Search Results (23)

Based on the Lie group method (symmetry transformation groups), an analysis of an unsteady (start-up) flow over a flat surface was performed. This approach enabled reducing the number of independent arguments, which significantly simplifies the process of numerical modeling. An unsteady solution was obtained for the velocity profile in the boundary layer. This enabled estimating the dynamics of the velocity profile transformation and its transition to a steady-state mode. It was shown that in the limit of infinite time of the process, the velocity profile tends to the classical steady-state Blasius profile in the boundary layer. The dynamics of the friction coefficient variation over time were elucidated too. Full article

A transient stability flow analysis is performed using the unsteady laminar boundary layer equations. The flow dynamics are studied via the Navier–Stokes equations. In the case of external spatially developing flow, the differential equations are reduced via Prandtl or boundary-layer assumptions, consisting of continuity and momentum conservation equations. Prescription of streamwise pressure gradients (decelerating and accelerating flows) is carried out by an impulsively started Falkner–Skan (FS) or wedge-flow similarity flow solution in the case of flat plate or a Blasius solution for particular zero-pressure gradient case. The obtained mean streamwise velocity and its derivatives from FS flows are then inserted into the well-known Orr–Sommerfeld equation of small disturbances at different dimensionless times ($\tau$). Finally, the corresponding eigenvalues are dynamically computed for temporal stability analysis. A finite difference algorithm is effectively applied to solve the Orr–Sommerfeld equations. It is observed that flow acceleration or favorable pressure gradients (FPGs) lead to a significantly shorter transient period before reaching steady-state conditions, as the developed shear layer is notably thinner compared to cases with adverse pressure gradients (APGs). During the transient phase (i.e., for $\tau <1$), the majority of the flow modifications are confined to the innermost 20–25% of the boundary layer, in proximity to the wall. In the context of temporal flow stability, the magnitude of the pressure gradient is pivotal in determining the streamwise extent of the Tollmien–Schlichting (TS) waves. In highly accelerated laminar flows, these waves experience considerable elongation. Conversely, under the influence of a strong adverse pressure gradient, the characteristic streamwise length of the smallest unstable wavelength, which is necessary for destabilization via TS waves, is significantly reduced. Furthermore, flows subjected to acceleration ($\beta$ > 0) exhibit a higher propensity to transition towards a more stable state during the initial transient phase. For instance, the time response required to reach the steady-state critical Reynolds number was approximately 1$\tau$ for $\beta$ = 0.18 (FPG) and $\tau$ = 6.8 for $\beta$ = −0.18 (APG). Full article

The pipeline flow behavior of suspensions of cellulose nanocrystals (CNCs) was investigated over the CNC concentration range of 0.24 to 3.65 wt% in different diameter pipelines. The CNC suspensions were Newtonian below the CNC concentration of 1 wt%. At higher concentrations, the CNC suspensions were non-Newtonian power-law fluids. For Newtonian CNC suspensions, the experimental friction factor–Reynolds number data were obtained only in the turbulent regime, and the data followed the Blasius equation closely. For power-law CNC suspensions, the experimental data of friction factor–Reynolds number covered both laminar and turbulent regimes. The experimental data followed the friction factor–Reynolds number relationships for power-law fluids reasonably well. Full article

In this work, the flow of a modified nanofluid is analysed as it passes over a moving surface to investigate the influence of nonlinear radiative heat transfer and the effects of magnetic fields that are aligned. In addition, ethylene glycol is used as the solvent while zirconium oxide and alumina are combined to generate a hybrid nanomaterial. Ternary nanomaterials consist of zirconium oxide, alumina, and copper dissolved in the ethylene glycol. For this mathematical model, Navier–Stokes equations were used to represent the assumed flow. The Navier–Stokes equations were approximated using the boundary layer method under the flow assumptions, yielding the PDE’s. Similarity transformations are used to translate this system into ODE’s. The bvp4c method is used to explain a dimensionless system. The impacts of the relevant physical parameters are elucidated quantitatively and visually. A greater temperature ratio parameter is observed to increase the temperature profile. In addition to this, when the magnetic field parameter is increased, the momentum layer becomes thicker. Full article

Flat mini heat pipes (FMHPs) are often used in cooling systems for various power electronic components, as they rapidly dissipate high heat flux densities. The main objective of the present work is to experimentally investigate whether differences in the rate of vapor formation occur on an internal structure containing trapezoidal microchannels and porous sintered copper powder material. Several parameters, such as hydraulic diameter and fluid velocity through the material, as a function of the internal structure porosity, were determined by calculation for a steady state regime. Reynolds number was determined as a function of porosity, according to Darcy’s law, and the Nusselt number was calculated. Since the flow is Darcy-type through the porous medium inside the FMHP, the Darcy friction factor was calculated using five methods: Colebrook, Darcy–Weisbach, Swamee–Jain, Blasius, and Haaland. After experimental tests, it was found that when the porous and trapezoidal microchannel layers are wetted at the same time, the vaporization progresses at a faster rate in the porous material, and the duration of the process is shorter. This recommends the use of such an internal structure in FMHPs since the manufacturing technology is simpler, the materials are cheaper, and the heat flux transport capacity is higher. Full article

This study investigates the magnetohydrodynamics of a micropolar fluid consisting of a hybrid nanofluid with mixed convection effects. By using the dimensionless set of variables, the resulting equations of ordinary differential equations are solved numerically using the bvp4c solver in MATLAB. In the present work, the water-based alumina–copper hybrid nanofluid is analytically modeled with modified thermophysical properties. The study reveals that the highest critical value of opposing flow is the hybrid nanofluid (ϕ₁ = ϕ₂ = 2%). By comparing the hybrid nanofluid with Cu–water nanofluid (ϕ₁= 0%, ϕ₂= 1%) as well as water (ϕ₁= 0%, ϕ₂= 0%), hybrid nanoparticle volume fraction enhances the dynamic viscosity performance and surface shear stress. In addition, the augmentation of the nanoparticle volume fraction and magnetic field parameter will increase the physical quantities Re_x^1/2 C_f, Re_x M_x, and Re_x^−1/2 Nu_x. The result from the stability inquiry discloses that the first solution is more physically stable and trustworthy. It is proven that magnetohydrodynamics could contribute to controlling the fluid flow in a system, i.e., engineering operations and the medical field. In addition, this theoretical research can be a benchmark for experimental research. Full article

Current study solves heat transfer and fluid flow problem in Newtonian and non-Newtonian nano-fluids through a permeable surface with a magnetic field effects which is done in the presence of injection and suction for the first time. In order to solve the governing partial differential equations numerically, we used the Runge-Kutta Fehlberg (RKF45) technique in which the similarity transformation method is applied. This approach converts the governing partial differential equations into ordinary differential equations. In this particular investigation nano-particles of copper, copper oxide, titanium dioxide, and aluminium oxide are studied by considering CMC/water as a base fluid with the effect of magnetic field on the classical Blasius and Sakiadis flows of nano-fluids. Validation is carried out using the previously obtained numerical findings. We looked at the power-law index (n), the volume fraction ($\phi$) of nano-particles and the permeability parameter ($f_w$) which affects the flow of nano-fluid and the transfer of heat. Non-Newtonian nano-fluid demonstrates superior performance in terms of heat transfer when compared to Newtonian nano-fluid in both the injection and the impermeable surfaces. Altering the nano-particles’ composition, on the other hand, has a far greater impact on the heat transfer process that occurs during suction. Graphics show the impacts of governing physical parameters on Blasius and Sakiadis flow velocity, temperature, skin friction coefficient, and reduced Nusselt number. Physical and engineering interest are explored in detail. Full article

In the presented article a generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it a power-law form. After the introduction of the corresponding strain rate tensor, a generalization is made to the spatial case of flow and the rheological relation is presented in tensor form. Depending on the power value in this rheological ratio, one can come either to a description of a laminar flow regime (in the form of Navier–Stokes equations), or to a description of the flow in turbulent regime. In the latter case, a set of differential equations with the no-slip boundary condition is specified, which is significantly different from that for the laminar flow regime, but which also allows one to obtain analytical solutions for simple shear flows and obtain the Blasius resistance law for the flow in a pipe. Therefore, the considered approach to solving problems of turbulent flows compares favorably with modern differential turbulence models. Solutions are given for simple shear flows of a fluid, when there is only one longitudinal component of the velocity, which depends on the transversal coordinate only. These solutions in terms of velocity profiles and resistance coefficients are in satisfactory agreement with the experimental data. Full article

This study examines the Blasius flow with Cu-Al₂O₃ hybrid nanoparticles over a moving plate. Additionally, the effects of viscous dissipation and radiation are considered. Similarity transformation is employed to convert the respective model into similarity equations. The results are generated by using bvp4c in MATLAB. Findings reveal that two solutions are attained when both the free stream and the plate move in opposite directions. Moreover, the domains of the velocity ratio parameter are extended when suction is available. Besides, the upsurge of radiation and hybrid nanoparticles lead to the heat transfer enhancement. The rise in radiation heat energy incorporated in radiation parameter leads to the development of fluid temperature as well as the thermal boundary layer. Meanwhile, hybrid nanoparticles offer good thermal characteristics because of synergistic effects. However, the effects reduce with the rise in Eckert number. The first solution is stable and acceptable based on the temporal stability analysis. Furthermore, the critical/separation values of the physical parameters are also reported. With these findings, the optimized productivity will be achieved as well as the processes on certain products can be planned according to the desire output. This significant preliminary study provides future insight to the engineers and scientist on the real applications. Full article

The effect of Stefan blowing on the Cattaneo–Christov characteristics of the Blasius–Rayleigh–Stokes flow of self-motive Ag-MgO/water hybrid nanofluids, with convective boundary conditions and a microorganism density, are examined in this study. Further, the impact of the transitive magnetic field, ablation/accretion, melting heat, and viscous dissipation effects are also discussed. By performing appropriate transformations, the mathematical models are turned into a couple of self-similarity equations. The bvp4c approach is used to solve the modified similarity equations numerically. The fluid flow, microorganism density, energy, and mass transfer features are investigated for dissimilar values of different variables including magnetic parameter, volume fraction parameter, Stefan blowing parameter, thermal and concentration Biot number, Eckert number, thermal and concentration relaxation parameter, bio-convection Lewis parameter, and Peclet number, to obtain a better understanding of the problem. The liquid velocity is improved for higher values of the volume fraction parameter and magnetic characteristic, due to the retardation effect. Further, a higher value of the Stefan blowing parameter improves the liquid momentum and velocity boundary layer thickness. Full article

This paper presents an experimental study on a shell and tube mini heat exchanger (STMHE). The STMHE consisted of seven tubes in a triangular arrangement, with an 0.8 mm inner diameter and 1.0 mm outer diameter. The heat exchanger shell had an inner diameter of 11 mm, and the heat exchanger had no baffles. For the adopted operating conditions, the Reynolds number on the tube side varied in the range of 300–3000, and 2000–12,000 on the shell side. The aim of this study was to determine pressure drop values during fluid flow and Nusselt number correlations for the heat transfer. A new method based on optimisation was used to derive the equations for calculating the heat transfer coefficients. It allowed the determine of the correlation equations for the heat transfer coefficients simultaneously for both sides of the heat exchanger. The obtained correlations yielded overall heat transfer coefficient values that, in most cases, did not differ by more than $\pm 10\%$ from those determined experimentally. The experimentally determined critical Reynolds number value for the flow inside the tubes was equal to $R{e}_{cr}=1160$. The Darcy friction factors correlated well with the classical laminar flow correlation and with the Blasius correlation for turbulent flow. The derived correlations for the Nusselt number were best aligned with the Sieder–Tate, Gnielinski, and Kozioł correlations for tube side laminar flow, turbulent flow, and shell flow, respectively. Good agreement between the results obtained using the experimentally derived correlations and the correlations available in the literature confirms the effectiveness of the used optimisation–based method. Full article

Covalent-functionalized graphene nanoplatelets (CF-GNPs) inside a circular heated-pipe and the subsequent pressure decrease loss within a fully developed turbulent flow were discussed in this research. Four samples of nanofluids were prepared and investigated in the ranges of 0.025 wt.%, 0.05 wt.%, 0.075 wt.%, and 0.1 wt.%. Different tools such as field emission scanning electron microscopy (FE-SEM), ultraviolet-visible-spectrophotometer (UV-visible), energy-dispersive X-ray spectroscopy (EDX), zeta potential, and nanoparticle sizing were used for the data preparation. The thermophysical properties of the working fluids were experimentally determined using the testing conditions established via computational fluid dynamic (CFD) simulations that had been designed to solve governing equations involving distilled water (DW) and nanofluidic flows. The average error between the numerical solution and the Blasius formula was ~4.85%. Relative to the DW, the pressure dropped by 27.80% for 0.025 wt.%, 35.69% for 0.05 wt.%, 41.61% for 0.075 wt.%, and 47.04% for 0.1 wt.%. Meanwhile, the pumping power increased by 3.8% for 0.025 wt.%, 5.3% for 0.05 wt.%, 6.6% for 0.075%, and 7.8% for 0.1 wt.%. The research findings on the cost analysis demonstrated that the daily electric costs were USD 214, 350, 416, 482, and 558 for DW of 0.025 wt.%, 0.05 wt.%, 0.075 wt.%, and 0.1 wt.%, respectively. Full article

A boundary-layer is a thin fluid layer near a solid surface, and viscous effects dominate it. The laminar boundary-layer calculations appear in many aerodynamics problems, including skin friction drag, flow separation, and aerodynamic heating. A student must understand the flow physics and the numerical implementation to conduct successful simulations in advanced undergraduate- and graduate-level fluid dynamics/aerodynamics courses. Numerical simulations require writing computer codes. Therefore, choosing a fast and user-friendly programming language is essential to reduce code development and simulation times. Julia is a new programming language that combines performance and productivity. The present study derived the compressible Blasius equations from Navier–Stokes equations and numerically solved the resulting equations using the Julia programming language. The fourth-order Runge–Kutta method is used for the numerical discretization, and Newton’s iteration method is employed to calculate the missing boundary condition. In addition, Burgers’, heat, and compressible Blasius equations are solved both in Julia and MATLAB. The runtime comparison showed that Julia with $for$ loops is 2.5 to 120 times faster than MATLAB. We also released the Julia codes on our GitHub page to shorten the learning curve for interested readers. Full article

The objective of the present work is to propose an extended analytical wall function that is capable of predicting the bypass transition from laminar to turbulent flow. The algebraic $\gamma$ transition model, the $k-\omega$ turbulence model and the analytical wall function are integrated together in this work to detect the transition onset and start the transition process. The present analytical wall function is validated with the experimental data, the Blasius solution and the law of the wall. With this analytical wall function, the transition onset in the skin friction coefficient is detected and the growth rate of transition is properly generated. The predicted mean velocity profiles are found to be in good agreement with the Blasius solution in the laminar flow, the experimental data in the transition zone and the law of the wall in the fully turbulent flow. Full article

Symmetry in fluid flow is determined by external factors such as magnetic or electric fields. Owing to the electrical properties of fluids, liquids containing fine bubble or ionic surfactant molecules differ from the normal fluid flow. Therefore, the pressure drop and frictional coefficient in a pipe are measured and estimated for water alone, for mixed microbubble water (MB), and for complex fluids (anionic surfactant solution and polymer solution) in capillary flow with constant flow rate. For water alone, good agreement is obtained between the experimental and theoretical values for laminar Hagen–Poiseuille flow and the Blasius expression in turbulent flow. For the MB, pseudo-laminarization is suggested up to a Reynolds number of $4.2\times {10}^3$. Both the anionic surfactant solution and the polymer solution exhibit the same tendency as that of the MB. In explaining these behaviors, elasticity and electrical interaction are discussed, and electrical interaction on the capillary wall is strongly suggested to be a contributing factor. Additionally, surface tension is investigated and supports the discussion. Full article