An Improved Synthetic Eddy Method for Generating Inlet Turbulent Boundary Layers

An improved synthetic eddy method (SEM) is proposed in this paper for generating the boundary layer at the inlet of a computational domain via direct numerical simulation. The improved SEM modified the definition of the radius and the velocities of the eddies according to the distance of the eddies from the wall in the synthetic region. The regeneration location of the eddies is also redefined. The simulation results show that the improved SEM generates turbulent fluctuations that closely match the DNS results of the experiments. The skin friction coefficient of the improved SEM recovers much faster and has lower dimensionless velocity at the outer of the boundary layer than that of the traditional SEM.

Numerical simulations of a freely falling rigid sphere in bounded and unbounded water domains

Numerical studies were conducted on the hydrodynamics of a freely falling rigid sphere in bounded and unbounded water domains to investigate the drag coefficient, normalized velocity, pressure coefficient, and skin friction coefficient as a function of dimensionless time. The bounded domain was simulated by bringing the cylindrical water container's wall closer to the impacting rigid sphere and linking it to the blockage ratio (BR), defined as the ratio of the projection area of a freely falling sphere to that of the cross-section area of the cylindrical water container. Six cases of bounded domains (BR= 1%, 25%, 45%, 55%, 65%, and 75%) were studied. However, the unbounded domain was considered with a BR of 0.01%. In addition, the k–ω shear stress transport (SST) turbulence model was employed, and the computed results of the bounded domain were compared with those of other studies on unbounded domains. In the case of the bounded domain, which has a higher value of BR, a substantial reduction in normalized velocity and an increase in the drag coefficient were found. Moreover, the bounded domain yielded a significant increase in the pressure coefficient when the sphere was half-submerged; however, an insignificant effect was found on the skin friction coefficient. In the case of the unbounded domain, a significant reduction in the normalized velocity occurred with a decrease in the Reynold number (Re) whereas the drag coefficient increases with a decrease in Reynolds number.

Exploring the magnetohydrodynamic stretched flow of Williamson Maxwell nanofluid through porous matrix over a permeated sheet with bioconvection and activation energy

The evolution of compact density heat gadgets demands effective thermal transportation. The notion of nanofluid plays active role for this requirements. A comparative account for Maxwell nanofluids and Williamson nanofluid is analyzed. The bioconvection of self motive microorganisms, non Fourier heat flux and activation energy are new aspects of this study. This article elaborates the effects of viscous dissipation, Cattaneo–Christov diffusion for Maxwell and Williamson nanofluid transportation that occurs due to porous stretching sheet. The higher order non-linear partial differential equations are solved by using similarity transformations and a new set of ordinary differential equations is formed. For numerical purpose, Runge–Kutta method with shooting technique is applied. Matlab plateform is used for computational procedure. The graphs for various profiles .i.e. velocity, temperature, concentration and concentration of motile micro-organisms are revealed for specific non-dimensional parameters. It is observed that enhancing the magnetic parameter M, the velocity of fluid decreases but opposite behavior happens for temperature, concentration and motile density profile. Also the motile density profile decrease down for Pe and Lb. The skin friction coefficient is enhanced for both the Williamson and Maxwell fluid.

Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

Comparative Study of Thermal Performance of Different Nanofluids in a Double Backward-Facing Step Channel: A Numerical Approach

Two-dimensional numerical simulations are conducted to study forced convection flow of different water-based nanofluids (ZnO, Al2O3, and SiO2) with volume fractions ( ϕ ) = 0–5% and fixed nanoparticle size (dp) = 20 nm for Reynolds numbers (Re) = 50–225 over a double backward-facing step with an expansion ratio (ER) = 2 under constant heat flux (q″ = 3000 W/m2) condition using the finite volume method. Results indicate that the local Nusselt number increases with volume fraction and Reynolds number for all working fluids. In comparison to water, the maximum heat transfer augmentation of about 21.22% was achieved by using water-SiO2 nanofluid at Re = 225 with ϕ = 5% and dp = 20 nm. Under similar conditions, the Al2O3 and ZnO nanofluids demonstrated 14.23% and 11.86% augmentation in heat transfer in comparison to water. The skin friction coefficient decreases with the increase in Re for all working fluids. No significant differences are observed in the values of skin friction coefficient among all working fluids at a particular Re. These results indicate that the heat transfer enhancement has been achieved with no increased energy requirements. In addition, the velocity increases with the rise in Re, with SiO2 nanofluid exhibiting the highest velocity as compared to other working fluids.

Magnetohydrodynamic Flow Past a Nonlinear Stretching or Shrinking Cylinder in Nanofluid with Viscous Dissipation and Heat Generation Effect

The Tiwari-Das model is used to investigate magnetohydrodynamic stagnation point flow and heat transfer past a nonlinear stretching or shrinking cylinder in nanofluid with viscous dissipation and heat generation using. The partial differential equations, also known as governing equations, were reduced to nonlinear ordinary differential equations using similarity transformation. MATLAB with the bvp4c solver is used for numerical computing. The controlling parameter, such as nanoparticle volume fraction, magnetic, curvature, nonlinear, radiation, and heat generation parameters, as well as Eckert and Grashof numbers, influence the skin friction coefficient, heat transfer rate, velocity, and temperature profiles. The results are presented as graphs to show the influence of the variables studied. In some circumstances of stretching and shrinking cases, dual solutions can be obtained.

Heat Transfer and Flow Characteristics of Pseudoplastic Nanomaterial Liquid Flowing over the Slender Cylinder with Variable Characteristics

The present article investigates heat transfer and pseudoplastic nanomaterial liquid flow over a vertical thin cylinder. The Buongiorno model is used for this analysis. The problem gains more significance when temperature-dependent variable viscosity is taken into account. Using suitable similarity variables, nonlinear flow equations are first converted into ordinary differential equations. The generating structure is solved by the MATLAB BVP4C algorithm. Newly developed physical parameters are focused. It is observed that the heat transfer rate and the skin friction coefficient is increased remarkably because of mixing nano-particles in the base fluid by considering γb=1, 2, 3, 4 and λ=1, 1.5, 2, 2.5,3. It is found that the temperature field increases by inclining the values of thermophoresis and Brownian motion parameters. It is also evaluated that the velocity field decreases by increasing the values of the curvature parameter, Weissenberg number and buoyancy ratio characteristics.

Aligned Magnetic Field and Radiation Effects on Biomagnetic Fluid over an Unsteady Stretching Sheet with Various Slip Conditions

The aim of the present study is to analyze the effects of aligned magnetic field and radiation on biomagnetic fluid flow and heat transfer over an unsteady stretching sheet with various slip conditions. The magnetic field is assumed to be sufficiently strong enough to saturate the ferrofluid, and the variation of magnetization is approximated by a linear function of temperature difference. The governing boundary layer equations with boundary conditions are simplified by suitable transformations. Numerical solution is obtained by using the bvp4c function technique in MATLAB software. The numerical results are derived for the velocity, temperature, the skin friction coefficient, and the rate of heat transfer. The evaluated results are compared with analytical study documented in scientific literature. The present investigation illustrates that the fluid velocity is decreased with the increasing values of radiation parameter, magnetic parameter, and ferromagnetic interaction parameter, though is increased as the Prandtl number, Grashof number, permeable parameter and thermal slip parameter are increased. In this investigation, the suction/injection parameter had a good impact on the skin friction coefficient and the rate of heat transfer.

Hybrid Nanofluid Flow and Heat Transfer Past an Inclined Surface

This paper examines the hybrid nanoparticles and the magnetic field impacts on the mixed convection boundary layer flow and heat transfer caused by an inclined shrinking–stretching surface in a hybrid nanofluid. Silver (Ag) is added into a MgO–water nanofluid to form Ag-MgO–water hybrid nanofluid. By making use of proper similarity transformations, the governing equations are transformed to ordinary differential equations. The problem is numerically solved with the help of the MATLAB function bvp4c. The influences of the chosen parameters on the temperature, velocity, heat transfer rate and the skin friction coefficient are addressed and graphically illustrated. The results show that increasing the magnetic parameter substantially improves the heat transfer rate and increases the skin friction coefficient. The findings also suggest that increasing the nanoparticle volume fraction φ2 (Ag) improves the skin friction coefficient while decreasing the heat transfer rate. For both stretching and shrinking instances, non-unique (dual) solutions are discovered. Only the first solution is stable, according to the temporal stability analysis of the dual solutions.

An Analytical Study of Internal Heating and Chemical Reaction Effects on MHD Flow of Nanofluid with Convective Conditions

This research investigates the influence of the combined effect of the chemically reactive and thermal radiation on electrically conductive stagnation point flow of nanofluid flow in the presence of a stationary magnetic field. Furthermore, the effect of Newtonian heating, thermal dissipation, and activation energy are considered. The boundary layer theory developed the constitutive partial differential momentum, energy, and diffusion balance equations. The fundamental flow model is changed to a system of coupled ordinary differential equations (ODEs) via proper transformations. These nonlinear-coupled equations are addressed analytically by implementing an efficient analytical method, in which a Mathematica 11.0 programming code is developed for numerical simulation. For optimizing system accuracy, stability and convergence analyses are carried out. The consequences of dimensionless parameters on flow fields are investigated to gain insight into the physical parameters. The result of these physical constraints on momentum and thermal boundary layers, along with concentration profiles, are discussed and demonstrated via plotted graphs. The computational outcomes of skin friction coefficient, mass, and heat transfer rate under the influence of appropriate parameters are demonstrated graphically.