Narrow Results

The unsteady Casson and Williamson nanofluid flow via a radiative cone in a magnetic surface with cross-diffusion and chemical processes is investigated numerically. The Casson and Williamson nanofluid models characterize the behavior of non-Newtonian fluids. We transform the nonlinear dimensional PDEs into dimensionally free PDEs by implementing dimensionless parameters. The governed partial differential equations are addressed by adopting the Crank–Nicolson implicit approach. A parametric analysis is used to determine the outcomes of skin friction, Nusselt and Sherwood numbers. Increased Brownian motion and the Soret effect promote the transfer of heat and mass. The thermal and mass transfer characteristic of the Casson nanofluid is higher than the Williamson nanofluid. Regarding momentum dispersion, the Williamson nanofluid clearly dominates the Casson nanofluid. Conical mixers are used in polymer blending and plastics manufacturing. The relevance of this mixing step in achieving specified product attributes shows how mass and heat transfer concepts can boost productivity and output in engineering industries.

Purpose: This research aims to investigate the flow and heat transfer characteristics of a hybrid nanofluid comprising water, single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) over a stretching sheet under the influence of a magnetic field. Design/Methodology/Approach: The study employs a mathematical model that accounts for factors such as variable viscosity, thermal radiation, a porous medium and heat generation/absorption. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using similarity transformations and then solved numerically using the bvp4c solver in MATLAB. Findings: The numerical results reveal that the velocity profile of the hybrid nanofluid is significantly enhanced by the presence of MWCNTs. Additionally, the temperature profile is influenced by parameters like the magnetic field, heat source/sink and Prandtl number. The Yamada–Ota (Y–O) model is found to have a more pronounced effect on heat transfer compared to the Xue model. Originality/Value: This study provides valuable insights into the behavior of hybrid nanofluids in complex flow scenarios. The findings can be applied to the design and optimization of various thermal systems, such as heat exchangers and cooling devices.

Novel nanomaterial applications claim distinct uses in thermal engineering, cooling processes, heat transfer devices, and automobile industries, among others. Motivated research uses modified heat and mass flux theories to present thermal observations for the unsteady flow of magnetized Maxwell nanofluid, confined by porous bidirectionally stretched surfaces. The heat transfer model’s extension is based on Joule heating and heat source effects. The Cattaneo–Christov theories govern the expansion of mass and heat transfer. We analyze thermal problems under zero-mass diffusion constraints. The use of proper variables simplifies mathematical modeling into a dimensionless form. The Homotopy Analysis Method (HAM) solves the dimensionless system. The paper highlights the convergence criteria for the HAM procedure. Graphics underline the problem’s physical perspective. We observe that the Deborah number enhances heat and mass transfer. The temperature profile decreases when the parameter becomes unstable.

In this work, an explicit Taylor series expansion- and least square-based lattice Boltzmann method (LBM) is used to simulate two-dimensional unsteady incompressible viscous flows. The new method is based on the standard LBM with introduction of the Taylor series expansion and the least squares approach. The final equation is an explicit form and essentially has no limitation on mesh structure and lattice model. Since the Taylor series expansion is only applied in the spatial direction, the time accuracy of the new method is kept the same as the standard LBM, which seems to benefit for unsteady flow simulation. To validate the new method, two test problems, that is, the vortex shedding behind a circular cylinder at low Reynolds numbers and the oscillating flow in a lid driven cavity, were considered in this work. Numerical results obtained by the new method agree very well with available data in the literature.

We present detailed analysis of the accuracy of the lattice Boltzmann BGK method in simulating pulsatile flow in a 2D channel and a 3D tube. For the 2D oscillatory flow, we have observed a half time-steps shift between the theory and the simulation, that enhances the accuracy at least one order of magnitude. For 3D tube flow, we have tested the accuracy of the lattice Boltzmann BGK method in recovering the Womersley solution for pulsatile flow in a rigid tube with a sinusoidal pressure gradient. The obtained flow parameters have been compared to the analytical solutions. The influence of different boundary conditions such as the bounce-back and inlet-outlet boundary conditions on the accuracy was studied. Relative errors of the order of 0.001 in 2D with the bounce back on the nodes have been achieved. For the 3D simulations, it has been possible to reduce the error from 15% with the simple bounce-back to less than 5% with a curved boundary condition.

We present an adaptation of the lattice BGK method for fast convergence of simulations of laminar time-dependent flows. The technique is an extension to the recent accelerated procedures for steady flow computations. Being based on Mach number annealing, the present technique substantially improves the accuracy and computational efficiency of the standard lattice BGK method for such unsteady flows.

Motivated by the significant role of nanofluid in pollution cleaning and energy recovery, we decided to explore the unsteady three-dimensional rotating flow of nanofluid driven by the movement of a flat surface with the potencies of prescribed heat distributions. The modeling of the physical model is completed with the help of Buongiorno nanofluid model. Suitable arrangement of similarity variables is implemented to transform the model equations into strongly nonlinear ordinary differential equations. Numerical inspection of the model is made by employing Keller–Box algorithm. Influences of involved parameters on the distributions of heat and mass are discussed graphically, while the potencies of influential parameters on reduced Nusselt and reduced Sherwood numbers are physically discussed through tabular arrangements. It is deduced that increasing the values of Prandtl factor and heat controlling indices diminishes the temperature and concentration distributions, whereas intensification in the amount of rotation factor enhances the temperature as well as concentration distribution. Moreover, negative trends in the amounts of reduced Nusselt and Sherwood numbers are achieved with the escalations in the values of rotation and thermophoresis factors, whereas opposite trend is achieved with the intensification in the choice of Prandtl factor.

Carbon nanotubes (CNTs) influenced nanofluid is gaining popularity in the industry for solar energy and scratch heat exchanger applications. Consequently, this research focuses on evaluating the impact of nonlinear thermal radiation from a CNT-based nanofluid on an unsteady three-dimensional nonasymmetric Homann stagnant flux as a function of length and radius. CNTs have remarkable thermal physical properties that appear to be critical for nonlinear thermal transport. As a result, the nonlinear heat transfer properties of H₂O composed of single or multiple wall CNTs are studied. The nanomaterial has a length and radius of approximately $3\mathrm{\text{nm}}\le L\le 70\mathrm{\text{nm}}$ and $10\mathrm{\text{nm}}\le R\le 40\mathrm{\text{nm}}$. Partially differential equations with appropriate similarity transformations serve as a mathematical model for the process. The numerical solution of the simplified system of equations is achieved via the use of the well-known Runge–Kutta (RK) method in conjunction with the shooting approach. An effective way to show how a component affects velocity and temperature, skin frictions in both direction and Nusselt number are utilized in graphical representations. Increasing the unsteadiness parameter causes a reduction in the temperature profile and the velocity profile in both directions. As $\epsilon$ grows larger with $\varphi$, the skin friction in both directions decreases, while the Nusselt number profile grows larger. In addition, the variation in the Nusselt number is included in the tables, along with a comparison of the model without radiation to the model with radiation.

This research is focused on the examination of an unsteady flow of an electromagnetic nanofluid close to a stagnation point over an expanded sheet kept horizontally. Buongiorno’s nanofluid model is revised with the combined influence of the externally applied electric and magnetic fluxes. Moreover, the underneath surface offers multiple slips into the nanofluid flow. The leading partial differential equations (PDE) are renovated to the nonlinear ordinary differential equations (ODE) with the assistance of similarity transformations. Thus, the outcomes are received numerically by using the RK-6 with Nachtsheim–Swigert shooting technique. The enlistment of the outcomes for the momentum, energy and concentration profiles along with the skin-friction coefficient $(C_{fx}^{\ast })$, Nusselt number $({\text{Nu}}_x^{\ast })$ and Sherwood number $({\text{Sh}}_x^{\ast })$ for several parametric values are presented in a graphical and tabular form and discussed in detail. The variation of streamlines with respect to the unsteadiness parameter is also recorded. Statistical inspection reveals that the flow parameters are highly correlated with the wall shear stress, wall heat and mass fluxes. Findings indicate that the escalation of electric flux tries to intensify the hydrodynamic boundary layer meanwhile the magnetic flux assists to stabilize the growth by reducing it for both the steady and unsteady flow patterns. Influence of velocity slip parameter $\xi$ from 0.0 to 1.5 causes the reduction in ${\text{Nu}}_x^{\ast }$ by 16.98% for steady flow while 60.27% for time-dependent flow case. Moreover, we expect that these theoretical findings are very much helpful for several engineering and industrial applications such as polymer sheet productions, manufacturing automobile machines, cooling microelectronic chips, etc.

This investigation deals with the time-dependent flow of an incompressible viscous fluid bounded by an infinite plate. The fluid is electrically conducting under the influence of a transverse magnetic field. The plate moves with a time dependent velocity in its own plane. Both fluid and plate exhibit rigid body rotation with a constant angular velocity. The solutions for arbitrary velocity and magnetic field is presented through similarity and numerical approaches. It is found that rotation induces oscillations in the flow.

This paper looks at the mass transfer effects on the unsteady two-dimensional and magnetohydrodynamic flow of an upper-convected Maxwell fluid bounded by a stretching surface. Homotopy analysis method is used for the development of series solution of the arising nonlinear problem. Plots of velocity and concentration fields are displayed and discussed. The values of surface mass transfer and gradient of mass transfer are also tabulated.

Mesh adaptation is a reliable and effective method to improve the precision of flow simulation with computational fluid dynamics. Mesh refinement is a common technique to simulate steady flows. In order to dynamically optimize the mesh for transient flows, mesh coarsening is also required to be involved in an iterative procedure. In this paper, we propose a robust mesh adaptation method, both refinement and coarsening included. A data structure of $k$-way tree is adopted to save and access the parent–children relationship of mesh elements. Local element subdivision is employed to refine mesh, and element mergence is devised to coarsen mesh. The unrefined elements adjacent to a refined element are converted to polyhedrons to eliminate suspending points, which can also prevent refinement diffusing from one refined element to its neighbors. Based on an adaptation detector for vortices recognizing, the mesh adaptation was integrated to simulate the unsteady flow around a tri-wedges. The numerical results show that the mesh zones where vortices located are refined in real time and the vortices are resolved better with mesh adaptation.

In this study, we investigated dual solutions for the influence of chemical reaction and radiation effect on axisymmetric flow of magneto-Cross nanomaterial towards a radially shrinking disk on taking account of stagnation point. The governing expressions which describe the assumed flow are reduced to ordinary differential equations by opting suitable similarity variables. The dual solutions on the performance of dimensionless velocity, thermal, concentration gradients, skin friction, rate of heat and mass transfer with the impact of relevant parameters are studied using suitable graphs. Result outcomes reveal that, upsurge in Brownian motion parameter improves the thermal gradient in case of both the solution but, converse trend is detected in concentration gradient. The uplift of thermophoresis parameter boosts up the concentration gradient in both branch solution but reverse trend is noticed in concentration profile for inclined values of Schmidt number. Further, dual nature of solutions exists only for certain range of shrinking parameter.

For practical purposes, the study of ternary hybrid nanofluid flows near stretching/ shrinking surfaces, including heat generation/ absorption and velocity slip, has enormous value. It is crucial to understand how fluid mechanics deals with stagnation point flow, which is a common phenomenon in both engineering and scientific domains. In the evaporation process, the polymer enterprises, and the aircraft counter jet, the stagnation point flow may be found. An unsteady stagnation point flow is used to explore a ternary hybrid nanofluid (Cu–TiO₂–Al₂O₃/ polymer) in relation to a convectively heated stretching/ shrinking sheet. This research also considers the velocity slip condition in addition to the traditional surface under no-slip conditions. The differential equations and their partial derivatives are changed to ordinary differential equations by applying approved similarity transformations. The MATHEMATICA operating system employs the Shooting with Runge–Kutta-IV process to explain the reduced mathematical model. When preliminary assumptions are appropriate, the technique may provide solutions. According to the data, nanoparticle volume fraction has an effect on the skin friction coefficient and local Nusselt number. The coefficient of skin friction decreases when velocity slip occurs at the border, while the rate of heat transfer increases. According to the research, increasing the unstable parameter led to large increases in the coefficient of skin friction and heat transfer as opposed to just altering velocity slip. The outcomes show that ternary fluid has a greater skin fraction and heat transmission profile than hybrid and traditional nanofluids for all parameters. The recent evidence and published results for a particular case were contrasted to validate the findings, and good agreement was established.

The model presented in this paper deals with the investigation of the unsteady laminar flow past a stretchable disk. The nanofluids Al₂O₃/H₂O and Cu/H₂O are considered for the analysis where the thermal characteristics and flow behavior of these nanofluids are compared. In addition, the system is subjected to the suction force that has significant impacts on velocity of the nanofluid flow. Further, the nanoparticle solid volume fraction is another important parameter that is discussed which has a prominent role on both profiles of the nanofluid. Furthermore, the investigated mathematical model is framed using PDEs that are transformed to ODEs using suitable transformations. The system of equations obtained in this regard is solved by employing the RKF-45 numerical method where the results are obtained in the form of graphs. Various nanofluids flow parameters arise in the study and the impact of all these parameters has been analyzed and interpreted. Some of the major outcomes are that the higher values of nanoparticle solid volume fraction enhance the temperature while it decreases velocity of the flow. The comparison of flow of the two nanofluids concluded that alumina–water nanofluid has a better velocity while the copper–water nanofluid has a better thermal conductivity.

Heat transfer and entropy generation are crucial considerations in the nuclear industry, where the safe and efficient transfer of heat is essential for the operation of nuclear reactors and other nuclear systems. Casson fluid is a useful tool in the nuclear industry for simulating the flow behavior of nuclear fuels and coolants, and for optimizing the design and operation of nuclear reactors. In view of this, the current investigation deals with the heat and fluid flow of unsteady Casson fluid in a circular pipe under the influence of magnetic field, internal heat generation, entropy generation and porous media. The governing equations have been simplified under suitable assumptions and nondimensional quantities. The simplified dimensionless governing equations have been solved using the method of separation of variables along with Bessel functions. It is concluded from the investigation that the temperature increases with time. The Casson fluid parameter raises the temperature and entropy generation. The temperature, entropy generation and Bejan number are the decreasing functions of the Prandtl number.

This paper discusses the high heat transfer demand from application prospects. Hybrid nanofluid is a well-known liquid with higher heat transfer capabilities. Here, the time-dependent flow of hybrid nanocomposite, by hybridizing the metal (Cu) and metallic oxide (Al₂O₃) and inserting them into water-based nanofluid, is examined. The flow takes place over the upper half of a parabolic surface. The modified Buongiorno model is used to express the physical phenomenon in mathematical equations form. The governing system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs) by applying certain transformations. Computation of the final equations has been done by a numerical scheme, known as the Keller-box method. The significance of dimensionless flow causing physical parameters is shown through graphs and tables. The findings reveal that among the hybrid nanofluids with two types of nanoparticles varying from 0% to 5%, a nanofluid having 5% of both nanoparticles is the one with the maximum surface drag force and heat transport rate, which are 41.8% and 22.7% higher to water, respectively. A higher amount of Al₂O₃ than Cu results in a suitable hybrid combination for application purposes to produce higher cooling rate with less surface drag. Also, the thickness of the surface, unsteadiness, nanoparticles suspension and power index of wall temperature enhance the heat transfer rate. Thin parabolic surfaces experience less drag and have larger boundary layer thicknesses (momentum, thermal and concentration) as compared to thicker parabolic surfaces. Also, the addition of copper slows down the hybrid fluid flow field, but alumina magnifies the mobility of hybrid fluid.

The essence of the current examination is to carry out thermofluid parametric sensitivity with time-varying thermal migration of chemically reactive tiny species across an oscillating infinite plate surface. The impact of thermal motile tiny particles under the influence of many other oscillating flow parameters has yet to be investigated; hence the results obtained in this research are novel. Using a suitable non-dimensional variable, the leading PDEs (partial differential equations) are transmuted into dimensionless PDEs, ensuring equations are numerically solved using the MAPLE built-in approach. The numerical values produced in a limited scenario are linked with the outcomes found in the literature to validate the precision of the numerical approach utilized. The fluctuations in the profiles of the velocity, temperature, and concentration, in addition to the wall friction and rate of thermal and solutal transport, are illustrated via graphs and tables due to the modification of the critical parameters. The endmost results of the study concede that increasing permeability quantity and thermal and solutal buoyancy impellers intensify the fluid velocity. In contrast, a converse tendency is perceived with magnetic parameter and also, wall friction acts opposite to the velocity. The fluid temperature attenuated with dilation of the Prandtl number and radiation parameter, whilst a contrary trend was perceived with Eckert number. The increasing thermo-diffusion helps to develop fluid concentration whilst the Schmidt number and chemical reaction displayed opposite trend. Further, we achieved a tremendous conformity between the current findings and genuine results in the literature.

A numerical method for the simulation of parachute inflation process is presented in this paper. The unsteady compressible N-S equations are fully coupled with MSD (Mass Spring Damper) structure model and integrated forward in time. The CFD solver is based on an unstructured finite volume algorithm and the preconditioning technique is applied to alleviate the stiffness caused by low Mach number. The Spalart-Allmaras one-equation turbulence model is implemented to evaluate the turbulent viscosity. The whole system (fluid equations and structural model equations) is marched implicitly in time using a dual time stepping method. An overset deforming grids method is adopted in this paper to deal with the very large domain deformation during the parachute inflation process. Finally numerical test is performed to validate the robustness of this method.

A parallel Navier-Stokes solver based on dynamic overset unstructured grids method is presented to simulate the unsteady turbulent flow field around helicopter in forward flight. The grid method has the advantages of unstructured grid and Chimera grid and is suitable to deal with multiple bodies in relatively moving. Unsteady Navier-Stokes equations are solved on overset unstructured grids by an explicit dual time-stepping, finite volume method. Preconditioning method applied to inner iteration of the dual-time stepping is used to speed up the convergence of numerical simulation. The Spalart-Allmaras one-equation turbulence model is used to evaluate the turbulent viscosity. Parallel computation is based on the dynamic domain decomposition method in overset unstructured grids system at each physical time step. A generic helicopter Robin with a four-blade rotor in forward flight is considered to validate the method presented in this paper. Numerical simulation results show that the parallel dynamic overset unstructured grids method is very efficient for the simulation of helicopter flow field and the results are reliable.