Papers by Keyword: Couette Flow

Abstract: In the present study, an analytical solution for MHD flow-heat transfer highly non-linear equations of non-Newtonian third-grade nanofluid is established using the AGM method while considering the effect of the magnetic field, the radiation heat transfer, the inclination and the nanoparticles fraction. From dimensionless analysis, the main characteristic parameters are identified, specifically the viscoelastic parameter, the magnetic parameter, the gravitational parameter, the generalized pressure gradient, the thermal radiation parameter, the Brinkman number and the Hamilton number. Two classes of problems, namely, plane Couette flow and plane Poiseuille flow, are considered. Validation was conducted using results from established numerical methods, including Mathematica software, the Adomian Decomposition Method (ADM), and BVP4C solver to benchmark our findings derived via the Akbari Gangi Method. The comparative analysis reveals the reliability and accuracy of the established analytical solutions. The effect of the main parameters of water-SWCNT nanofluid on velocity and temperature profiles are graphically illustrated and discussed. The main results reveal that increasing a magnetic parameter results in a significant drop in the velocity. Furthermore, the rise in Brinkman's number and the radiation parameter affect the temperature differently. Additionally, the viscoelastic and gravitational parameters have opposite velocity and temperature effects. The results demonstrate the complex interaction between several physical characteristic parameters in the fluid dynamics and heat transfer processes. The efficient and highly accurate series-based analytical solutions for flow velocity and temperature obtained through the Akbari-Ganji Method provide valuable insights and are a powerful tool for addressing similar problems in fluid dynamics and heat transfer.

Abstract: The time-dependent magnetohydrodynamic (MHD) Couette flow of Maxwell material in a rotating system with ramped wall temperature has been examined under Ohmic (Joule) heating. The Continuity equation, Cauchy’s equation of motion, the constitutive equation for the Maxwell model, and the energy equation with Ohmic heating with relevant initial and boundary conditions are all considered in obtaining a mathematical model for the investigation. The finite element technique is applied to numerically solve the non-dimensionalized governing equations using the mathematical software MATLAB. The values of Weissenberg number, Hartmann number, Eckert number, and angular velocity of the rotating system are varied, and their effects on the fluid temperature and velocity are shown graphically and discussed.

Abstract: In this work, we examine the effects of viscous dissipation and local thermal non-equilibrium (LTNE) on Couette flow in a duct filled with a porous media under the influence of an angled magnetic field. The bottom plate of the duct is in motion and subjected to a constant heat flux, while the top plate remains stationary and adiabatic. The Jeffrey fluid flow model is consistent with the unidirectional flow in the porous zone. The studies provide more precise measurements of the effects of the Jeffrey parameter (λ), inclined angle (ϕ), Hartmann number (M_W), thermal conductivity ratio (ν), Brinkman number (Br_W), and Biot number (Bi_W) on improving heat transmission. The governing equations are solved analytically. The present investigation gives dimensionless temperatures for fluid-solid phases and fully developed Nusselt number (FDNN) profiles. Variation of Jeffrey parameter, inclined angle, Brinkman number, and Hartman number in the temperature field in both phases and FDNN. Furthermore, the temperature in the solid phase is higher than the temperature in the fluid phase for the Jeffrey parameter and Hartman number in the Couette flow, which supports LTNE validation.

Abstract: Recently, heat transfer problems where anisotropic porous medium or stably stratified fluid are taken into account have been separately studied. Developing a mathematical model that combines these physical quantities naturally results to complex coupled differential equations. In this paper, a fully developed time dependent natural convection Couette flow of stably stratified fluid between vertical parallel channels filled with anisotropic porous material is investigated. The governing partial differential equations are transformed into ordinary differential equations using Laplace transform techniques and then decoupled using D’Alembert method. Exact solutions in Laplace domain for the velocity and temperature equations are then obtained. A numerical method: Riemann-sum approximation is then used to invert the expressions for the velocity and temperature profiles, as well as the resulting skin friction, rate of heat transfer and volumetric mass flow rate into their corresponding time domain. The research establishes that both the anisotropic and the stratification parameters aid in regulating the fluid temperature and velocity. The research further reveals that the fluid velocity attains its maximum (or minimum) velocity when θ = 90⁰ (or θ = 0⁰) for k^*<1 and when k^*>1, the fluid velocity is least (or maximum) when θ = 90⁰ (or θ = 0⁰).

Abstract: Dissipative Particle Dynamics method is employed to model the particulate suspensions. The system input parameters are calibrated to capture the experimental relative viscosity versus volume fraction in dilute (φ≤ 0.2), semidilute (0.2<φ≤ 0.3) and dense regimes 0.3<φ≤ 0.45. Statistical uncertainties and system bulk and overall temperatures are monitored to guarantee that equilibrium has been quantitatively reached. It was found that increment of solvent drag coefficient or the dissipation rate (1≤γs≤200) between like solvent particles linearly increases the solvent and suspension viscosity. Solvent number density (ρs) changing from 2 to 20 in sync with the repulsion coefficient renders a parabolic variation for suspension and solvent viscosities. Two sets of calibrated simulation settings are ultimately proposed to reasonably capture the rheological behaviour of dilute to dense suspensions according to experiment and empirical relations for relative viscosity.

Abstract: The study concerns the application of the Smoothed Particle Hydrodynamics (SPH) method within the computational fluid dynamics (CFD). In the present study, some classical problems – the Poiseuille flow, the Hagen-Poiseuille flow, and the Couette flow – with the analytical solutions were investigated to verify a newly developed code of SPH. The code used for solving these problems, is an entirely parallel SPH solver in 3D and has been developed by the authors. Fluid was modelled as a viscous liquid with weak compressibility. The boundary walls were simulated with a special set of fixed boundary particles, and no-slip boundary condition was considered. Computational results were compared to available analytical solutions for transient hydraulic processes. Good agreement is achieved for the whole transient stage of the considered problems until steady state is reached. The results of this study highlight the potential of SPH to tackle a broad range of problems in fluid mechanics.

Abstract: In the present paper, the exact analysis of steady state fully developed natural convective Couette flow in a vertical parallel plate microchannel is performed. Exact solutions are derived for the dimensionless velocity, temperature, volume flow rate, vertical heat flux and Nusselt number. The effects of Grashof number, wall-ambient temperature difference ratio and Knudsen number on the velocity, volume flow rate and Nusselt number have been discussed through graphs. The study revealed that the fluid velocity and volume flow rate increases with increasing Grashof number whereas the Nusselt number decreases with increasing Grashof number.

Abstract: In this paper, Couette flow is mainly discussed by studying the general flow behaviour mechanism and importing the velocity slip and temperature jump boundary condition. By analyzing velocity, temperature and pressure profiles at different Knudsen numbers, we concluded that Couette flow is driven by shear stress. The shear stress lies in stream direction. Viscous heat causes the increasing of the fluid’s temperature. With the increasing of Knudsen numbers, the increasing speed increases. It’s in the beginning of transition region that the heat flux has the maximum.

Abstract: The present Dissipative Particles Dynamics (DPD) simulation study aims at extracting some correlations between velocity and temperature profiles, and dynamic viscosity with externally applied shear velocity via Lees-Edwards boundary condition. System physical and rheological behaviours are studied under changes made to shear velocity, cutoff radii and weight function exponent in the definition of conservative, dissipative and random forces. Two cutoff radii are altered up to the level where system of particles shows anomalous behaviour. Radial distribution function and temperature (T) are invoked to rule out invalid cutoff radii combinations. Calculated viscosity in a range of weight functions exponents (S) is compared against theory in a variety of shear velocities, where reasonable agreement with respect to T control is achieved.

Abstract: In this paper, based on the fractional model, we present an investigation on the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress which is affected by the internal constantly decelerated pressure gradient. By using the fractional derivatives Laplace and finite Hankel transforms, the obtained solutions for the velocity field and shear stress, written in terms of generalized R function, are presented the similar characteristics with Newtonian and non-Newtonian fluids. Moreover, the effects of various parameters are systematically analyzed.