Surface Drag Force Research Articles

Mixed convective flow of a magnetohydrodynamic Casson fluid through a permeable stretching sheet with first-order chemical reaction.

This research article presents the magnetohydrodynamic Casson fluid flow through an extending surface embedded in a porous medium. Furthermore, the Casson fluid flow is investigated under the effects of thermal radiation, Joule heating, viscous dissipation, and chemical reaction. The analytical solution of the modeled problem is utilized with the help of homotopy analysis method (HAM). The convergence region of the applied technique is portrayed graphically. The impacts of the embedded factors on the flow profiles are exhibited with the help of figures. Furthermore, numerical values of the surface drag force, heat, and mass transfer rates are highlighted via table. The results show that the augmented Darcy number, Casson and magnetic parameters have declined the velocity profile of the Casson fluid flow. Growth in Brownian motion augments the chaotic motion amongst the particles due to which the kinetic energy of the particles transforms to heat energy which consequently augmented the thermal profile, while reduced the concentration profile. The mass and energy profiles are positively effects with the increment of thermophoresis term. And the growing values of chemical reaction and Lewis number cause a reduction in the diffusivity of mass of fluid due to which less transfer of mass takes place that weakens the concentration layer thickness and declines the concentration profiles.

Visualization of multiple slip effects on the hydromagnetic Casson nanofluid past a nonlinear extended permeable surface: a numerical approach

This study intends to explore the interaction effects of the magnetic field and the slip effect of the MHD flow of the Casson nanofluid by a nonlinear stretching surface embedded in a porous medium. The nanofluids’ flow over a stretching surface is critically important due to their application in the broad spectrum of industries and scientific fields. The mathematical formulation for mass conservation, momentum, energy and concentration profiles is expressed in the form of partial differential equations. The dimensionless system of ordinary differential equations has been diminished from modeled equations via a transformation framework. A numerical algorithm bvc4c method is implemented for a local similar solution of highly nonlinear equations. The characteristics of material parameters on the flow field, temperature, concentration, surface drag force and Nusselt number are tackled via plotted graphs. The authentication of the numerical code has been verified with a homotopic solution and an excellent agreement is perceived as a limiting case. Higher values of the Casson parameter , magnetic parameter , porosity parameter and stretching parameter correspond to a reduction in the velocity profile gradually. As noticed from this graph, the deescalating temperature profile is subject to an increment in parameter . From this study, it is observed that the velocity profile increases with the velocity slip number , and the temperature profile decreases with the temperature slip number It is also investigated that the temperature profiles enhance with increasing and decline with . The concentration profiles increase with the increasing values of and .

Supervised neural networks learning algorithm for three dimensional hybrid nanofluid flow with radiative heat and mass fluxes

Hybrid nanofluid is an emerging field due to the rapid enhancement of heat transfer and stable nanoparticles in base fluid properties. A three dimensional hybrid nanofluid flow model is constructed over biaxial porous stretching/shrinking sheet with heat transfer, Radiative heat and mass flux (3D-HNF-RHF). Bayesian Regularization technique based on Backpropagated neural networks (BRT-BNNs) is employed to estimate the solution of proposed model. It is the mathematical process which converts nonlinear regression fitting into a well-posed statistical process in the form of ridge regression. This method diminishes length cross validation need and more robust then Backpropagation technique. The proposed flow system 3D-HNF-RHF is transferred to ordinary differential equations (ODEs) possessing physical variations through self-similar transformations. The effect of derived variations such as thermal relaxation parameter, mass flux parameter, Stretching/shrinking parameter, Prandtl number, Skin friction and Nusselt number observed over the velocity and temperature fields. Numerical results of these physical parameters have been presented in tabulated form obtained from a dataset constructed through Homotopy Analysis Method imposed on 3D-HNF-RHF model. Statistical tests through mean square error, histogram curve and regression fitting curves are employed to check the accuracy and convergences of the solution obtained through BRT-BNNs. It is observed that Stretching/shrinking quantity and mass flux parameter slow down the flow rate whereas, increase radiative heat flux upsurges the temperature gradient. The impacts of surface drag force and heat transfer are illustrated through the different graphical illustrations.

Development of an underwater robotic arm using multibody dynamics approach

Underwater robotic arms are important devices that enables workers to carry out tasks remotely from a safe distance reducing or eliminating the risks that are involved with the task. The primary objective of the robotic manipulator is to perform maintenance and cleaning activities of the hull of a ship. However, the control of these devices underwater is quite complicated due to the numerous factors that make these systems unstable and non-linear. The aim of this study is to develop a multibody dynamic robotic manipulator model, integrated with a control strategy to optimize and obtain stable kinematics solutions. The hydrodynamic forces are integrated to the manipulator model considering buoyancy forces and surface drag forces. A basic algorithm is used to generate the joint angles using 7 geometrical parameters. The control of the manipulator was done to simply follow any path that represents the given coordinates. The P, I and D parameters are tuned individually to optimize the kinematic solution of the manipulator. 3-DOF articulated manipulator is the commonly used manipulator configuration. However, a 6-DOF manipulator configuration was selected in this study to allow for change in orientation using wrist motions.

Entropy Generation in Magneto-Casson Nanofluid Flow Along an Inclined Stretching Sheet Under Porous Medium with Activation Energy and Variable Heat Source/Sink

The current paper deals with the study of magneto-convective and chemically reactive Casson nanofluid flow along an inclined permeable stretching surface embedded in a fluid-saturated uniform porous medium. As a novelty of the work, entropy generation analysis in the presence of multiple slips at the surface and a nonuniform heat source/sink is carried out. Moreover, viscous dissipation, Arrhenius activation energy, Joule dissipation and thermal radiation are included in the investigation. To the best of authors’ knowledge, no such study on Casson nanofluid is reported yet in the literature. Dimensionless similarity transformations have been introduced to convert the regulating model PDEs into ODEs in dimensionless form. As the model equations are highly nonlinear in nature, shooting technique based on the Runge-Kutta Cash-Karp method is used to solve those equations numerically. The updated values of the initial guesses are computed with the help of secant iteration. Profiles for fluid velocity, temperature, nanoparticle concentration and entropy generation have been drawn to explain the impacts of several important parameters on momentum, thermal and mass fields. However, the surface drag force, heat and mass transport rates at the solid wall are illustrated using numerical data displayed in tabular form. Also, a linear regression model is derived for the local Nusselt number and the related physical parameters. Moreover, a comparison table is presented to confirm the correctness of the obtained results. A fantastic correlation of the present results with the existing results is reported. Graphical results reveal that for the rising values of the angle of inclination parameter and magnetic parameter velocity profiles are declined, but for the growing values of Eckert number and thermal radiation parameter temperature profiles are enhanced.

Numerical investigation of ohmically dissipated mixed convective flow

The impact of ohmic heating and thermal radiation plays a prominent role in industrial and technological applications, for example aerodynamic heating and process flows. Thus the current study provides the convective heat transfer of magnetohydrodynamics mixed convection flow towards a penetrable stretching wedge with ohmic heating and thermal radiation. By utilizing suitable similarity transformation the set of ODEs are transformed to set of highly nonlinear PDEs. The reduced equations are elucidated by employing bvp4c method in MATLAB software. The effects of numerous emerging parameters were examined and disclosed graphically. In contrast, the inclusion of stretching wedge, the temperature and velocity distribution upraises with the increase of R. Numerical outcomes of skin friction and Nusselt number are disclosed by addition of these parameters. At R = 0.6, the upgraded values of radiation parameter upsurges the temperature gradient. The similar trend is noted at R = 1.2. The augmented values of Ec rises the temperature gradient for both the cases of wedge (R ≶ 1). Observations shows that varying R and M upsurges the absolute values of surface drag force. However increased values of M lessened the temperature gradient.

Irreversibility analysis in dissipative flow of Darcy-Forchheimer viscous fluid

Entropy minimization is an innovative approach in several thermal processes and having dynamical applications in thermal polymer processing. The importance of entropy is perceived in, combustion, porous media turbine systems, heat exchangers, thermal systems, cooling system, and nuclear reactions, etc. In view of such thermal applications, the prime is here to discuss the hydromagnetic entropy optimized flow of Darcy-Forchheimer viscous liquid by a curved stretchable surface is scrutinized. Heat expression is assisted with heat source/sink, dissipation, and Joule heating effects. Entropy rate and energy equations are developed through the implementation of the second and first laws of thermodynamic. The governing equations are established in a curvilinear coordinate. Nonlinear differential systems are altered into ordinary ones by employing the transformation variables. The obtained system is computed with one of the numerical methods (Newton built-in shooting technique). Entropy rate, velocity field, temperature, and Bejan number variation for several sundry variables are scrutinized. The computation result of surface drag force is studied for variation of curvature parameter and Hartman numbers. Thermal transportation rate for both prescribed heat flux (PHF) and prescribed surface temperature (PST) cases are scrutinized.

Analysis of Wu's slip and CNTs (single and multi-wall carbon nanotubes) in Darcy-Forchheimer mixed convective nanofluid flow with magnetic dipole: Intelligent nano-coating simulation

The analysis of viscous materials flow subject to diverse configurations with remarkable physical applications has many utilizations in the electrical, mechanical, industrial, applied physics and mathematics fields. Besides these, carbon nanotubes (CNTs) have numerous applications in energy storage, nanotechnology, chemical sensors, industry, optics, structural diverse materials and conductive plastics. Such consideration in mind, ferro-fluid flow of viscous liquid submerged in CNTs towards a stretchable surface affected by magnetic dipole interaction is addressed. Mixed convection and Darcy-Forchheimer effects are accounted. The energy relation is discussed in the presence of radiative heat flux and viscous dissipation. First and second order velocity slips are implemented at the boundary surface. The governing expressions specifying the flow are altered into ordinary ones with the assistance of appropriate similarity quantities. The obtained ordinary system is computationally tackled via Runge-Kutta 4th Order Method (RK4OM). Our obtained outcomes reveal that velocity of working fluid particles declines with an enhancement in ferromagnetic interaction parameter and Darcy-Forchheimer number. Also, behavior of temperature distribution increases more speedily for heightening of radiative parameter and Biot number. Coefficient of skin friction (surface drag force) and Nusselt number (heat transport rate) are calculated in view of important flow parameter numerically. The range of parameters are β=0.0,0.3,0.5,ε=0.1,0.5,1.0,Fr=0.1,0.5,1.0,γ1=0.0,0.5,1.0,γ2=0.0,0.1,0.2,δ=1.0,5.0,10.0,R=0.0,0.2,0.5,Bi=0.5,1.0,1.5 and.λ=0.0,1.0,3.0.

Analysis of joule heating and generalized slip flow in ferromagnetic nanoparticles in a curved channel using Cattaneo-Christov heat flux theory

This paper investigates the heat transport phenomenon by utilizing Cattaneo- Christov heat flux model on magnetic nanoparticles through a semi porous curved wall channel, incorporated with generalized slip condition and bent in a circle of radius, Rc. In addition, the energy equations takes into account the impacts of heat generation and Joule heating. To construct the flow model, a curvilinear co-ordinate scheme is used. The derived PDE are converted into system of ODE by incorporating appropriate similarity variables. Numerical simulation is used to achieve a numerical solution of the flow equations by using shooting technique. The influence of various parameters on temperature, rate of heat transfer, velocity and surface drag force are analyze and discussed in detail by using graphs and table. Also a well-known finite difference technique known as Keller box method is also used to verify and validate the obtained numerical results.

Darcy-Forchheimer Flow of Magnetized Bioconvective Williamson Nanofluid with Variable Thermal Conductivity

In this article modeling and theoretical analysis of magnetized Williamson nanomaterial flow by permeable surface of cylinder is studied. The idea of self-propelled gyrotactic microorganisms is implemented to stabilize the suspended nanoparticles in Williamson liquid. Darcy-Forchheimer together with porosity effects are accounted in the flow. Energy relation is modeled in view of thermal radiation, variable thermal conductivity and Joule heating. Activation energy linked with chemical reaction is executed at the surface. Furthermore, Brownian dispersion and thermophoresis effects are also considered. Flow governing dimensional model is acquired using boundary layer suppositions. Suitable transformations are used to alter the system of PDE’s into non-dimensional. NDSolve code in Mathematica package is utilized to solve the model. Impacts of various flow regulating variables on velocity, temperature, mass concentration and motile density are investigated by plotting. Coefficient of skin friction, Sherwood number, motile density number and heat transfer rate are tabulated and analyzed. It is observed that velocity field decays while temperature field enhances versus rising dimensionless magnetic parameter. Moreover, due to magnetic field more Lorentz force is applied to the flow as a result surface drag force enhances while heat transfer rate decays.

Analysis of entropy generation and Joule heating on curvilinear flow of thermally radiative viscous fluid due to an oscillation of curved Riga surface

This paper investigates the phenomena of heat transfer and entropy generation on time-dependent electro-magnetohydrodynamic boundary layer flow of viscous fluid past a curved oscillatory stretchable Riga surface. Also, the impacts of thermal radiation and Joule heating are accounted for in the energy equation. To develop the flow model in mathematical form, curvilinear coordinates system is followed. The series solution of the governing nonlinear partial differential equations is attained with the help of the homotopy analysis method (HAM). The impacts of various involved parameters like dimensionless radius of curvature, modified magnetic parameter, the proportion of frequency of oscillation of the sheet to its stretchable rate parameter, magnetic parameter, Prandtl number, Eckert number, radiation parameter and Brinkman number on entropy generation, Bejan number, temperature and flow equations are comprehensively examined and results are displayed through graphs. Numerical variation in the magnitude of surface drag force and local Nusselt number under the influence of aforesaid parameters are presented through the tables. Entropy generation is enhanced with an enhancement in a radius of curvature and Brinkman number, while the Bejan number shows opposite behavior for both parameters. The amplitude of velocity distribution shows growing behavior with modified magnetic parameter.

Nanofluid Transport through a Complex Wavy Geometry with Magnetic and Permeability Effects

The current article incorporates the numerical investigation of heat exchange rate and skin friction carried out through nanofluid saturated with thermally balanced porous medium over a rough horizontal surface that follows the sinusoidal waves. The effects of the external magnetic field are discussed by managing the magnetic field strength applied normally to the flow pattern. The occurring partial differential governing equations are grasped through a strong numerical scheme of the Keller box method (KBM) against the various parameters. The findings are elaborated through tables and diagrams of velocity, temperature, skin friction, Nusselt number, streamlines, and heat lines. The percentage increase in Nusselt number and coefficient of skin friction over the flat and wavy surface is calculated which leads to the conclusion that the copper (Cu) nanoparticles are better selected as compared to the silver (Ag) for heat transfer enhancement. It is also evident from sketches that the current analysis can be used to enhance the surface drag force by means of nanoparticles. It is a matter of interest that the magnetic field can be used to manage the heat transfer rate in such a complicated surface flow. The current readings have been found accurate and valid when compared with the existing literature.

Significance of heat source/sink on the radiative flow of Cross nanofluid across an exponentially stretching surface towards a stagnation point with chemical reaction

AbstractA numerical review on magnetohydrodynamics radiative motion of Cross nanofluid across an exponentially stretchable surface near stagnation point with varying heat source/sink is addressed. Brownian movement and thermophoretic impacts are assumed. The governing equations for this study are first altered as a system of ordinary differential equations by similarity transformation. With an aid of the Runge–Kutta 4th order mechanism together with the shooting procedure, the impacts of several pertinent parameters including chemical reaction on regular profiles (velocity, temperature, and concentration) are explicated. The consequences of the same parameters on surface drag force, transfer rates of heat, and mass are visualized in tables. From the analysis, it was noticed that the magnetic field parameter enhances the temperature and decreases the velocity of the Cross nanofluid. Also, fluid temperature is an increasing function with thermal radiation and nonuniform heat source/sink. The rate of heat transfer is increased with thermophoresis and diminished with Brownian motion. Sherwood's number is diminished with Brownian motion but it was boosted up with thermophoresis. The present results are compared with published results and those are in agreement.

Impact of non-Fourier heat flux in bidirectional flow of carbon nanotubes over a stretching sheet with variable thickness

Three-dimensional stretched flow of carbon nanotubes with variable thickness is examined. Christov proposed non-Fourier heat flux to capture impact of thermal relaxation time. Suitable transformations are used to obtain nonlinear ordinary differential systems. Convergent series solutions are derived. Influence of certain variables on the fluid properties is discussed. Findings demonstrate that the magnitude of the surface drag force is suppressed with increment in wall thickness parameter whereas it intensified for increasing nanoparticles volume fraction. Increase in the shape parameter and nanoparticles volume fraction enhanced the flow. Temperature is noticed higher with an increase in thermal relaxation time.

Bioconvection and nonlinear thermal extrusion in development ofchemically reactive Sutterby nano-material due to gyrotactic microorganisms

Wide range of applications of Bioconvection with microorganisms and nanoparticles in the field of biotechnology, mechanical energy, biosensors, engineering and bioinformatics attracted the research community towards this field. Main objective of current communication is to present a mathematical modeling and numerical simulation for the unsteady Bioconvection flow of chemically reactive Sutterby nanofluid under the influences of gyrotactic microorganisms and nonlinear radiation. Additionally, activation energy influences are considered. Furthermore, we have adopted a newly developed revised nanofluid model to examine flow characteristics in nanofluid. Boundary layer theory is invoked to develop the basic PDEs for microorganism field, nanoparticles concentration, energy, momentum and mass and then reduced to the highly nonlinear ODEs with the help of transforming variables. Numerical solutions for current study are achieved via (RK45) shooting Fehlber approach. Numerical computations for density number of microorganism, Sherwood number, wall heat transfer and surface drag force are also conducted. For the authenticity of current study, a comparison analysis is performed between existing data and current study and revealed in excellent agreement. It is interesting to noticed that microorganism field is upgraded for higher estimation of microorganism difference parameter and Peclet number. It is also noted that larger Bioconvection Rayleigh number depreciates the fluid velocity.

Intelligent supervised learning for viscous fluid submerged in water based carbon nanotubes with irreversibility concept

This article examined the Silver based Di‑hydrogen carbon nanotubes flow model (SDH-CNTFM) between two stretchable coaxially disks by utilizing the Method of Levenberg Marquardt with Back-propagated Neural Networks (MLM-BPNN). Here the base liquid is silver (Ag) and the nanoparticles are SWCNTs and MWCNTs (single and multiwall carbon nanotubes). The governing PDEs for SDH-CNTFM are transformed into ODEs by utilizing similarity transformation. Energy equations are developed through heat generation and viscous dissipation joule heating. Also calculated the total entropy optimization. Flow parameters velocity, entropy optimization, temperature, Nusselt number and Bejan number are discussed for both single and multi-walls carbon nanotubes (SWCNTs and MWCNTs) graphically and in Tabular form. The reference dataset is calculated through implementation of Optimal Homotopy Analysis method (OHAM) for variants of SDH-CNTFM. For the variation of different parameters this reference dataset is utilized in MATLAB to clarify the solution and error analysis plots. Moreover, the approximated solution is assessed through adopting training/testing/validation procedure and comparing it with standard solution which is endorsed by performance study based on MSE convergence, error histogram and regression studies. Heat transfer rate and surface drag force are discussed for both SWCNTs and MWCNTs numerically by using different flow parameters. From obtained outcomes, it is observed that entropy rate boosts up for higher approximation of nanoparticles of volume friction and Brickman number (Br) which is controlled due to the minimization of Brickman number.

Investigation of mixed convection magnetized Casson nanomaterial flow with activation energy and gyrotactic microorganisms

Present article addresses mixed convection magnetohydrodynamic Casson nanomaterial flow by stretchable cylinder. The effects of thermal, solutal and motile density stratifications at the boundary of the surface are accounted. Flow governing expressions are acquired considering aspects of permeability, thermal radiation, chemical reaction, viscous dissipation and activation energy. The obtained flow model is made dimensionless through transformations and then tackled by NDsolve code in Mathematica. Physical impacts of sundry variables on nanomaterial velocity, temperature distribution, volume fraction of microorganisms and mass concentration is investigated through plots. Furthermore, quantities of engineering interest like surface drag force, heat transfer rate, density number and Sherwood number are computed and analyzed. We observed that fluid velocity diminishes for higher curvature variable, Casson fluid material variable, Hartmann number and permeability parameter. Fluid temperature has a direct relation with Eckert number, thermophoresis variable, Brownian dispersal parameter, Prandtl number and Hartmann number. Volume fraction of gyrotactic microorganisms is decreasing function of bioconvection Lewis number, stratification parameter and bioconvection Peclet number. Detailed observations are itemized at the end.

Analytical simulation of time dependent electromagneto-hydrodynamic flow of Williamson fluid due to oscillatory curved convectively heated Riga surface with variable thermal conductivity and diffusivity

The main objective of the present article is to provide an analytical simulation for time dependent boundary layer flow of non-Newtonian Williamson fluid due to stretchable curved oscillatory Riga surface. Also the characteristics of heat and mass transport are studied under the influence of variable thermal conductivity and diffusivity along with convective heat and mass boundary conditions. Additionally, energy equation is also characterized with the impact of heat production. Curvilinear coordinate scheme is followed to attain the boundary layer expressions for the flow model. The governing nonlinear partial differential equations are solved analytically via homotopy analysis method (HAM). Graphs are plotted to examine comprehensively the consequences of various concerned parameters like modified magnetic parameter and radius of curvature, Williamson fluid parameter, relation of the surface's oscillating frequency to its stretching rate constant, Prandtl number, variable conductivity and heat production parameters, Schmidt number and variable diffusivity parameter on concentration, temperature, pressure and velocity profile. Also the outcomes of afore said variables on surface drag force, rate of temperature and mass transmission (Nusselt and Sherwood numbers) are shown in tabular form. The liquid velocity amplitude is enhanced with modified magnetic parameter and shows opposite behavior for Williamson fluid parameter.

Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet.

The wide range of industrial applications of flow across moving or static solid surfaces has aroused the curiosity of researchers. In order to generate a more exact estimate of flow and heat transfer properties, three-dimensional modelling must be addressed. This plays a vital role in metalworking operations, producing plastic and rubber films, and the continuous cooling of fibre. In view of the above scope, an incompressible, laminar three-dimensional flow of a Casson nanoliquid in the occurrence of thermophoretic particle deposition over a non-linearly extending sheet is examined. To convert the collection of partial differential equations into ordinary differential equations, the governing equations are framed with sufficient assumptions, and appropriate similarity transformations are employed. The reduced equations are solved by implementing Runge Kutta Fehlberg 4th 5th order technique with the aid of a shooting scheme. The numerical results are obtained for linear and non-linear cases, and graphs are drawn for various dimensionless constraints. The present study shows that improvement in the Casson parameter values will diminish the axial velocities, but improvement is seen in thermal distribution. The escalation in the thermophoretic parameter will decline the concentration profiles. The rate of mass transfer, surface drag force will reduce with the improved values of the power law index. The non-linear stretching case shows greater impact in all of the profiles compared to the linear stretching case.

Theoretical Analysis of Cu-H2O, Al2O3-H2O, and TiO2-H2O Nanofluid Flow Past a Rotating Disk with Velocity Slip and Convective Conditions

The nanofluids can be used in the subsequent precise areas like chemical nanofluids, environmental nanofluids, heat transfer nanofluids, pharmaceutical nanofluids, drug delivery nanofluids, and process/extraction nanofluids. In short, the number of engineering and industrial applications of nanofluid technologies, as well as their emphasis on particular industrial applications, has been increased recently. Therefore, this exploration is carried out to analyze the nanofluid flow past a rotating disk with velocity slip and convective conditions. The water-based spherical-shaped nanoparticles of copper, alumina, and titanium have been considered in this analysis. The modeled problem has been solved with the help of homotopic technique. Convergence of the homotopic technique is shown with the help of the figure. The role of the physical factors on radial and tangential velocities, temperature, surface drag force, and heat transfer rate are displayed through figures and tables. The outcomes demonstrate that the surface drag force of the water-based spherical-shaped nanoparticles of Cu, Al2O3, and TiO2 has been reduced with a greater magnetic field. The radial and tangential velocities of the water-based spherical-shaped nanoparticles of Cu, Al2O3, and TiO2, and pure water have been augmented via magnetic parameter. The radial velocity of the water-based spherical-shaped nanoparticle of Cu has been augmented via nanoparticle volume fraction, whereas reduced for the Al2O3 and TiO2 nanoparticles. The tangential velocity of the water-based spherical-shaped nanoparticles of Cu, Al2O3, and TiO2 has reduced via nanoparticle volume fraction. Also, the variations in radial and tangential velocities are greater for slip conditions as compared to no-slip conditions.