B-spline collocation simulation of non-linear transient magnetic nanobio-tribological squeeze-film flow

A mathematical model is presented for magnetized nanofluid bio-tribological squeeze film flow between two approaching disks. The nanofluid comprises a suspension of metal oxide nanoparticles with an electrically-conducting base fluid, making the nano-suspension responsive to applied magnetic field. The governing viscous momentum, heat and species (nano-particle) conservation equations are normalized with appropriate transformations which renders the original coupled, nonlinear partial differential equation system into a more amenable ordinary differential boundary value problem. The emerging model is shown to be controlled by a number of parameters, viz nanoparticle volume fraction, squeeze number, Hartmann magnetic body force number, disk surface transpiration parameter, Brownian motion parameter, thermophoretic parameter, Prandtl number and Lewis number. Computations are conducted with a B-spline collocation numerical method. Validation with previous homotopy solutions is included. The numerical spline algorithm is shown to achieve excellent convergence and stability in nonlinear bio-tribological boundary value problems. The interaction of heat and mass transfer with nanofluid velocity characteristics is explored. In particular smaller nanoparticle (high Brownian motion parameter) suspensions are studied. The study is relevant to enhanced lubrication performance in novel bio-sensors and intelligent knee joint (orthopaedic) systems

Computational analysis of viscous dissipation and joule-heating effects on non-Darcy MHD natural convection flow from a horizontal cylinder in porous media with internal heat generation

In the present paper we examine the effects of viscous dissipation, Joule heating and heat source/sink on non-Darcy MHD natural convection heat transfer flow over permeable horizontal circular cylinder in a porous medium. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. A parametric study illustrating the influence of Darcy parameter (Da), Forchheimer parameter (Λ), Grashof number(Gr), heat source/sink parameter (Ω) and viscous dissipation parameter (Ec) on the fluid velocity, temperature as well as local skin-friction and Nusselt numbers is conducted Increasing Forchheimer inertial drag parameter (Λ) retards the flow considerably but enhances temperatures. Increasing viscous dissipation parameter(Ec) is found to elevate velocities i.e. accelerate the flow and increase temperatures. Increasing heat source/sink parameter (Ω) is found to elevate velocities and increase temperatures. Increasing the Grashof number (Gr) is found to elevate the velocity and decrease the temperatures. Local skin friction number is found to be increases with increasing heat source/sink parameter (Ω) where as Local Nusselt number is found to decrease with increasing heat source/sink parameter (Ω)

Modeling magnetic nanopolymer flow with induction and nanoparticle solid volume fraction effects : solar magnetic nanopolymer fabrication simulation

A mathematical model is presented for the nonlinear steady, forced convection, hydromagnetic flow of electro-conductive magnetic nano-polymer with magnetic induction effects included. The transformed two-parameter, non-dimensional governing partial differential equations for mass, momentum, magnetic induction and heat conservation are solved with the local non-similarity method (LNM) subject to appropriate boundary conditions. Keller’s implicit finite difference “box” method (KBM) is used to validate solutions. Computations for four different nanoparticles and three different base fluids are included. Silver nanoparticles in combination with various base fluids enhance temperatures and induced magnetic field and accelerate the flow. An elevation in magnetic body force number decelerates the flow whereas an increase in magnetic Prandtl number elevates the magnetic induction. Furthermore, increasing nanoparticle solid volume fraction is found to substantially boost temperatures. Applications of the study arise in advanced magnetic solar nano-materials (fluids) processing technologies

Partial Differential Equations in Applied Mathematics https://www.sciencedirect.com/journal/partial-differential-equations-in-applied- mathematics Analysis of unsteady thermo-solutal MoS2-EO Brinkman electro-conductive reactive nanofluid transport in a hybrid rotating Hall MHD generator

MHD rotating generators offer a plausible renewable energy mechanism. New designs are emerging in which nanotechnology is contributing. Such systems are increasingly deploying more complex functional fluid materials such as base fluids containing magnetic nanoparticles which constitute electromagnetic nanofluids and can be tuned to enhance efficiencies. Motivated by these developments, a mathematical model is presented for the combined effects of Hall current, heat source, chemical reaction and radiative flux on the unsteady rotating thermo-solutal magnetohydrodynamic transport of a Molybdenum disulphide (MoS2)-EO oil electroconductive Brinkman nanofluid to study the boundary layer characteristics in the vicinity of the side wall of an MHD generator system. The governing dimensional conservation equations are scaled using appropriate transformations into a system of dimensionless coupled partial differential equations. Under appropriate initial and boundary conditions, solutions are derived using the Laplace Transform Method (LTM) and complex variables. The physical impacts of the magnetic, nanoscale, thermal and species control parameters on primary and secondary velocity, temperature and concentration are visualized graphically. The judicious doping of the base fluid with MoS2 nanoparticles is shown to achieve superior thermal performance for MHD rotating energy generators

Finite element stress analysis and topological optimization of a commercial aircraft seat structure

In recent years, the Finite Element Method (FEM) has emerged as a cornerstone in the field of seating design, particularly within the aircraft industry. Over the past decade, significant advancements in Finite Element (FE) analysis techniques have revolutionized the seat industry, enabling the creation of safer and more cost-effective seat designs. The accuracy of FE analysis plays a pivotal role in this transformation. In the process of constructing a reliable finite element model, the selection and precise manipulation of key parameters are paramount. These crucial parameters encompass element size, time scale, analysis type, and material model. Properly defining and implementing these parameters ensures that the FE model produces accurate results, closely mirroring real-world performance. Verification of Finite Element Analysis (FEA) results is commonly accomplished through experimental methods. Notably, when the parameters are appropriately integrated into the modelling process, FE analysis outcomes closely align with experimental results. This study aims to leverage the power of FEM in performing static stress analysis and topology optimization of aircraft seats using the SOLIDWORKS commercial finite element platform. By simulating loading conditions, this research calculates static stresses and displacements experienced by the aircraft seat. For AL7075-T6(SN) the structural analysis demonstrates that this material had a maximum stress of 125.2 N/mm 2 and a minimum stress of 0.0039 N/mm 2. Due to its strong 4.034 factor of safety, the component may have been over-engineered for its intended use. However, at 2.32 kg, the component's mass and $2.304/kg material cost showed a high design cost. The maximum Y-component of displacement was 0.0606 mm, which was acceptable but could have been optimized to decrease material use and expense without affecting structural integrity. After performing topology optimization on Simulation 1 of AL7075-T6(SN), several improvements have been achieved. The maximum stress sustained by the component has been elevated to 189.4 N/mm 2. However, it is worth noting that the minimum stress has also risen, although to a negligible value of 0.0006 N/mm 2. The compromise in this scenario is characterized by a fall in the factor of safety to 2.666, suggesting a design that is more optimal but possibly associated with more risk. The most notable improvements, however, concern weight reduction. The overall mass of the component saw a substantial reduction, reaching 1.89 kg, which represents a notable improvement on the original design. Through a comprehensive topology optimization study, the weight of the airplane seat is remarkably reduced by up to 30%, while still prioritizing passenger safety. The success of this optimization showcases the potential for substantial weight savings in aircraft seat design without compromising safety standards

Metachronal propulsion of a magnetized particle-fluid suspension in a ciliated channel with heat and mass transfer

Biologically inspired pumping systems are of great interest in modern engineering since they achieve enhanced efficiency and circumvent the need for moving parts and maintenance. Industrial applications also often feature two-phase flows. In this article, motivated by these applications, the pumping of an electrically conducting particle-fluid suspension due to metachronal wave propulsion of beating cilia in a two-dimensional channel with heat and mass transfer under a transverse magnetic field is investigated theoretically. The governing equations for mass and momentum conservation for fluid- and particle-phases are formulated by ignoring the inertial forces and invoking the long wavelength approximation. The Jeffrey viscoelastic model is employed to simulate non-Newtonian characteristics. The normalized resulting differential equations are solved analytically. Symbolic software is employed to evaluate the results and simulate the influence of different parameters on flow characteristics. Results are visualized graphically with carefully selected and viable data

Nanofluid slip flow over a stretching cylinder with schmidt and péclet number effects

A mathematical model is presented for three-dimensional unsteady boundary layer slip flow of Newtonian nanofluids containing gyrotactic microorganisms over a stretching cylinder. Both hydrodynamic and thermal slips are included. By applying suitable similarity transformations, the governing equations are transformed into a set of nonlinear ordinary differential equations with appropriate boundary conditions. The transformed nonlinear ordinary differential boundary value problem is then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple 18 symbolic software. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fractions and microorganism motile density functions have been illustrated graphically. Comparisons of the present paper with the existing published results indicate good agreement and supports the validity and the accuracy of our numerical computations. Increasing bioconvection Schmidt number is observed to depress motile micro-organism density function. Increasing thermal slip parameter leads to a decrease in temperature. Thermal slip also exerts a strong influence on nano-particle concentration. The flow is accelerated with positive unsteadiness parameter (accelerating cylinder) and temperature and micro-organism density function are also increased. However nano-particle concentration is reduced with positive unsteadiness parameter. Increasing hydrodynamic slip is observed to boost temperatures and micro-organism density whereas it decelerates the flow and reduces nano-particle concentrations. The study is relevant to nano-biopolymer manufacturing processes

Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic (MHD), incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted

Unsteady reactive magnetic radiative micropolar flow, heat and mass transfer from an inclined plate with joule heating: a model for magnetic polymer processing

Magnetic polymer materials processing involves many multi-physical and chemical effects. Motivated by such applications, in the present work a theoretical analysis is conducted of combined heat and mass transfer in unsteady mixed convection flow of micropolar fluid over an oscillatory inclined porous plate in a homogenous porous medium with heat source, radiation absorption and Joule dissipation. A first order homogenous chemical reaction model is used. The transformed non-dimensional boundary value problem is solved using a perturbation method and Runge-Kutta fourth order numerical quadrature (shooting technique). The emerging parameters dictating the transport phenomena are shown to be the gyro-viscosity micropolar material parameter, magnetic field parameter, permeability of the porous medium, Prandtl number, Schmidt number, thermal Grashof number, species Grashof number, thermal radiation-conduction parameter, heat absorption parameter, radiation absorption parameter, Eckert number, chemical reaction parameter and Eringen coupling number (vortex viscosity ratio parameter). The impact of these parameters on linear velocity, microrotation (angular velocity), temperature and concentration are evaluated in detail. Results for skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are also included. Couple stress is observed to be reduced with stronger magnetic field. Verification of solutions is achieved with earlier published analytical results

Unsteady flow of a nanofluid over a sphere with nonlinear Boussinesq approximation

A theoretical study is presented of transient mixed convection boundary layer flow of a nanofluid in the forward stagnation region of a heated sphere which is rotating with time dependent angular velocity. The effect of the non-linear Boussinesq approximation is taken into account. The nanofluid is treated as a two-component mixture i.e. nano-particles distributed homogenously in a base fluid (water or gas). The effects of the Brownian motion and thermophoresis are included for the nanofluid and constant wall temperature is imposed at the sphere surface. The first and second laws of thermodynamics are employed in order to study thermophysics as well as heat and mass transfer phenomena. By introducing appropriate similarity variables the governing equations are transformed into a system of dimensionless, nonlinear, coupled, ordinary differential equations which are solved numerically by applying the second-order accurate implicit finite difference Keller box method. The reliability and efficiency of the obtained numerical results are validated via comparison with the previously published results for special cases. The effects of various parameters on primary and secondary velocities, temperature, nanofluid volume fraction (concentration), primary and secondary shear stress functions, Nusselt number function (wall heat transfer rate) and Sherwood number function (wall nanoparticle mass transfer rate) are visualized. Furthermore the influence of non-linear temperature parameter, Brinkman parameter (ratio of Brinkman number to dimensionless temperature ratio), local Reynolds number and unsteadiness parameter on entropy generation number is computed. A strong elevation in entropy generation number is computed with both increasing Brinkman parameter and unsteadiness parameter. Primary and secondary surface shear stresses, Nusselt number and Sherwood number also increase with unsteadiness and rotation parameters. Primary shear stress is boosted with increasing mixed convection parameter and Brownian motion effect whereas secondary shear stress is depressed. Temperatures are suppressed with increasing nonlinear temperature parameter whereas nano-particle concentrations are elevated. Increasing thermophoresis parameter enhances both temperatures and nano-particle concentration values. The simulations find applications in rotating chemical engineering mixing systems and nano-coating transport phenomena