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.

Impacts of Nanoparticle Shape on Al₂O₃-Water Nanofluid Flow and Heat Transfer over a Non-Linear Radically Stretching Sheet

The results of this article can be useful in science and technology advancement, such as nanofluidics, micro mixing and energy conversion. The purpose of this article is to examine the impacts of nanoparticle shape on Al2O3-water nanofluid and heat transfer over a non-linear radically stretching sheet in the existence of magnetic field and thermal radiation. The different shapes of Al2O3 nanoparticles that have under contemplation are column, sphere, hexahedron, tetrahedron, and lamina. The governing partial differential equations (PDEs) of the problem are regenerated into set of non-linear ordinary differential equations (ODEs) by using appropriate similarity transformation. The bvp4c program has used to solve the obtained non-linear ordinary differential equation (ODEs). The Nusselt number for all shapes of Al2O3 nanoparticle shapes in pure water with is presented in graphical form. It has reported that the heat transfer augmentation in lamina shapes nanoparticles is more than other shapes of nanoparticle. The relation of thermal boundary layer with shapes of nanoparticles, solid volume fraction, magnetic field and thermal radiation has also presented with the help of graphical representation. It is also demonstrated that lamina shape nanoparticles have showed large temperature distribution than other shapes of nanoparticles.

Boundary layer flow of Maxwell fluid due to torsional motion of cylinder: modeling and simulation

This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field.The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature.The torsional motion of the cylinder is considered with the constant azimuthal velocity E.The partial differential equations(PDEs)governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept.The current analysis is valid only for a certain range of the positive Reynolds numbers.However,for very large Reynolds numbers,the flow becomes turbulent.Thus,the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers.The numerical simulations for the flow,heat,and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB.The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid.It is also noted that the phenomenon of stress relaxation,described by the Deborah number,causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion.The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers.An excellent validation of the numerical results is assured through tabular data with the existing literature.

Truss-type maintenance devices and corresponding pipeline lifting control strategies

For new submarine pipeline maintenance lifting equipment,a specialized analysis model is constructed in this study.A pipeline can be divided into the lifted portion and the touch-down portion that lies on the seabed,and each of these portions can be analyzed separately by converting the continuity conditions at the touch-down points to boundary conditions.The typical two-point sequence secant iterative technique is used to obtain the unknown lifted length and determine pipeline lifting confgurations.The BVP4C module in MATLAB software is used to solve this multiple-point boundary value problem issued from frst-order diferential equations.Also,the triple-point lifting mode of truncated maintenance and the two-point lifting mode of online maintenance are discussed.When the lifted heights at truss positions are shown,the lifting deformation,lifting forces,bending moment distribution,and axial force distribution can be analyzed using a dedicated analysis program.Numerical results can then be used to design a lifting strategy to protect the pipeline.

Numerical Simulation of Reiner–Rivlin Nanofluid Flow under the Influence of Thermal Radiation and Activation Energy over a Rotating Disk

In current study,the numerical computations of Reiner–Rivlin nanofluid flow through a rotational disk under the influence of thermal radiation and Arrhenius activation energy is considered.For innovative physical situations,the motile microorganisms are incorporated too.The multiple slip effects are considered in the boundary conditions.The bioconvection of motile microorganism is utilized alongside nanofluids to provide stability to enhanced thermal transportation.The Bioconvection pattern in various nanoparticles accredits novel applications of biotechnology like the synthesis of biological polymers,biosensors,fuel cells,petroleum engineering,and the natural environment.By deploying some suitable similarity transformation functions,the governing partial differential equations(PDEs)of the flow problem are rehabilitated into dimensionless forms.The accomplished ordinary differential equations(ODEs)are solved numerically through the bvp4c scheme via a built-in function in computational MATLAB software.The upshots of some prominent physical and bioconvection parameters including wall slip parameters,thermophoresis parameter,Brownian motion parameter,Reiner–Revlin nanofluid parameter,Prandtl number,Peclet number,Lewis number,bioconvection Lewis number,and the mixed convection parameter against velocity,temperature,nanoparticles concentration,and density of motile microorganism profiles are dichotomized and pondered through graphs and tables.The presented computations show that the velocity profiles are de-escalated by the wall slip parameters while the thermal and solutal fields are upgraded with augmentation in thermophoresis number and wall slip parameters.The presence of thermal radiation enhances the temperature profile of nanofluid.The concentration profile of nanoparticles is boosted by intensification in activation energy.Furthermore,the increasing values of bioconvection Lewis number and Peclet number decay the motile microorganisms’field.

Coupled flow and heat transfer of power-law nanofluids on non-isothermal rough rotary disk subjected to magnetic field

We study the coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subjected to a magnetic field.The problem is formulated in terms of specified curvilinear orthogonal coordinate system.An improved BVP4C algorithm is proposed,and numerical solutions are obtained.The influence of volume fraction,types and shapes of nanoparticles,magnetic field and power-law index on the flow,and heat transfer behavior are discussed.The obtained results show that the power-law exponents(PLE),nanoparticle volume fraction(NVF),and magnetic field inclination angle(MFIA)have almost no effects on velocities in the wave surface direction,but have small or significant effects on the azimuth direction.The NVF has remarkable influences on local Nusselt number(LNN)and friction coefficients(FC)in the radial direction and the azimuth direction(AD).The LNN increases with NVF increasing while FC in AD decreases.The types of nanoparticles,magnetic field strength,and inclination have small effects on LNN,but they have remarkable influences on the friction coefficients with positively correlated heat transfer rate,while the inclination is negatively correlated with heat transfer rate.The size of the nanoparticle shape factor is positively correlated with LNN.

多因素影响下的毛细血管中血液流动和热量传输问题研究

文章对毛细管中血液的磁流体动力学行为进行了理论分析,流场和温度场的不稳定性是由与时间有关的拉伸速度和表面温度引起的,我们考虑了热辐射、磁场、速度滑移和热滑移条件。为了研究流场和温度场,该问题被描述为耦合的偏微分方程组,利用相似变换,控制方程组被转化为了具有无穷边界的常微分方程组。利用bvp4c函数对所得到的方程组进行了数值求解。对不同的抽吸参数S、磁场参数M、速度滑移参数Sf、热滑移参数St、普朗特数Pr、热辐射参数Nr描绘出了速度分布和温度分布图并进行了分析。由于该文关注血液流动中的热辐射,我们得到的结果对热疗的治疗过程可能有一个有重要影响,尤其是在了解/调节毛细血管中血液的流动和传热方面。

Numerical computation of Brownian motion and thermophoresis effects on rotational micropolar nanomaterials with activation energy

The current article investigates the numerical study of the micropolar nanofluid flow through a 3D rotating surface.This communication may manipulate for the aim such as the delivery of the drug,cooling of electronic chips,nanoscience and the fields of nanotechnology.The impact of heat source/sink is employed.Brownian motion and thermophoresis aspects are discussed.The rotating sheet with the impacts of Darcy-Forchheimer law is also scrutinized.Furthermore,the influence of activation energy is analyzed in the current article.The numerical analysis is simplified with the help of befitted resemblance transformations.The succor of the shooting algorithm with built-in solver bvp4c MATLAB software is used for the numerical solution of nonlinear transformed equations.The consequences of different physical factors on the physical engineering quantities and the subjective fields were examined and presented.According to outcomes,it can be analyzed that the flow profile declined with the rotational parameter.It is observed that angular velocity diminishes via a larger porosity parameter.Furthermore,the temperature gradient is declined via a larger magnitude of the Prandtl number.The heat transfer is enhanced in the occurrence of Brownian motion.The activations energy parameter causes an increment in the volumetric concentration field.Moreover,the local Nusselt number is reduced via a greater estimation of the porosity parameter.

Second law analysis of Blasius flow with nonlinear Rosseland thermal radiation in the presence of viscous dissipation

In the present article,we perform the second law analysis of classical Blasius flow accounting the effects of nonlinear radiation and frictional heating.The two-dimensional boundary layer momentum and energy equations are converted to self-similar equations using similarity transformations.The set of resultant ordinary differential equations are solved numerically.The numerical results obtained from solutions of dimensionless momentum and energy equations are used to calculate the entropy generation number and Bejan number.The velocity profile f'(ξ),temperature distributionθ(ξ),entropy production number Ns and Bejan number Be are plotted against the physical flow parameters and are discussed in detail.Further,for the sake of validation of our numerical code,the obtained results are reproduced using Matlab built-in boundary value solver bvp4c resulting in an excellent agreement.It is observed that entropy generation is increasing function of heating parameter,Prandtl number,Eckert number and radiation parameter.Further,it is observed that entropy generation can be minimized by reducing the operating temperatureΔT=T_(w)−T_(∞).

Three-dimensional mixed convection flow with variable thermal conductivity and frictional heating

In this article,three-dimensional mixed convection flow over an exponentially stretching sheet is investigated.Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity.Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations.Resulting nonlinear ordinary differential equations are solved numerically employing the Runge-Kutta shooting method.In order to check the accuracy of the method,these equations are also solved using bvp4c built-in routine in Matlab.Both solutions are in excellent agreement.The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs.The novelty of this analysis is the self-similar solution of the threedimensional boundary layer flow in the presence of mixed convection,viscous dissipation and variable thermal conductivity.

Non-similar mixed convection analysis for magnetic flow of second-grade nanofluid over a vertically stretching sheet

The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction.The buoyancy effects in terms of temperature and concentration differences are inserted in the x-momentum equation.The aspects of heat and mass transfer are studied using dimensionless thermophoresis,Schmidt and Brownian motion parameters.The governing coupled partial differential system(PDEs)is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations.The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c.Finally,the quantitative effects of emerging dimensionless quantities on the nondimensional velocity,temperature and mass concentration in the boundary layer are conferred graphically,and inferences are drawn that important quantities of interest are substantially affected by these parameters.It is concluded that non-similar modeling,in contrast to similar models,is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.

A Numerical Study of Multiple Solutions for Laminar Flows in a Porous and Moving Channel

In this paper,based on the finite element formulation,we focus on multiple solutions and their evolution with time for a laminar flow in a permeable channel with expanding or contracting walls.Both Newtonian fluid and micropolar fluid are consid-ered.For the Newtonian fluid model,we find that the profile of the unique solution in the case of injection remains the same for long time,which indicates that the solution may be stable.On the other hand,in the case of large suction,the profile of multiple solutions changes in time,which suggests that the multiple solutions may be unstable.Similar behaviors and conclusions are observed for the micropolar fluid model under different boundary parameters.