The Phenomenon of Friction Resistance Due to Streamwise Heterogeneous Roughness with Modified Wall-Function RANSE

Surface roughness can reduce the performance of a system of fluid mechanics due to an increase in frictional resistance. The ship hull, which is overgrown by biofouling, experiences a drag penalty which causes energy wastage and increased emission levels. The phenomenon of fluid flow that passes over a rough surface still has many questions, one of which is the phenomenon of frictional resistance on heterogeneous roughness in the streamwise direction. In the ship hull, biofouling generally grows heterogeneous along the hull with many factors. RANSE-based Computational Fluid Dynamics was used to investigate the friction resistance for heterogeneous roughness phenomenon. The modified wall-function method represented equivalent sand grain roughness (ks) and a roughness function were applied together with k-epsilon turbulence model to simulate rough wall turbulent boundary layer flow. As the heterogeneous roughness, three different ks values were denoted as P (ks = 81.25 μm), Q (ks = 325.00 μm) and R (ks = 568.75 μm), and they are arranged by all possible combinations. The combined roughness, whether homogeneous (PPP, QQQ, or RRR) and inhomogeneous (PQR, PRQ, QPR, etc.), results in unique skin friction values. The step-change in the height of the heterogeneous roughness produced a sudden change in the local skin friction coefficient in the form of overshoot or undershoot, followed by a relaxation where the inhomogeneous local skin friction is slowly returning to the homogeneous local one, which was explained in more detail by plotting the distribution of the mean velocity profile near the step-up or step-down. The order of roughness arrangement in a streamwise heterogenous roughness pattern plays a key role in generating overall skin friction with values increasing in the following order: PQR < PRQ < QPR < QRP < RPQ < RQP. Those inhomogeneous cases with three different values of ks can be represented by a single value (being like homogeneous) by the calculations provided in this paper.

On Numerical Thermal Transport Analysis of Three-Dimensional Bioconvective Nanofluid Flow

In this paper, a numerical study is presented for the 3D mathematical model of bioconvective boundary layer flow having nanoparticles and motile microorganisms on a curved sheet under isothermal conditions. Using an appropriate choice of similarity transformations, the problem reduces to coupled ordinary nonlinear equations, and this system is then treated with bvp4c (a MATLAB-based solver) to get the desired solution with good accuracy. The repercussion of distinct important dimensionless numbers such as thermophoresis, buoyancy ratio, Lewis number, and Brownian number on the velocity, temperature, and volume fraction of nanoparticles is presented graphically and is discussed in context with their importance on flow dynamics. Moreover, the physical impact of various parameters on motile microorganism density, the local Sherwood number, the local Nusselt number, and the local skin friction coefficients is analyzed and presented in tables. Qualitative analysis also reveals that the Brownian motion parameter, Peclet number, and Schmidt number have an inverse impact on the density microorganisms.

Stagnation Point Heat Flow and Mass Transfer in a Casson Nanofluid with Viscous Dissipation and Inclined Magnetic Field

Influence of slip and inclined magnetic field on stagnation-point flow with chemical reaction are studied. Implementation of the similarity transformations, transformed the fluid non-linear ordinary differential equations and numerical computation is performed to solve those equations using Spectral Collocation Method. Various pertinent parameters on fluid flow, temperature and concentration distributions of the Casson nanofluid flow as well as the local skin friction coefficient, local Nusselt number, and Sherwood number are graphically displayed. The results indicate that thermophoresis parameter N_t enhanced the temperature and nanoparticle concentration profiles, because a rise in thermophoresis parameter enhances the thermophoresis force within the flow regime. Values of both local Nusselt and Sherwood numbers are enhanced with an increase in Hartman number (magnetic field parameter). The present results are compared with previously reported ones and are found to be in excellent agreement.

Soret and Dufour Effects on MHD Nonlinear Convective Flow of Tangent Hyperbolic Nanofluid Over a Bidirectional Stretching Sheet with Multiple Slips

The purpose of the present analysis is to investigate the Soret and Dufour effects on steady and incompressible MHD nonlinear convective flow of tangent hyperbolic nanofluid over a permeable stretching surface with multiple slip conditions at the wall. Also, nonlinearly varying thermal radiation, heat generation and chemical reaction along with a vanishing nanoparticle mass flux condition at the surface are taken into account. Further, Rosseland’s approximation for an optically thick and grey medium is used to approximate heat flux due to radiation. Suitable similarity transformations are employed to transform governing PDEs into a system of ODEs. The resulting nonlinear equations are then solved numerically using the shooting technique based on the Runge-Kutta Cash-Karp method. The upshots of various physical parameters on velocity, temperature and concentration distributions are illustrated and displayed through figures. The variations in coefficients of local skin friction, Nusselt and Sherwood numbers are explained and presented in tabular form. The obtained results are validated with the previously reported results for a particular case of the present fluid flow problem, and an outstanding correlation is noticed from the comparison. Graphical results reveal that the nonlinear convection parameters for both temperature and concentration accelerate the primary flow. However, the Dufour number diminishes the fluid temperature near the wall, and the Soret number uplifts the concentration profile within the boundary layer.

Ternary-hybrid nanofluids: significance of suction and dual-stretching on three-dimensional flow of water conveying nanoparticles with various shapes and densities

Increasing knowledge of hybrid nanofluid can be traced to its unique improvement of thermal performance and enhancement of heat transfer rate as applicable in the dynamics of fuel and coolant in automobiles. However, the case of water-based nanofluid conveying three kinds of nanoparticles (i.e., ternary-hybrid nanofluid) with various shapes and densities is far-fetched. The transport phenomena of water conveying smaller densities nanoparticles (i.e., copper nanotubes, graphene, and aluminum oxide) and substantial large densities of nanoparticles (i.e., copper oxide, copper, and silver) of various types through a rectangular closed domain with major emphasis on the significance of suction and dual stretching was investigated. The dimensional equation that model the aforementioned transport phenomenon, for the two cases, were non-dimenzionalized using appropriate similarity variables, parameterized, and solved numerically using shooting techniques together with fourth-order Runge-Kutta integration scheme and in-built bvp4c package of MATLAB. Enhancement in suction and stretching ratio causes the vertical velocity of the motion along x-direction and Nusselt number to be an increasing function. Due to an increase in suction and stretching ratio, fluid flow along (x, y)-directions, temperature distribution, and the local skin friction coefficients are decreasing functions. At all the levels of suction and stretching ratio, higher Nusselt numbers were found in the case of water conveying Copper oxide, Copper, and Silver nanoparticles due to their heavy densities.

Transient free convection heat and mass transfer of Casson nanofluid over a vertical porous plate subjected to magnetic field and thermal radiation

In this present study, the transient magnetohydrodynamics free convection heat and mass transfer of Casson nanofluid past an isothermal vertical flat plate embedded in a porous media under the influence of thermal radiation is studied. The governing systems of nonlinear partial differential equations of the flow, heat and mass transfer processes are solved using implicit finite difference scheme of Crank-Nicolson type. The numerical solutions are used to carry out parametric studies. The temperature as well as the concentration of the fluid increase as the Casson fluid and radiation parameters as well as Prandtl and Schmidt numbers increase. The increase in the Grashof number, radiation, buoyancy ratio and flow medium porosity parameters causes the velocity of the fluid to increase. However, the Casson fluid parameter, buoyancy ratio parameter, the Hartmann (magnetic field parameter), Schmidt and Prandtl numbers decrease as the velocity of the flow increases. The time to reach the steady state concentration, the transient velocity, Nusselt number and the local skin-friction decrease as the buoyancy ratio parameter and Schmidt number increase. Also, the steady-state temperature and velocity decrease as the buoyancy ratio parameter and Schmidt number increase. Also, the local skin friction, Nusselt and Sherwood numbers decrease as the Schmidt number increases. However, the local Nusselt number increases as the buoyancy ratio parameter increases. It was established that near the leading edge of the plate), the local Nusselt number is not affected by both buoyancy ratio parameter and Schmidt number. It could be stated that the present study will enhance the understanding of transient free convection flow problems under the influence of thermal radiation and mass transfer as applied in various engineering processes.

Impact of heat generation/absorption of magnetohydrodynamics Oldroyd-B fluid impinging on an inclined stretching sheet with radiation

In this paper, we have investigated thermally stratified MHD flow of an Oldroyd-B fluid over an inclined stretching surface in the presence of heat generation/absorption. Similarity solutions for the transformed governing equations are obtained. The reduced equations are solved numerically using the Runge–Kutta Fehlberg method with shooting technique. The influences of various involved parameters on velocity profiles, temperature profiles, local skin friction, and local Nusselt number are discussed. Numerical values of local skin friction and local Nusselt number are computed. The significant outcomes of the study are that the velocity decreases when the radiation parameter $$R_{d}$$ R d is increased while the temperature profile is increased for higher values of radiation parameter $$R_{d}$$ R d in case of opposing flow, moreover, growth in Deborah number $$\beta_{2}$$ β 2 enhance the velocity and momentum boundary layer. The heat transfer rate is decrease due to magnetic strength but increase with the increased values of Prandtl and Deborah numbers. The results of this model are closely matched with the outputs available in the literature.

MHD Natural Convective Flow of Cu-Water Nanofluid over a Past Infinite Vertical Plate with the Presence of Time Dependent Boundary Condition

In this paper, unsteady electrically conducting, incompressible, heat and mass transfer Magnetohydrodynamic free convective fluid flow with Cu-nanoparticles over a vertical plate embedded in a porous medium and variable boundary conditions are considered. The governing PDE's have been converted to non-dimensional equations then solved by FET for velocity, temperature and concentration profiles with the influence of buoyancy force due to heat and mass transfer, Prandtl and Schmidt number , time, magnetic and chemical reaction parameter in case of pure fluid and Cu-water nanofluid. The Cu-water nanofluid velocity is low than pure fluid, these are presented through graphical form . Also presented the local Skin-friction coefficient, rate of heat and mass transfer and code of validation through tabular forms.

Viscous Dissipation and Joule Heating Effects on MHD Bioconvection Flow of a Nanofluid Containing Gyrotactic Microorganisms Over a Vertical Isothermal Cone

The main objective of the present study is to explore the flow of a nanofluid containing gyrotactic microorganisms over a vertical isothermal cone surface in the presence of viscous dissipation and Joule heating. The combined effects of a transverse magnetic field and Navier slip in the flow are considered. Using appropriate transforms the set of partial differential equations governing the flow are converted to a set of ordinary differential equations. Influence of the parameters governing the flow is shown for velocity, temperature, concentration and motilemicroorganisms as well as local skin Friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number. An increasing in the value of Eckert number rises the velocity of the fluid and reduce the temperature, concentration and density of motile microorganisms profiles, while buoyancy ratio Nr and magnetic field parameters increase local skin friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number decrease as a result of the presence of Lorentz force which resist the motion of the flow. On the other hand, the motile microorganisms boundary layer thickness decreases with an increasing on the bioconvection Lewis number.

The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion

The present study is related to the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion. The activation energy and thermal conductivity of steady micropolar fluid are also discussed. The equation of motion, angular momentum, temperature, concentration, and their boundary conditions are presented for the micropolar fluid. The detail of geometry reveals the effects of several parameters on the parts of the system. The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. The comparison of the obtained results by the shooting technique and the numerical bvp4c technique is presented. The behavior of local skin friction numbers and couple stress number is tabulated for different parameters, and some figures are plotted to present the different parameters. For uplifting the values of AE for parameter λA, the concentration profile is increased because of the Arrhenius function, and AE increases with the reduction of this function. The increasing values of the parameter of rotation G show the decrement in velocity because of the rotation of the particle of the fluid, so the linear motion decreases. Thermophoresis is responsible for shifting the molecules within the fluid, and due to this, an increment in boundary layer thickness is found, so by a greater value of Nt, the concentration profile decreases and temperature profile goes down.