY ANALYSIS OF TRANSIENT MAGNETO-BIO-FLUID DYNAMICS OF MICROPOLAR SQUEEZE FILM IN A POROUS MEDIUM: A MODEL FOR MAGNETO-BIO-RHEOLOGICAL LUBRICATION

The transient squeezing flow of a magneto-micropolar biofluid in a noncompressible porous medium intercalated between two parallel plates in the presence of a uniform strength transverse magnetic field is investigated. The partial differential equations describing the two-dimensional flow regime are transformed into nondimensional, nonlinear coupled ordinary differential equations for linear and angular momentum (micro-inertia). These equations are solved using the robust Homotopy Analysis Method (HAM) and also numerical shooting quadrature. Excellent correlation is achieved. The influence of magnetic field parameter (Ha), micropolar spin gradient viscosity parameter (Γ) and unsteadiness parameter (S) on linear and angular velocity (micro-rotation) are presented graphically, for specified values of the micropolar vortex viscosity parameter (R), Darcy number (Da i.e. permeability parameter) and medium porosity parameter (e). Increasing magnetic field (Ha) serves to decelerate both the linear and angular velocity i.e. enhances lubrication. The excellent potential of HAM in bio-lubrication flows is highlighted.

COMPARATIVE NUMERICAL STUDY OF SINGLE-PHASE AND TWO-PHASE MODELS FOR BIO-NANOFLUID TRANSPORT PHENOMENA

A computational fluid dynamics (CFD) simulation of laminar convection of Al2O3–water bio-nanofluids in a circular tube under constant wall temperature conditions was conducted, employing a single-phase model and three different two-phase models (volume of fluid (VOF), mixture and Eulerian). The steady-state, three-dimensional flow conservation equations were discretised using the finite volume method (FVM). Several parameters such as temperature, flow field, skin friction and heat transfer coefficient were computed. The computations showed that CFD predictions with the three different two-phase models are essentially the same. The CFD simulations also demonstrated that single-phase and two-phase models yield the same results for fluid flow but different results for thermal fields. The two-phase models, however, achieved better correlation with experimental measurements. The simulations further showed that heat transfer coefficient distinctly increases with increasing nanofluid particle concentration. The physical properties of the base fluid were considered to be temperature-dependent, while those of the solid particles were constant. Grid independence tests were also included. The simulations have applications in novel biomedical flow processing systems.

Lie group analysis and numerical solutions for non-Newtonian nanofluid flow in a porous medium with internal heat generation

A mathematical model is presented and analysed for steady two-dimensional non-isothermal boundary layer flow from a heated horizontal surface which is embedded in a porous medium saturated with a non-Newtonian power-law nanofluid. It is assumed that the wall temperature and nanoparticle volume fraction vary nonlinearly with the axial distance. By applying appropriate group transformations, the governing transport equations are reduced to a system of coupled, nonlinear ordinary differential equations with associated boundary conditions. The reduced equations are then solved numerically using the Runge–Kutta–Fehlberg fourth–fifth-order numerical method with Maple 13 software. The effects of several thermophysical parameters including rheological power-law index, non-isothermal index, Lewis number, Brownian motion parameter, thermophoresis parameter, buoyancy ratio and internal heat generation/absorption parameter on the non-dimensional velocity, temperature, nanoparticle volume fraction (concentration) and also on the friction factor, heat and mass transfer rates are investigated. A comparison of the present results with the existing published results shows excellent agreement, verifying the accuracy of the present numerical code. The study finds applications in nano biopolymeric manufacturing processes and also thermal enhancement of energy systems employing rheological working fluids.

Homotopy semi-numerical simulation of peristaltic flow of generalised Oldroyd-B fluids with slip effects.

This investigation deals with the peristaltic flow of generalised Oldroyd-B fluids (with the fractional model) through a cylindrical tube under the influence of wall slip conditions. The analysis is carried out under the assumptions of long wavelength and low Reynolds number. Analytical approximate solutions are obtained by using the highly versatile and rigorous semi-numerical procedure known as the homotopy analysis method. It is assumed that the cross section of the tube varies sinusoidally along the length of the tube. The effects of the dominant hydromechanical parameters, i.e. fractional parameters, material constants, slip parameter, time and amplitude on the pressure difference across one wavelength, are studied. Graphical plots reveal that the influence of both fractional parameters on pressure is opposite to each other. Interesting responses to a variation in the constants are obtained. Pressure is shown to be reduced by increasing the slip parameter. Furthermore, the pressure in the case of fractional models (fractional Oldroyd-B model and fractional Maxwell model) of viscoelastic fluids is considerably more substantial than that in the corresponding classical viscoelastic models (Oldroyd-B and Maxwell models). Applications of the study arise in biophysical food processing, embryology and gastro-fluid dynamics.

A numerical study of magnetohydrodynamic transport of nanofluids over a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects

Abstract In this paper, a mathematical study is conducted of steady incompressible flow of a temperature-dependent viscous nanofluid from a vertical stretching sheet under applied external magnetic field and gravitational body force effects. The Reynolds exponential viscosity model is deployed. Electrically-conducting nanofluids are considered which comprise a suspension of uniform dimension nanoparticles suspended in viscous base fluid. The nanofluid sheet is extended with a linear velocity in the axial direction. The Buonjiornio model is utilized which features Brownian motion and thermophoresis effects. The partial differential equations for mass, momentum, energy and species (nano-particle concentration) are formulated with magnetic body force term. Viscous and Joule dissipation effects are neglected. The emerging nonlinear, coupled, boundary value problem is solved numerically using the Runge–Kutta fourth order method along with a shooting technique. Graphical solutions for velocity, temperature, concentration field, skin friction and Nusselt number are presented. Furthermore stream function plots are also included. Validation with Nakamura’s finite difference algorithm is included. Increasing nanofluid viscosity is observed to enhance temperatures and concentrations but to reduce velocity magnitudes. Nusselt number is enhanced with both thermal and species Grashof numbers whereas it is reduced with increasing thermophoresis parameter and Schmidt number. The model is applicable in nano-material manufacturing processes involving extruding sheets.

Mathematica simulation of peristaltic pumping with double-diffusive convection in nanofluids: a bio-nano-engineering model:

A theoretical study is presented to examine the peristaltic pumping with double-diffusive (thermal and concentration diffusive) convection in nanofluids through a deformable channel. The model is motivated by the need to explore nanofluid dynamic effects on peristaltic transport in biological vessels as typified by transport of oxygen and carbon dioxide, food molecules, ions, wastes, hormones and heat in blood flow. Analytical approximate solutions are obtained under the restrictions of large wavelength ( a ≪ λ → ∞ ) and low Reynolds number ( Re → 0 ), for nanoparticle fraction field, concentration field, temperature field, axial velocity, volume flow rate, pressure gradient and stream function in terms of axial and transverse coordinates, transverse vibration of the wall, amplitude of the wave and averaged flow rate. The influence of the dominant hydrodynamic parameters (Brownian motion, thermophoresis, Dufour and Soret) and Grashof numbers (thermal, concentration, nanoparticle) on peristaltic flow patterns with double-diffusive convection are discussed with the help of computational results obtained with the Mathematica software. The classical Newtonian viscous model constitutes a special case ( G r T = 0 , G r C = 0 , G r F = 0 ) of the present model. Applications of the study include novel pharmaco-dynamic pumps and engineered gastro-intestinal motility enhancement.

Modelling laminar transport phenomena in a Casson rheological fluid from a horizontal circular cylinder with partial slip

The laminar boundary layer flow and heat transfer of Casson non-Newtonian fluid from a permeable horizontal cylinder in the presence of thermal and hydrodynamic slip conditions is analysed. The cylinder surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalised into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. Increasing velocity slip induces acceleration in the flow near the cylinder surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in Casson rheological parameter acts to elevate considerably the skin friction (non-dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures are however very slightly decreased with increasing values of Casson rheological parameter. Increasing mass flow injection (blowing) at the cylinder surface causes a strong acceleration, whereas increasing suction is found to induce the opposite effect. The study finds applications in rheological chocolate food processing.

Explicit numerical study of unsteady hydromagnetic mixed convective nanofluid flow from an exponentially stretching sheet in porous media

A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (Gr), species Grashof number (Gm), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (Ec), Lewis number (Le), Brownian motion parameter (Nb) and thermophoresis parameter (Nt). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.