The Coriolis Effect on Thermal Convection in a Rotating Sparsely Packed Porous Layer in Presence of Cross-Diffusion

The effect of rotation and cross-diffusion on convection in a horizontal sparsely packed porous layer in a thermally conducting fluid is studied using linear stability theory. The normal mode method is employed to formulate the eigenvalue problem for the given model. One-term Galerkin weighted residual method solves the eigenvalue problem for free-free boundaries. The eigenvalue problem is solved for rigid-free and rigid-rigid boundaries using the BVP4c routine in MATLAB R2020b. The critical values of the Rayleigh number and corresponding wave number for different prescribed values of other physical parameters are analyzed. It is observed that the Taylor number and Solutal Rayleigh number significantly influence the stability characteristics of the system. In contrast, the Soret parameter, Darcy number, Dufour parameter, and Lewis number destabilize the system. The critical values of wave number for different prescribed values of other physical parameters are also analyzed. It is found that critical wave number does not depend on the Soret parameter, Lewis number, Dufour parameter, and solutal Rayleigh number; hence critical wave number has no impact on the size of convection cells. Further critical wave number acts as an increasing function of Taylor number, so the size of convection cells decreases, and the size of convection cells increases because of Darcy number.

Taylor-Couette-Poiseuille flow heat transfer in a high Taylor number test rig

As technology advances, rotating machinery are operating at higher rotational speeds and increased pressures with greater heat concentration (i.e. smaller and hotter). This combination of factors increases structural stresses, while increasing the risk of exceeding temperature limits of components. To reduce stresses and protect components, it is necessary to have accurately designed thermal management systems with well-understood heat transfer characteristics. Currently, available heat transfer correlations operating within high Taylor number (above 1×10^10) flow regimes are lacking. In this work, the design of a high Taylor number flow experimental test rig is presented. A non-invasive methodology, used to capture the instantaneous heat flux of the rotating body, is also presented. Capability of the test rig, in conjunction with the use of high-density fluids, increases the maximum Taylor number beyond that of previous works. Data of two experiments are presented. The first, using air, with an operating Taylor number of 8.8± 0.8 ×10^7 and an effective Reynolds number of 4.2± 0.5 ×10^3, corresponds to a measured heat transfer coefficient of 1.67 ± 0.9 ×10^2 W/m2K and Nusselt number of 5.4± 1.5×10^1. The second, using supercritical carbon dioxide, demonstrates Taylor numbers achievable within the test rig of 1.32±0.8×10^12. A new correlation using air, with operating Taylor numbers between 7.4×10^6 and 8.9×10^8 is provided, comparing favourably with existing correlations within this operating range. A unique and systematic approach for evaluating the uncertainties is also presented, using the Monte-Carlo method.

Analytical Estimates of Critical Taylor Number for Motion between Rotating Coaxial Cylinders Based on Theory of Stochastic Equations and Equivalence of Measures

The purpose of this article was to present the solution for the critical Taylor number in the case of the motion between rotating coaxial cylinders based on the theory of stochastic equations of continuum laws and the equivalence of measures between random and deterministic motions. Analytical solutions are currently of special value, as the solutions obtained by modern numerical methods require verification. At present, in the scientific literature, there are no mathematical relationships connecting the critical Taylor number with the parameters of the initial disturbances in the flow. The result of the solution shows a satisfactory correspondence of the obtained analytical dependence for the critical Taylor number to the experimental data.

Structural Analysis of Couette-Taylor Flow With Periodic Oscillation of the Inner Cylinder in Different Flow Regimes

The structures of flow in laminar Couette-Taylor flow with periodic oscillation of the inner cylinder rotation velocity (which linearly increases from zero to a fixed maximum value and then goes to zero again in each period) for different three regimes; Couette flow, Taylor vortex and wavy vortex, with the effect of the Womersley number, Wo, for different periods and the critical Taylor number are investigated numerically. The Wo varies between. 0.38 ≤ Wo ≤ 8.59. To understand how the flow responds to a given boundary conditions, the critical Taylor number is calculated and the structure of vortices which formed in the flow field is investigated. The results show that if Wo is increased, i.e. when the slope of rotational velocity of inner cylinder is increased, more delay in changing the flow regime compare to the steady state (when the inner cylinder rotates with constant velocity) is observed. Also for large values of Wo, due to the inertia, the flow does not follow the given boundary condition so for the higher value of the Womersley number, Wo = 8.59, there is a time lag and vortices do not appear until the second period of the inner cylinder oscillations. The reason is that the time scale of the dynamics of flow is less than the time scale that is associated with the flow instability, thus the flow regime behaves like a laminar Couette flow at the initial period. Comparing the present results with that of steady state, it is appeared that for a minimum value of Wo used in this paper, i.e. Wo = 0.38, the primary critical Taylor number is 50% higher than that of steady state.

A numerical technique and effect of magnetic field dependent (MFD) viscosity on thermal instability in a ferrofluid pores with Coriolis force for Darcy model

Purpose The effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system. Design/methodology/approach The thermal perturbation method is employed for analytical solution. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a fluid layer contained between two impermeable boundaries for which an exact solution is obtained. Findings The conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number Ta is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number Ta leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system. Originality/value This research paper is new and original.

Scrutiny the Heat Transfer Effect in an Annulus by Mounting Axial Fins with Different Shapes: Without and with Taylor Number

This study aimed to investigate numerically the heat transfer improvement and pressure drop inside annular channel of a rotor-stator provided with fins mounted on the stator without and with Taylor number. The impact of mounting various types of fins (triangular, rectangular, trapezoidal shapes with small and large base) is studied by varying the fin width b from 0 to 14 mm. In the presence of axial air flow, numerical simulations are carried out by solving the governing continuity, momentum and energy equations of turbulent flow in cylindrical coordinates using the Finite Volume Method. The results obtained by Reynolds Stress Model RSM model have indicated that the heat transfer enhances as the surface area of the fins and the effective Reynolds number increase, while there is an increase in pressure drop. Furthermore, we have shown that the presence of Taylor number has a slight increase in Nusselt number and pressure drop compared to the case without Taylor number. Among the four geometries, it is found that the rectangular cavity is the best geometry which gives maximum heat transfer and minimum pressure loss.

Non-linear Stability in Transitional and Rotatory Regime of the Cooking of Gari, Food Based on Cassava Tubers

The present study focuses on the non-linear stability in the transient rotary regime of the cooking process of gari. The process of cooking gari consists of a rotating rectangular cavity filled with grated cassava flour, pressed, retted and considered to be an anisotropic porous medium in a permeably saturated viscoelastic fluid. The cavity is heated from below to a constant temperature. The lower wall of the cavity is impermeable and the upper wall is permeable. Using a numerical method, we have established the transient expressions of the Nusselt number, the flow and temperature fields as a function of the anisotropy parameters of the porous medium and of the Taylor number. The results obtained showed that the anisotropy of the porous medium and the Taylor number greatly influenced the cooking of gari over time.

Computational study on drilling mud flow through wellbore annulus by Giesekus viscoelastic model

Cuttings transport from wellbore annulus to the surface via drilling fluids is one of the most important problems in gas and oil industries. In the present paper, the effects of viscoelastic property of drilling fluids on flow through wellbore annulus are studied numerically by use of computational fluid dynamics simulation in OpenFOAM software. This problem is simulated as the flow between two coaxial annulus cylinders and the inner cylinder is rotating through its axes. Here, the Giesekus model is used as the nonlinear constitutive equation. This model brings the nonlinear viscosity, normal stress differences, extensional viscosity and elastic property. The numerical solution is obtained using the second order finite volume method by considering PISO algorithm for pressure correction. The effect of elasticity, Reynolds number, Taylor number and mobility factor on the velocity and stress fields, pressure drop, and important coefficient of drilling mud flow is studied in detail. The results predicted that increasing elastic property of drilling mud lead to an initial sharp drop in the axial pressure gradient as well as Darcy-Weisbach friction coefficient. Increasing the Reynolds number at constant Taylor number, resulted an enhancing in the axial pressure drop of the fluid but Darcy-Weisbach [Formula: see text] friction coefficient mainly reduced.

Electrohydrodynamic Instability of a Rotating Walters’ (model B’) Fluid in a Porous Medium: Brinkman model

In this study, the instability of Walters’ (model B’) viscoelastic fluid in a Darcy-Brinkman-Boussinesq system heated from below saturating a porous medium in electrohydrodynamics is considered. By applying the linear stability analysis and normal modes, the dispersion relation accounting for the effect of Prandtl number, electric Rayleigh number, Darcy number, Brinkman-Darcy number, Taylor number and kinematic viscoelasticity parameter is derived. The effects of electric Rayleigh number, Darcy number, Brinkman-Darcy number and Taylor number on the onset of stationary convection have been investigated both analytically and graphically.

Flow characteristics analysis of a two-phase suspension between rotating porous cylinders with radial and axial flows

The flow characteristics problem of the two-phase suspension in the design of filters is presented, and the hydrodynamic stability is carried out to study the flow characteristics of a two-phase suspension between a rotating porous inner cylinder and a concentric, stationary, porous outer cylinder when radial flow and axial flow are present. Linear stability analysis results in an eigenvalue problem that is solved numerically by Wan?s method. The results reveal that the critical Taylor number for the onset of instability is altered by other parameters. For given correlation parameters, increasing the axial Reynolds number increases the critical Taylor number for transition very slightly, the critical Taylor number decreases as the axial Reynolds number becomes negative.