Wall Drag Coefficient Research Articles

Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction

Abstract Non-uniform heat sources and sinks are used to control the temperature of the reaction and ensure that it proceeds at the desired rate. It is worldwide in nature and may be found in all engineering applications such as nuclear reactors, electronic devices, chemical reactors, etc. In food processing, heat is used to cook such as microwave ovens, pasteurize infrared heaters, and sterilize food products. Non-uniform heat sources are mainly used in biomedical applications, such as hyperthermia cancer treatment, to target and kill cancer cells. Because of its ubiquitous nature, the idea is taken as our subject of study. Heat and species transfer analysis of a non-Newtonian fluid flow model under magnetic effects past an extensible moving sheet is modelled and examined. Homogeneous chemical reaction inside the fluid medium is also investigated. This natural phenomenon is framed as a set of Prandtl boundary layer equations under the assumed convective surface boundary constraint. Self-similarity transformation is employed to convert framed boundary layer equations to ordinary differential equations. The resultant system is solved using the efficient finite difference utilized Keller box method with the help of MATLAB programming. The influence of various fluid-affecting parameters on fluid momentum, energy, species diffusion and wall drag, heat, and mass transfer coefficients is studied. Accelerating the Weissenberg number decelerates the fluid velocity. The temperature of the fluid rises due to variations in the non-uniform heat source and sink parameters. Ohmic dissipation affects the temperature profile significantly. Species diffusion reduces when thermophoresis parameter and non-uniform heat source and sink parameters vary. The Eckert number enhances the heat and diffusion transfer rate. Increasing the chemical reaction parameter decreases the shear wall stress and energy transmission rate while improving the diffusion rate. The wall drag coefficient and Sherwood number decrease as the thermophoretic parameter increases whereas the Nusselt number increases. We hope that this work will act as a reference for future scholars who will have to deal with urgent problems related to industrial and technical enclosures.

Impact of activation energy on carreau nanofluid flow over non-linear stretching surface

- The main goal of this article is to outline the key elements of activation energy that govern the slip flow of Carreau fluid over a non-linear stretched surface with heat transfer. By using the Arrhenius relation, activation energy aspects are included. Brownian diffusion and thermophoretic effects are shown through the study of nanoparticle dispersion using the Buongiorno model. The governing issue was first formulated as PDEs with appropriate boundary conditions, which were then converted into non-linear ODEs by applying a comparable transformation. Then, using Runge-Kutta integration and shooting techniques, the solution to the obtained complex differential system is discovered. Graphs reveal the effect of flow on linked profiles with respect to parameters. A published study that compares the current result describes the accuracy and reliability of the work. Through graphs and tables, the amount of engineering interest for shear thinning and thickening aspects of Carreau fluid is assessed. This includes wall drag coefficient, heat, and mass flux at the surface in comparison. It is calculated that by increasing non-linearity index velocity field depreciates for n = 0.5 and n = 1.5. Additionally, opposite behavior in momentum distribution is found against power law index (n) by fixing (m). Temperature of fluid decreases against power law index for m = 1.0 and m = 0.5.

Mathematical modeling of viscoelastic fluid flow across a nonlinear stretching surface in porous media with varying magnetic field

We investigate the cross-diffusion on MHD mixed convective thermo-solutal transport in viscoelastic fluid from a nonlinear stretching sheet. The novelty of the work is the analytical evaluation of the nonlinear stretching sheet in a porous medium with a variable magnetic parameter and radiative flux. Also, thermo-solutal transport of a mixed convective flow is analyzed with Dufour and Soret effects in the presence of the chemical reaction, heat source/sink. The governing PDEs are reduced into ODEs by similarity variables. ODEs were tackled analytically using the homotopy analysis method (HAM). The analysis is carried out up to the 15th order of approximation. HAM contains an h-curve, allowing a flexible method of controlling the series solution convergence area. Graphs and tables are plotted to analyze the influence of different parameters on the fluid. Rates of heat and mass flux are depicted using tables. Our results indicate that the increasing viscoelastic flow enhances the boundary layer, and the thermal boundary layer reduces as radiation enhances. The numerical demonstrations of the wall drag coefficient, Nusselt number and Sherwood number have been tabulated. The growing parameters are taken as [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]

Overlapping grid SQLM for third-grade modified nanofluid flow deformed by porous stretchable/shrinkable Riga plate

Abstract The improvement in thermal performance of fluid and the control of energy loss are equitably significant. Therefore, the purpose of this study is to analyze entropy generation, stagnation point flow, and thermal characteristics of non-Newtonian third-grade modified hybrid nanofluid generated by a stretchable/shrinkable Riga plate in a porous medium with varying flow viscosity. In this analysis, a modification of hybrid nanofluid is considered by using pure water as a base fluid and three various nanomaterials (aluminium oxide, copper, and nickel) as nanoparticles in the characterization of heat transfer. Furthermore, the contribution of heat source/sink and viscous dissipation are accounted for in the model. The suited transformations are enforced to remodel the governing mathematical equations to produce ordinary differential equations that are conveniently tackled via spectral quasilinearization method (SQLM) along with the overlapping grid idea to yield numerical solutions. The preference of this approach over others has been justified through discussion of error bound theorems, residual and solution errors, computational time, and conditioning of matrices. The physical significance of disparate governing parameters on flow variables, velocity gradient, thermal rate, and entropy generation are scrutinized through graphs and tables. Crucial findings of the study include that temperature of the modified hybrid nanofluid enhances quickly (better thermal conductor) than temperature of single nanofluid, hybrid nanofluid, and conventional third-grade fluid for higher Biot number, variable viscosity, and heat source parameters. Mass suction enhances fluid flow and physical quantities of interest, but suppresses the fluid temperature. An increase in variable fluid viscosity, modified Hartmann number, and third-grade parameters enhances the wall drag coefficient while lowering the rate of heat transfer, and the opposite is true for porous media. More entropy is generated in the system by high variable fluid viscosity, suction, viscous dissipation, modified Hartman number, and non-Newtonian parameters. Owing to high velocity and temperature associated with modified hybrid nanoparticles, modified hybrid technology is recommended in enhancing the physical attributes of the fluid with minimal cost effects. In engineering and industrial point of view, this study can contribute significantly in thermal improvement of the working fluid.

Thermophoretic particle deposition in Carreau-Yasuda fluid over chemical reactive Riga plate

Marangoni convection is very useful in coating flow technology, surfactant replacement therapy for neonatal children, microfluidics, drying of semi-conductor vapors in microelectronics, foams, and film drainage in emulsions. The behavior of gyrotactic microorganisms and chemical reaction on the Marangoni convected Carreau-Yasuda liquid flowing over Riga plate with thermophoretic particle deposition is reported in this research. The Riga plate is self-possessed of magnets and electrodes. The fluid conducted electricity and the vertical Lorentz force has been exponentially increased. Thermal and mass species phenomena are investigated within the context of Dufour and Soret impacts. The PDEs are transformed into ODEs by the implication of suitable transformations. The resulting system of equations is solved by using homotopy analysis method (HAM). Using tables and graphs, the effects of dimensionless parameters on flow fields are described. The wall drag coefficient and pertinent flow rates are organized and stated. The results revealed that the temperature, concentration, and microorganisms profiles decay but the velocity profile augmented as the Marangoni ratio parameter increases.

Analysis of buoyancy driven flow inside a vertical filter chamber

Designs based on scientific evidence play an essential role when engineering machinery. The current case study seeks an alternative way of filtering particles using a permeable surface. The filter is designed so that the effects of heat from a permeable bottom wall create a force that drives permeates out of the filter chamber. The model follows the mass conservation, incompressible Navier-Stokes and the energy conservation equations. Effects of parameters arising from flow dynamics and heat distribution are studied to better understand the theory behind the filtrations process. Graphical representations of skin friction and Nusselt number inside the filter chamber are plotted against filtration dynamics parameters. We found that more permeates are produced when the internal energy is low since the system loses internal temperature when less dense fluid, which possesses heat, is withdrawn from the chamber. In addition, the chamber volume increase permeates outflow since it enhances the pulling effects of the buoyancy force. It is found that increasing the Richardson number enhances the buoyancy forces and viscous effects; thus, decreasing permeates outflow velocity and eventually reduces wall drag coefficient. The wall drag coefficients on the left and right vertical walls have extrema towards the bottom of the filter chamber, in the region, 0 <y < 2 % H.

A comprehensive mathematical structuring of magnetically effected Sutterby fluid flow immersed in dually stratified medium under boundary layer approximations over a linearly stretched surface

On the implication of tension force, viscoelastic materials deform in accordance with viscous and elastic characterization. Dilute polymer solutions portray the examples of viscoelastic liquids and Sutterby model successfully represent it due to high degree polymerization distributions. In addition, polymer aqueous solutions behave as shear thinning and thickening liquids in response to infinite shear stress so Sutterby fluid is considered as best model to depict the features of liquids at high stress magnitude. Diverse utilities of diluted polymeric solutions are encountered in industrial, biological and technological practices, for instance, agricultural sprayers, cleansing products, clay coaters, polymerized melts and many more. So, this research communicates theoretical and computational thermal assessment of Sutterby fluid containing radiation aspects over a linearly moving sheet embedded in stratified medium which exposes the novelty of work. Moreover, the impacts of magnetic field and chemical reactions are also obliged. So, the principal objective pertains to adumbrate flow behavior of Sutterby liquid in the attendance of aforementioned physical parameters. Mathematical formulation in view of governing relations are changed into non-dimensionalized form through transformation approach. Convergent and accurate solution is accessed through renowned numerical shooting procedure along with integrated Runge-Kutta scheme. The computed results of emerged parameters on velocity, concentration and thermal fields are revealed by means of snapshots. Magnitude of associated wall drag coefficient and reduced heat and mass fluxes are explained in graphical and tabular formats. The salient outcomes are as follows. Consequence of the proposed research investigation infers that augmenting power index momentum distribution decays whereas skin friction uplifts. Furthermore, it is inferred that concentration distribution amplifies against upsurging magnitude of solutal stratification parameter while opposite nature is noticed in case of temperature profile against associated stratification parameter. Additionally, it is concluded that escalating magnitude of radiation parameter tends to elevates the dimensionless temperature profile. Subsequently, rise in concentration profile against Schmidt number is observed whereas against Prandtl number temperature of fluid expressing declining aptitude. Also, declining response in momentum of fluid is manifested against Reynold and Deborah numbers.

On analysis of magnetized viscous fluid flow in permeable channel with single wall carbon nano tubes dispersion by executing nano-layer approach

The prime motive of this pagination is to adumbrate attributes of water-based hybrid nanoliquid flow with dispersion of single wall carbon nanotubes. An innovative thermal conductance model containing the aspects of nanolayer formation along with shape and size of inserted particles is obliged. Flow transport mechanism is addressed mathematically in the form Navier Stokes equations with magnetization. In addition, heat and mass transport mechanism is manipulated by considering the impression of viscous dissipation and chemical reactions. Walls of channels are assumed to be porous in order to examine the phenomenon of suction and injection. Mathematical formulation of problem is represented in view of ODE’s and simulated computationally by Keller Box scheme. Subsequently, Newton method is utilized to solve system of nonlinear equations. Results are revealed through graphs and tables showing behavior of associated momentum, temperature and concentration profile against involved parameters. Quantities of engineering interest like wall drag coefficient, heat and mass fluxes are computed. Credibility of work is shown by creating match with existing study and an excellent agreement is found. After thorough analysis it is determined that heat flux increases with induction of single wall carbon nanotubes in base liquid. It is also manifested that thermal conductance of base fluid enriches with increase in thickness of nanolayer and radius of particles. In addition, positive trend in skin friction and heat flux coefficients is measured against elevation in nanoparticle volume fraction. Opposite behavior in velocity and temperature distributions against all flow variables near upper and lower walls of channel is depicted due to provision suction and injection wall velocities. Due to consideration of viscous dissipation heat transfer rate with in the flow domain reduces. By increasing Reynold number concentration distribution diminishes due to dominant effect of inertial forces. Decline in momentum distribution against Hall current parameter is adhered. Uplift and decrement in temperature distribution is manifested against heat source and sink parameters respectively.

Predicting wall drag coefficient and settling velocity of particle in parallel plates filled with Newtonian fluids

The hindrance of boundary to particle transport exists widely in various industrial applications. In this study, the wall drag force of parallel plates on settling particles was revealed through settling experiment. High-speed camera was used to record and analyze the settling process of particles in parallel plates that are filled with Newtonian fluids. A total of 600 experiments were carried out, involving the range of relative diameter and particle Reynolds number of 0.01–0.95 and 0.004–14.30, respectively. The wall drag coefficient was defined to quantitatively analyze the wall drag force of the parallel plates. The influence of relative diameter, particle properties, rheological properties, and the settling dynamic process on the wall drag coefficient was revealed, and the wall drag coefficient model with mean relative error of 5.90% was established. Furthermore, an explicit settling velocity model with mean relative error of 8.96% for the particle in parallel plates was developed by introducing a dimensionless variable independent of settling velocity, the Archimedes number. Finally, a calculation example was provided to clarify the using process of the explicit model. This research is expected to provide guidance for optimizing water hydraulic fracturing in the oil and gas industry.

Thermosoluted Marangoni convective flow towards a permeable Riga surface

AbstractThis study reveals the characteristics of chemical reaction on Marangoni mixed convective stream towards a penetrable Riga surface. The heat and mass phenomena are analysed within the sight of Dufour and Soret impacts. The administering partial differential equations system is converted into three nonlinear ordinary differential equations utilizing appropriately adjusted transformations. The resultant system of highly nonlinear equations is analytically solved by invoking the homotopy analysis method. Thereafter, the convergence of series solutions is discussed. The impact of appropriate parameters on various flow fields is thoroughly explained with the help of graphs and tables. The wall drag coefficient and relevant flux rates are arranged and discussed for dimensionless parameters. The outcomes show that the stronger Dufour effect of liquid causes a notable incremental variation in heat and mass flux, whereas an opposite trend is noted in the heat flux rate for the Soret effect. However, the mass flux is still found increasing for the stronger Soret effect.

Brownian motion and thermophoretic diffusion influence on thermophysical aspects of electrically conducting viscoinelastic nanofluid flow over a stretched surface

Current investigation elaborates the impacts of Brownian motion and thermophoretic force on electrically conducting Prandtl-Eyring nanofluid flow yielded by stretched surface. Buongiorno nano-model is used to trace the heat and mass transfer characteristics in the flow regime. The mathematical formulation concerning to the adopted physical parameters is modeled in the form of complex partial differential structure. Boundary layer theory is obliged to reduce non-linearity of subsequent equations by truncating higher order terms. To facilitate the computation process, the governing problem in partial differential form is converted into dimensionless ordinary differential expressions. Numerical solution for attained boundary value problem is procured by R-K-Fehlberg methodology. The consequences of flow governing parameters on interested physical quantities (momentum, heat, concentration) are depicted in graphical manner while tabular representation is used to demonstrate the variations in wall drag coefficient, wall thermal flux and particles concentration flux. The computed results show that the presence of magnetic field is not favorable for fluid momentum, albeit, both Brownian motion and thermophoresis phenomenon surges the thermal energy of fluid. Besides these, concentration profile increases versus Brownian motion while thermophoresis phenomenon has reverse impacts on it. Surface drag force enriched by magnifying the magnetic field intensity, furthermore, the surface heat flux shows reduction versus Brownian motion and thermophoresis parameters. In addition, the surface mass flux shows increasing trend versus all governing parameters.

Assisting or opposing MHD flow of cross fluid along a non-isothermal surface with variable thermal conductivity

Locally similar solutions are developed for aiding or opposing MHD flow near stagnation-point on a vertical stretchable surface immersed in a generalized Newtonian fluid obeying Cross rheology equation. Heat transfer problem is resolved by assuming a linear surface temperature distribution. Furthermore, fluid having variable thermal conductivity is treated. By choosing the usual transformations, the governing equations of fluid motion and energy transfer are changed into similar forms. The structure of boundary layer is controlled by a parameter measuring the ratio of free stream velocity to the wall velocity. Numerical computations are performed to address the influences of Cross fluid parameters on mean physical quantities. In particular, shear thinning character of Cross fluid is visible from the obtained simulations. Computations are found in perfect line with those of the existing literature. The physical outcomes concerning the effects of embedded parameters on wall drag coefficient and heat transfer rates are also explained in detail.

Shear localisation with 2D viscous froth and its relation to the continuum model

Simulations of monodisperse and polydisperse (μ 2(A) = 0.13±0.002) 2D foam samples undergoing simple shear are performed using the 2D viscous froth (VF) model. These simulations clearly demonstrate shear localisation. The dependence of localisation length on the product λV (shearing velocity V times the wall drag coefficient λ) is examined and is shown to agree qualitatively with published experimental data. A wide range of localisation lengths is found at low λV, an effect which is attributed to the existence of distinct yield and limit stresses. The general continuum model is extended to incorporate such an effect and its parameters are subsequently related to those of the VF model. A Herschel–Bulkley exponent of a = 0.3 is shown to accurately describe the observed behaviour. The localisation length is found to be independent of λV for monodisperse foam samples.

A numerical, three‐layered, stationary salt wedge model

A numerical, three‐layered, stationary salt wedge model is presented. It contains the effects of wind stress, interfacial stress, bed and wall stress, breadth variations, and mixing between the upper fresh layer and the homogeneous saline bottom layer. Because of the mixing an intermediate mixing layer develops which increases in thickness along the estuary toward the sea. The solutions obtained are compared with observations reported by Sorgard et al. (1990). Good agreement is obtained, both with regard to the thickness and position of the pycnocline, and with the velocities in each layer. The model was tested with different values for the bed and wall drag coefficient. To obtain a best fit with the observations, the modeled interfacial stress had to be decreased when the bed and wall drag coefficient was increased. The modifications to the dynamics due to the presence of the mixing layer are analyzed by comparing with the two‐layer model of Schijf and Schonfeld (1953). It turns out that the modeled interfacial stress has to be decreased because of the changed pressure field introduced by the mixing layer.