Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on Peristaltic Flow with Viscous Dissipation and Induced Magnetic Field

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

Computational Investigation of Brownian Motion and Thermophoresis Effect on Blood-Based Casson Nanofluid on a Non-linearly Stretching Sheet with Ohmic and Viscous Dissipation Effects

Motivated by the widespread applications of nanofluids,a nanofluid model is proposed which focuses on uniform magnetohydrodynamic(MHD)boundary layer flow over a non-linear stretching sheet,incorporating the Casson model for blood-based nanofluid while accounting for viscous and Ohmic dissipation effects under the cases of Constant Surface Temperature(CST)and Prescribed Surface Temperature(PST).The study employs a twophase model for the nanofluid,coupled with thermophoresis and Brownian motion,to analyze the effects of key fluid parameters such as thermophoresis,Brownian motion,slip velocity,Schmidt number,Eckert number,magnetic parameter,and non-linear stretching parameter on the velocity,concentration,and temperature profiles of the nanofluid.The proposed model is novel as it simultaneously considers the impact of thermophoresis and Brownian motion,along with Ohmic and viscous dissipation effects,in both CST and PST scenarios for blood-based Casson nanofluid.The numerical technique built into MATLAB’s bvp4c module is utilized to solve the governing system of coupled differential equations,revealing that the concentration of nanoparticles decreases with increasing thermophoresis and Brownian motion parameters while the temperature of the nanofluid increases.Additionally,a higher Eckert number is found to reduce the nanofluid temperature.A comparative analysis between CST and PST scenarios is also undertaken,which highlights the significant influence of these factors on the fluid’s characteristics.The findings have potential applications in biomedical processes to enhance fluid velocity and heat transfer rates,ultimately improving patient outcomes.

Analytical Solution for Laminar Viscous Flow inthe Gap Between Two Parallel Rotary Disks

Aim To get the analytical for laminar viscous flow in the gap of two parallel rotating disks. Methods By estimating the order of magnitude of each term in the Navier-Stokes equations to drop small terms and achieve the required simplified differential equations, and by integrating the equations to obtain the solution for theflow between two rotary disks. Results Parameters related to the laminar viscous flow in the gap between two parallel rotary disks, such as the velocity, the pressure, the flowrate, the force, the shearing stress, the torque and the power derived. Conclusion The result provides a theoretical basis and an effective method for the designs of the devices connected with the laminar viscous flow in the gap between two parallel rotary disks.

GRIDLESS METHOD FOR UNSTEADY VISCOUS FLOWS

Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.

Numerical Simulation of Viscous Flow Around a Rolling Cylinder with Ship-Like Section

Two-dimensional unsteady incompressible viscous flow around a rolling cylinder with ship-like section is numerically simulated by employing the computational scheme previously developed by the authors, in which the continuity and momentum equations are satisfied simultaneously at each time step for oscillating flow. The numerical results show that the motion of vortices around a rolling ship hull is cyclical. It is found that the location of the vortices is very similar to the existing experimental result. Using these simulation results, we can calculate the roll damping of ships including viscous effects.

Viscous-Flow-Based Analysis of Wave Near-Trapped in a Four-Cylinder Structure

The hydrodynamic analysis of multi-floating bodies is important and widely used in marine engineering. In this study, we systematically simulated the wave diffraction problem of a fixed vertical four-cylinder structure in regular waves in the time domain in a viscous numerical wave tank. The hydrodynamic interaction of waves with a bottom-mounted structure consisting of four vertical cylinders arranged at the corners of a square shows a complicated interference phenomenon. In this paper, we illustrate and analyze the run-up around the structure and the corresponding wave forces. To investigate the viscous effect on the near-trapping phenomenon, we pay particular attention to investigating the waves near-trapped inside the four-cylinder structure,and make a comparative study of the viscous-and inviscid-flow solutions with the experimental measurements. The results show that the maximum wave elevation occurs on the inner side of the leeside cylinder, and that the wave elevations on the outer side of the cylinders are lower than those on the inner side. We can conclude that viscosity has an obvious damping effect on wave elevations inside the structure. The cylinders show a tendency to drift apart from each other when the near-trapping phenomenon occurs.

Planar Velocity Distribution of Viscous Debris Flow at Jiangjia Ravine,Yunnan,China:A Field Measurement Using Two Radar Velocimeters

Characteristics of planar velocity distribution of viscous debris flow were analyzed using the measured data at Jiangjia Ravine, Yunnan, China. The velocity data were measured through using two radar velocimeters. The cross-sectional mean velocities were calculated and used to examine Kang et al＇s （2004） relationship, which was established for converting the flow velocity at river centerline measured by a radar velocimeter into the mean velocity based on the stop-watch method. The velocity coefficient, K, defined by the ratio of the mean velocity to the maximum velocity, ranges from 0.2 to 0.6. Kang et al＇s （2004） relationship was found being inapplicable to flows with K smaller than 0.43. This paper contributes to show the complexity of the planar velocity distribution of viscous debris flows and the applicability of Kang et al＇s relationship.

VISCOUS-INVISCID INTERACTING FLOW THEORY

In this paper a viscous-inviscid interacting flow theory(IFT)is developed for an incompressible, two-dimensional laminar flow.IFT's main points are as follows.(1)By introducing a concept of interaction lay- er where the normal momentum exchange is dominating,a new three layer structure is established.(2)Through the conventional manipulations and by introducing an interaction model,both the streamwise and normal length scales are proved to be functions of a single parameter m,which is related to the streamwise pressure gradient and Reynolds number.(3)The approximate equations governing the flow of each layer as well as the whole interaction flow are derived.The present IFT is applicable to both attached and attached-separation bubble-reattached flows, The classical boundary layer theory and Triple-deck theory are shown to be two special cases of the present theory under m=0 and 1/4,respectively.Furthermore IFT provides new distinctions of both the normal and streamwise length scales for flow-field numerical computation and also gives a new approach to developing the simpli- fied Navier-Stokes(SNS)equations.

The Optimal Cross-section Design of the “Trapezoid-V” Shaped Drainage Canal of Viscous Debris Flow

Debris flow drainage canal is one of the most widely used engineering measures to prevent and manage debris flow hazards.The shape and the sizes of the cross-section are important parameters when design debris flow drainage canal.Therefore,how to design the appropriate shape and sizes of the cross-section so that the drainage canal can have the optimal drainage capacity is very important and few researched at home and abroad.This study was conducted to analyze the hydraulic condition of a Trapezoid-V shaped drainage canal and optimize its cross-section.By assuming characteristic sizes of the cross-section,the paper deduced the configuration parameter of the cross-section of a Trapezoid-V shaped debris flow drainage canal.By theory analysis,it indicates that the optimal configuration parameter is only related to the side slope coefficient and the bottom transverse slope coefficient.For this study,the Heishui Gully,a first-order tributary of the lower Jinsha River,was used as an example to design the optimal cross-section of the drainage canal of debris flow.

Natural consolidation characteristics of viscous debris flow deposition

Pore water pressure and water content are important indicators to both deposition and consolidation of debris flows, enabling a direct assessment of consolidation degree. This article gained a more comprehensive understanding about the entire consolidation process and focused on exploring pore water pressure and volumetric water content variations of the deposit body during natural consolidation under different conditions taking the viscous debris flow mass as a study subject and by flume experiments. The results indicate that, as the color of the debris changed from initial dark green to grayish-white color, the initial deposit thickness declined by 3% and 2.8% over a permeable and impermeable sand bed, respectively. A positive correlation was observed between pore water pressure and depth in the deposit for both scenarios, with deeper depths being related to greater pore water pressure. For the permeable environment, the average dissipation rate of pore water pressure measured at depths of 0.10 m and 0.05 m were 0.0172 Pa/d and 0.0144 Pa/d, respectively, showing a positivechanging trend with increasing depth. Under impermeable conditions, the average dissipation rates at different depths were similar, while the volumetric water content in the deposit had a positive correlation with depth. The reduction of water content in the deposit accelerated with depth under impermeable sand bed boundary conditions, but was not considerably correlated with depth under permeable sand bed boundary conditions. However, the amount of discharged water from the deposit was greater and consolidation occurred faster in permeable conditions. This indicates that the permeability of the boundary sand bed has a significant impact on the progress of consolidation. This research demonstrates that pore water and pressure dissipations are present during the entire viscous debris consolidation process. Contrasting with dilute flows, pore pressure dissipation in viscous flows cannot be completed in a matter of minutes or even hours, requiring longer completion time — 3 to 5 days and even more. Additionally, the dissipation of the pore water pressure lagged the reduction of the water content. During the experiment, the dissipation rate fluctuated substantially, indicating a close relationship betweenthe dissipation process and the physical properties of broadly graded soils.

Numerical computation and analysis of unsteady viscous flow around autonomous underwater vehicle with propellers based on sliding mesh

The flexible transmission shaft and wheel propeller are combined as the kinetic source equipment, which realizes the nmlti-motion modes of the autonomous underwater vehicle （AUV） such as vectored thruster and wheeled movement. In order to study the interactional principle between the hull and the wheel propellers while the AUV navigating in water, the computational fluid dynamics （CFD） method is used to simulate numerically the unsteady viscous flow around AUV with propellers by using the Reynolds-averaged Navier-Stokes （RANS） equations, shear-stress transport （SST） k-w model and pressure with splitting of operators （PISO） algorithm based on sliding mesh. The hydrodynamic parameters of AUV with propellers such as resistance, pressure and velocity are got, which reflect well the real ambient flow field of AUV with propellers. Then, the semi-implicit method for pressure-linked equations （SIMPLE） algorithm is used to compute the steady viscous flow field of AUV hull and propellers, respectively. The computational results agree well with the experimental data, which shows that the numerical method has good accuracy in the prediction of hydrodynamic performance. The interaction between AUV hull and wheel propellers is predicted qualitatively and quantitatively by comparing the hydrodynamic parameters such as resistance, pressure and velocity with those from integral computation and partial computation of the viscous flow around AUV with propellers, which provides an effective reference to the shady on noise and vibration of AUV hull and propellers in real environment. It also provides technical support for the design of new AUVs.

Application Progress of Computational Fluid Dynamic Techniques for Complex Viscous Flows in Ship and Ocean Engineering

Complex flow around floating structures is a highly nonlinear problem,and it is a typical feature in ship and ocean engineering.Traditional experimental methods and potential flow theory have limitations in predicting complex viscous flows.With the improvement of high-performance computing and the development of numerical techniques,computational fluid dynamics(CFD)has become increasingly powerful in predicting the complex viscous flow around floating structures.This paper reviews the recent progress in CFD techniques for numerical solutions of typical complex viscous flows in ship and ocean engineering.Applications to free-surface flows,breaking bow waves of high-speed ship,ship hull-propeller-rudder interaction,vortexinduced vibration of risers,vortex-induced motions of deep-draft platforms,and floating offshore wind turbines are discussed.Typical techniques,including volume of fluid for sharp interface,dynamic overset grid,detached eddy simulation,and fluid-structure coupling,are reviewed along with their applications.Some novel techniques,such as high-efficiency Cartesian grid method and GPU acceleration technique,are discussed in the last part as the future perspective for further enhancement of accuracy and efficiency for CFD simulations of complex flow in ship and ocean engineering.

A CFD Based Investigation of the Unsteady Hydrodynamic Coefficients of 3-D Fins in Viscous Flow

The motion of the fins and control surfaces of underwater vehicles in a fluid is an interesting and challenging research subject.Typically the effect of fin oscillations on the fluid flow around such a body is highly unsteady, generating vortices and requiring detailed analysis of fluid-structure interactions.An understanding of the complexities of such flows is of interest to engineers developing vehicles capable of high dynamic performance in their propulsion and maneuvering.In the present study, a CFD based RANS simulation of a 3-D fin body moving in a viscous fluid was developed.It investigated hydrodynamic performance by evaluating the hydrodynamic coefficients (lift, drag and moment) at two different oscillating frequencies.A parametric analysis of the factors that affect the hydrodynamic performance of the fin body was done, along with a comparison of results from experiments.The results of the simulation were found in close agreement with experimental results and this validated the simulation as an effective tool for evaluation of the unsteady hydrodynamic coefficients of 3-D fins.This work can be further be used for analysis of the stability and maneuverability of fin actuated underwater vehicles.

Effect of Viscosity on Free-Surface Waves in Oseen Flows

Based on the complex dispersion relation for the two-dimensional free-surface waves generated by a moving body in the steady Oseen flows, the effect of viscosity on wavelength and wave amplitude was investigated by means of an asymptotic method and a numerical analysis. A comparison between the asymptotic and numerical analysis for the viscous decay factor demonstrates the validity of the perturbation expansions for the wave profile. The numerical result shows that the wavelength of viscous wave is slightly elongated in comparison with that of inviscid wave.

Gravel Accumulation in Deposits of Viscous Debris Flows with Hyper-concentration

According to the observational data of viscous debris flows with hyper-concentration, debris flows can be classified into three types:high-viscous, viscous, and sub-viscous debris flows.Distinct formation mechanism of different graded bedding structures in deposits of viscous debris flows was analyzed in this paper by using their yield-stress ratio and flow plug ratio.This paper specially analyzed the effect of Weissenberg which the gravels in squirm condition of hyper-concentration viscous flows would tend to move vertically, and the formation mechanism of the gravels accumulated at surface was also studied.The analysis in this paper can establish a foundation for the studies on differentiation of bedding structures of debris flow deposits and studies on dynamic parameters of debris flows.

Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet

The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations （ODEs） are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ~, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.

Computation of Viscous Uniform and Shear Flow over A Circular Cylinder by A Finite Element Method

The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional Navier-Stokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from 100 to 1000. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem.

Study on MHD Viscous Flow over a Stretching Sheet Using DTM-Pade’ Technique

In this paper, we present the study of momentum characteristics in a MHD viscous flow over a stretching sheet. First the partial differential equations of motion have been transformed to an ordinary differential equation. The analytical method called Differential Transformation Method (DTM) powered by the Pade’ approximation is applied to solve the nonlinear equation derived from MHD viscous flow over a stretching sheet, the effect of parameters variation has been investigated for two numerical cases and finally the analytical results have been compared with numerical one in a numerical case. The obtained results approve its efficiencies and capabilities beside numerical solutions achieved from Runge Kutta method.

Heat Transfer with Viscous Dissipation in Couette-Poiseuille Flow under Asymmetric Wall Heat Fluxes

Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes.

Laminar Flow in the Gap between Two Rotating Parallel Frictional Plates in Hydro-viscous Drive

The velocity, pressure and temperature distributions of the flow in the gap between hydro-viscous drive friction disks are the key parameters in the design of hydro-viscous drive and angular velocity controller. In the previous works dealing with the flow in the gap between disks in hydro-viscous drive, few authors considered the effect of Coriolis force on the flow. The object of this work is to investigate the flow with consideration of the effects of centrifugal force, Coriolis force and variable viscosity. A simplified mathematical model based on steady and laminar flow is presented. An approximate solution to the simplified mathematical model is obtained by using the iteration method assuming that the fluid viscosity remains constant. Then the model considering the effect of variable viscosity is solved by means of computational fluid dynamics code FLUENT. Numerical results of the flow are obtained. It is found that radial velocity profile diverges from the ideal parabolic curve due to inertial forces and tangential velocity profile is nonlinear due to Coriolis force, and pressure has two possible solution branches. In addition, it is found that variable viscosity plays an important role on pressure profiles which are significantly different from those of fluid with constant viscosity. The experimental device designed for this work consists of two disks, and one of them is fixed. Experimental pressure and temperature of the flow within test rig are obtained. It is shown that the trend of numerical results is in agreement with that of experimental ones. The research provides a theoretical foundation for hydro-viscous drive design.