Search results

The paper aims to examine the boundary layers of a three-dimensional stagnation point flow of Al-Cu nanoparticle-suspended water-based nanofluid in an electrically conducting medium. The effect of magnetic field on second-order slip effect and convective heating is also taken into account.

The thermophysical properties of alloy nanoparticles such as density, specific heat capacity and thermal conductivity are computed using appropriate formula. The non-linear parabolic partial differential equations are transformed to ordinary differential equations and solved by shooting technique.

The influence of compositional variation of alloy nanoparticle, nanoparticle concentration, magnetic effect, slip parameters and Biot number are presented for various flow characteristics. Interesting results on skin friction and Nusselt number are obtained for different composition of aluminium and copper.

A novel result of the analysis reveals that impact of magnetic field near the boundary is suppressed by the slip effect.

The purpose of this study is to discuss the Darcy–Forchheimer nanoliquid bio-convection flow by stretching cylinder/plate with modified heat and mass fluxes, activation energy and gyrotactic motile microorganism features.

The proposed flow model is based on flow rate, temperature of nanomaterials, volume fraction of nanoparticles and gyrotactic motile microorganisms. Heat and mass transport of nanoliquid is captured by the usage of popular Buongiorno relation, which allows us to evaluate novel characteristics of thermophoresis diffusion and Brownian movement. Additionally, Wu’s slip (second-order slip) mechanisms with double stratification are incorporated. For numerical and graphical results, the built-in bvp4c technique in computational software MATLAB along with shooting technique is used.

The influence of key elements is illustrated pictorially. Velocity decays for higher magnitude of first- and second-order velocity slips and bioconvection Rayleigh number. The velocity of fluid has an inverse relation with mixed convection parameter and local inertia coefficient. Temperature field enhances with the increase in estimation of thermal stratification Biot number and radiation parameter. A similar situation for concentration field is observed for mixed convection parameter and concentration relaxation parameter. Microorganism concentration profile decreases for higher values of bioconvection Lewis number and Peclet number. A detail discussion is given to see how the graphical aspects justify the physical ones.

To the best of the authors’ knowledge, original research work is not yet available in existing literature.

The purpose of this study is to describe the steady mixed convection stagnation point of a hybrid nanofluid with a second-order velocity slip.

Using appropriate similarity variables, the partial differential equations are transformed into ordinary (similar) differential equations, which are numerically solved using the bvp4c function in MATLAB. The numerical results are used to present graphical illustrations for the reduced skin friction, reduced Nusselt number, velocity and temperature profiles.

Dual solutions are discovered in this study. Thus, stability analysis is implemented and the first (upper branch) and second (lower branch) solutions are determined and analyzed.

Hybrid nanofluids have many practical applications in the modern industry such as in micro-manufacturing, periodic heat exchanges process, nano drug delivery system and nuclear reactors.

Despite numerous studies on the mixed convection stagnation point of classical viscous fluids past a vertical plate flow, none of the researchers have focused on the effect of second-order slip velocity on hybrid nanofluids. The behavior of the flow and heat transfer has been thoroughly analyzed with the variations in governing parameters such as heat source/sink and nanoparticle volume fraction. Moreover, the use of the wall slip velocity in this hybrid nanofluid model strengthened the novelty of this study.

The purpose of this study is to analyze the impact of inclined magnetohydrodynamics (MHD) and thermal radiation on the flow of a ternary micropolar nanofluid on a sheet that is expanding and contracting while applying mass transpiration and velocity slip conditions to the flow. The nanofluid, which is composed of Au, Ag and Cu nanoparticles dispersed in water as the base fluid, possesses critical properties for increasing the heat transfer rate and is frequently used in manufacturing and industrial establishments.

The set of governing nonlinear partial differential equations is transformed into a set of nonlinear ordinary differential equations. The outcome of this differential equation is solved and obtained the closed-form solution and energy equation in the form of hypergeometric functions.

The velocity, micro-rotation and temperature field are investigated versus a parametric variation. The physical domains of mass suction or injection and micropolar characteristics play an important role in specifying the presence, singleness and multiplanes of exact solutions. In addition, many nondimensional characteristics of the profiles of temperature, angular velocity and velocity profiles are graphically shown with substantial consequences. Furthermore, adding nanoparticles increases the heat transfer rate of the fluid used in manufacturing and industrial establishments. The current findings may be used for better oil recovery procedures, smart materials such as magnetorheological fluids, targeted medicine administration and increased heat transmission. Concerning environmental cleanup, nanomaterial fabrication and biomedical devices, demonstrate their potential influence in a variety of disciplines.

The originality of this paper is to analyze the impact of inclined MHD at an angle with the ternary nanofluid on a micropolar fluid over an expanding and contracting sheet with thermal radiation effect.

The purpose of this paper is to investigate the effect of fluid–structure interaction in micro-scale on the performance of the hydrostatic spindle and improve the analysis precision of the dynamic performance of hydrostatic spindle.

Dynamic analysis of hydrostatic spindle before and after fluid–structure interaction is carried out according to stiffness and damping performance of the bearing, which demonstrates that the natural frequency and peak response of the spindle are increased in the micro-scale.

It is concluded from the simulation and experimental results that there is micro-scale effect in the actual operation of the spindle system and slippage exists in the oil film flow. The error between the modal detection result and the theoretical value is within 10 per cent, which also verifies the correctness of the above conclusions.

This paper analyzes the changes of the bearing performance parameters at macro- and micro-scale, which present the influence of the static and dynamic performance of the spindle in the micro-scale.

This study aims to explore the stagnation flow over a shrinking surface in a hybrid nanofluid consists of Al₂O₃ and Cu nanoparticles. Here, the flow is subjected to the magnetohydrodynamic (MHD) and the melting phenomenon effects.

The similarity variables are used to gain the similarity equations. These equations are solved via the bvp4c solver. The effects of several physical parameters on the flow and the thermal characteristics of the hybrid nanofluid are analysed and discussed. Later, the temporal stability analysis is used to determine the stability of the dual solutions obtained as time evolves.

Results show that two solutions are found for the limited range of the stretching/shrinking parameter λ, and then these solutions are terminated at λ=λc. The rise of the melting parameter Me from 0 to 2 contributes to enhance 109.63% of the local Nusselt number Rex-1/2Nux and 3.30% of the skin friction coefficient Rex1/2Cf. Contrarily, the values of Rex-1/2Nux and Rex1/2Cf decline by 25.04% and 5.58%, respectively, as the magnetic parameter Mg increases from 0 to 0.3. Additionally, Al₂O₃-Cu/water has the highest values of Rex1/2Cf and the lowest values of Rex-1/2Nux. Lastly, it is found that the first solution is physically stable as time evolves.

This paper considers the MHD stagnation point flow of a hybrid nanofluid over a shrinking surface with the melting phenomenon effects. Most importantly, it is shown that there exist dual solutions within a specific range of the physical parameters. Besides, the temporal stability of the solutions is also reported in this study. The finding can contribute to foresee the flow and thermal behaviours in industrial applications. Also, the suitable values of parameters can be determined to avoid misjudgement in flow and heat transfer analysis.

The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions.

The paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other.

The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions.

The novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.

The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.

The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.

The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

This paper aims to present the steady dual solutions on three-dimensional flow and heat transfer of nanofluid over a permeable non-linearly shrinking surface with two-order velocity slips conditions. Boundary layer assumption is considered in the mathematical modelling. Authors comprehend from previous studies and papers that the shrinking surfaces are extremely important in current engineering and environmental systems.

Using appropriate similarity variables, the full partial differential equations (PDF) are modified into a specific set of ordinary (similar) differential equations (ODE). The resulting non-linear ordinary differential system is then solved both analytically for some particular cases and numerically for the general case using the function bvp4c from MATLAB for characteristic values of the parameters which govern the equations. The transformed mathematical model is analysed using the bvp4c procedure. Based on the given assumptions, this study is able to produce multiple solutions of the problem.

The ordinary (similarity) differential equations have two branches solutions, upper and lower branch solutions, given some interval of shrinking and velocity slip parameters. The authors consider here a temporal stability analysis, as they want to establish which of the solutions are stable and which are not. In a distinct paragraph, the authors discuss in detail and present in a graphical manner the effects of shrinking and second-order slip flow model on the skin friction coefficient, surface wall heat flux and dimensionless velocity and temperature profiles. The analysis reveals that the second order slip has a big influence on the flow and heat transfer characteristics.

The present discoveries are unique and truly new for the research of the three-dimensional stretching/shrinking forced convection flow and heat transfer nanofluids. The nanofluid is a water-based nanofluid (H₂O), which contains one type of nanoparticles, namely, copper (Cu). Of course, the analysis can be further extended considering other types of nanoparticles such as alumina (Al₂O₃). The authors assume that the thermal equilibrium is reached for the base fluid together with the suspended nanoparticles and that the nanoparticles are uniform in dimension and form.

The purpose of this study is to investigate the influence of the second order slip velocity on the boundary layer stagnation point flow of a nanofluid past a non-aligned stretching/shrinking sheet.

Proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved numerically using the bvp4c solver in MATLAB software. As in the papers by Kuznetsov and Nield (2010, 2013) and Fang et al. (2009), the authors considered the stretching/shrinking parameter λ, the first-order (a₁, a₂) and second-order (b₁) slip parameters and the Lewis number Le, Nb the Brownian parameter and Nt the thermophoresis parameter fixed at Le = 10, Nb = Nt = 0.5 when the Prandtl number Pr is fixed at Pr = 1.

Dual solutions are found as the sheet is shrunk in the horizontal direction. Stability analysis shows that the first solution is physically realizable, whereas the second solution is not practicable.

The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Wang (2008) and Lok et al. (2011) to the case of nanofluids.