Numerical Analysis of the Magnetic Dipole Effect on a Radiative Ferromagnetic Liquid Flowing over a Porous Stretched Sheet

The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidflowing over a stretched surface in the presence of Brownian motion and thermophoresis are investigated.By means of a similarity transformation,ordinary differential equations are derived and solved afterwards using a numerical(the BVP4C)method.The impact of various parameters,namely the velocity,temperature,concentration,is presented graphically.It is shown that the nanoparticles properties,in conjunction with the magnetic dipole effect,can increase the thermal conductivity of the engineered nanofluid and,consequently,the heat transfer.Comparison with earlier studies indicates high accuracy and effectiveness of the numerical approach.An increase in the Brow-nian motion parameter and thermophoresis parameter enhances the concentration and the related boundary layer.The skin-friction rises when the viscosity parameter is increased.A larger value of the ferromagnetic para-meter results in a higher skin-friction and,vice versa,in a smaller Nusselt number.

Finite Element Analysis for Magneto-Convection Heat Transfer Performance in Vertical Wavy Surface Enclosure:Fin Size Impact

The goal of this paper is to represent a numerical study of magnetohydrodynamic mixed convection heat transfer in a lid-driven vertical wavy enclosure with a fin attached to the bottomwall.We use a finite elementmethod based on Galerkin weighted residual(GWR)techniques to set up the appropriate governing equations for the present flow model.We have conducted a parametric investigation to examine the impact of Hartmann and Richardson numbers on the flow pattern and heat transmission features inside a wavy cavity.We graphically represent the numerical results,such as isotherms,streamlines,velocity profiles,local and mean Nusselt numbers,and average surface temperature.Comparisons between the results of this work and previously published work in a literature review have been produced to examine the reliability and consistency of the data.The different sizes of the fin surface significantly impact flow creation and temperature fields.Additionally,the long fin size is necessary to enhance the heat transfer rate on the right surface at large Richardson numbers and low Hartmann numbers.Fin surfaces can significantly increase the mixing of fluid inside the enclosure,which can mean reductions in reaction times and operating costs,along with increases in heat transfer and efficiency.

Magneto-Hydro-Convective Nanofluid Flow in Porous Square Enclosure

In this work,a steady mixed convection in a two-dimensional enclosure filled viananoliquid Cu/H2O through a porous medium was numerically analyzed.The nanoliquid flow is designated utilizing the Brinkman-Forchheimer model.The upper and the bottom horizontal walls are considered to be hot(Th)and cold temperature(Tc),respectively,whereas the other walls are thermally insulated.The impact of various dimensionless terms such as the Grashof number(Gr)in the ranges(0.01–20),the Reynolds number(Re)in the ranges(50–500),the Hartman number(Ha)in the ranges(0–20),and three different location cases(0.25,0.5,and 0.75)are carefully analyzed.The obtained outcomes are established in the form of isotherms,streamlines,and the average Nusselt number.It has been found that heat transport increases significantly through rising Reynolds number(Re).For the location cases L=0.25,Re=50,and Gr=105,the heat transfer is maximum.

Slip Effects on Casson Nanofluid over a Stretching Sheet with Activation Energy:RSM Analysis

The current study is dedicated to presenting the Casson nanofluid over a stretching surface with activation energy.In order to make the problem more realistic,we employed magnetic field and slip effects on fluid flow.The governing partial differential equations(PDEs)were converted to ordinary differential equations(ODEs)by similarity variables and then solved numerically.The MATLAB built-in command‘bvp4c’is utilized to solve the system of ODEs.Central composite factorial design based response surface methodology(RSM)is also employed for optimization.For this,quadratic regression is used for data analysis.The results are concluded bymeans of tables and pictorial representations.The present study discloses that the temperature profile increases with enhancement in Ha,Nr,Nb,and Nt and it shows opposite behavior forλ.The included parameters show same trend for heat transfer rate(Nux).It is also concluded thatδshould bemaximum for any value ofNb and Nt to maximize the heat transfer rate.

Melting Flow Analyzation of Radiative Riga Plate Two-Phase Nano-Fluid Across Non-Flatness Plane with Chemical Reaction

There is a strong relationship between analytical and numerical heat transfers due to thermodynamically anticipated findings,making thermo-dynamical modeling an effective tool for estimating the ideal melting point of heat transfer.Under certain assumptions,the present study builds a mathematical model of melting heat transport nanofluid flow of chemical reactions and joule heating.Nanofluid flow is described by higher-order partial non-linear differential equations.Incorporating suitable similarity transformations and dimensionless parameters converts these controlling partial differential equations into the non-linear ordinary differential equations and resulting system of nonlinear equations is established.Plotted graphic visualizations in MATLAB allow for an indepth analysis of the effects of distinguishing factors on fluid flow.Innovative applications of the findings include electronic cooling,heat transfer,reaction processes,nuclear reactors,micro heat pipes,and other related fields.If the exponential index increases,however,the thermal profile becomes worse.By comparing the current findings to those already published in the literature for this particular example,we find that they are highly congruent,therefore validating the present work.Every one of the numerical findings exhibits asymptotic behavior by meeting the specified boundary conditions.

Cross-Diffusion Effects on an MHD Williamson Nanofluid Flow Past a Nonlinear Stretching Sheet Immersed in a Permeable Medium

The primary aim of this research endeavor is to examine the characteristics of magnetohydrodynamicWilliamson nanofluid flow past a nonlinear stretching surface that is immersed in a permeable medium.In the current analysis,the impacts of Soret and Dufour(cross-diffusion effects)have been attentively taken into consideration.Using appropriate similarity variable transformations,the governing nonlinear partial differential equations were altered into nonlinear ordinary differential equations and then solved numerically using the Runge Kutta Fehlberg-45 method along with the shooting technique.Numerical simulations were then perceived to show the consequence of various physical parameters on the plots of velocity,temperature,and concentration of the nanofluid flow.Boosting the magnetic,Williamson,porosity,and stretching sheet index parameters,the velocity of the fluid flow decreases.The temperature is enhanced as theWilliamson and Brownian motion parameters upsurge,but it decreases as the Prandtl,thermophoresis,stretching sheet index,and Dufour parameters escalate.The concentration distribution decreases as the thermophoresis andmagnetic parameters upsurge,but it escalates as the Soret,Schmidt,Brownian motion,and stretching sheet index parameters increase.Skin friction coefficient boosted as the stretching sheet index and magnetic parameters enhanced against the Williamson parameter.The findings from this study have been contrasted with earlier findings on local Nusselt numbers,which show substantial support and endorse the existing approach’s validity.The numerical values of the local Sherwood number gradually increase as the Schmidt,Soret,stretching sheet index,and thermophoresis parameters are upsurged.

Pressure-Driven Gas Flows in Micro Channels with a Slip Boundary:A Numerical Investigation

In this paper,flow of slightly rarefied compressible nitrogen in microchannels has been investigated numerically for low values of Reynolds and Mach numbers.The 2D governing equations were solved using Finite Element Method with first-order slip boundary conditions(Comsol Multiphysics software).A validation was performed by comparing with similar configuration from the literature.It was found that our model can accurately predict the pressure driven flow in microchannels.Several interesting findings are reported about the Relative pressure,longitudinal velocity,Mach number,effect of gas rarefaction and flow rate.

Galerkin finite element analysis of magneto-hydrodynamic natural convection of Cu-water nanoliquid in a baffled U-shaped enclosure

In this paper,single-phase homogeneous nanofluid model is proposed to investigate the natural convection of magneto-hydrodynamic(MIID)flow of Newtonian Cu—H20 nanoli­quid in a baffled U-shaped enclosure.The Brinkman model and Wasp model are considered to measure the effective dynamic viscosity and effective thermal conductivity of the nanoliquid coreespondingly.Nanoliquid's effective properties such as specific heat,density and thermal expansion coefficient are modeled using mixture theory.The complicated PDS(partial differ­ential system)is treated for numeric solutions via the Galerkin finite element method.The perti­nent parameters Hartmann number(1≤Ha≤60),Rayleigh number(10^(3)≤Ra≤10^(6))and nanoparticles volume fraction (0% ≤Ф≤4%) are taken for the parametric analysis, and it is conducted via streamlines and isotherms. Excellent agreement between numerical results and open literature. It is ascertained that heat transfer rate enhances with Rayleigh number Ra and volume fraction 0, however it is diminished for laiger Hartmann number Ha.