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Mixed recirculatory flow in the annuli of stationary and rotating horizontal cylinders were studied numerically. A set of distorted ‘false transient’ parameters were introduced to speed up the steady state solution of the unsteady vorticity, energy and stream function—vorticity equations. The inner cylinder of the annuli is assumed heated and rotating at Reynolds numbers that exclude the effects of centrifugal acceleration and three‐dimensional Taylor vortices. The Prandtl number considered is in the range of 0.01 to 1.0 and Rayleigh number in the range of 10² to 10⁶. Radius ratios of the cylinders considered are 1.25, 2.5 and 5.0. For a radius ratio of 2.5, inner cylinder rotation in the Reynolds number range of 0 to 1120 was considered. Vertical eccentricities in the range of ±2/3 were studied for cases of the rotating inner cylinder. Numerical experiments show that the mean Nusselt number increases with Rayleigh number for both cases of concentric and eccentric stationary inner cylinder. At a Prandtl number of order 1.0 with a fixed Rayleigh number, when the inner cylinder is made to rotate, the mean Nusselt number decreases throughout the flow. At lower Prandtl number of the order 0.1 to 0.01, the mean Nusselt number remained fairly constant with respect to the rotational Reynolds number.

The effect of radiation on unsteady natural convection in a two‐dimensional participating medium between two horizontal concentric and vertically eccentric cylinders is investigated numerically. The equations of transfer are written by using a bicylindrical coordinates system, the stream function, and the vorticity. The finite volume radiation solution method and the control volume approach are used to discretize the coupled equations of radiative transfer, momentum, and energy. Original results are obtained for three eccentricities, Rayleigh number equal to 10⁴, 10⁵, and a wide range of radiation‐conduction parameter. The effects of optical thickness, wall emissivity, and scattering on flow intensity and heat transfer are discussed.

A numerical scheme is proposed to solve double‐diffusive problems using a boundary‐fitted coordinate system to introduce finer grids in the boundary layer regions and an accurate high‐order difference method. Numerical stability is improved by using fourth‐order accurate upwind‐biased differences to approximate the convection terms. The other terms in the governing differential equations are discretized using fourth‐order central difference. To demonstrate the versatility of the boundary‐fitted coordinate system, natural convection in an eccentric annulus is first simulated. The numerical results are consistent with the experimental results by Kuehn and Goldstein and better than the numerical results by Projahn et al. for eccentric cases. Secondly, the symmetry breaking and overturning states in thermohaline‐driven flows in a two‐dimensional rectangular cavity are simulated first to validate the numerical scheme. The numerical results agree well with those by Dijkstra and Molemaker and Quon and Ghil. Finally, the effect of the Lewis number on the flow system is investigated in detail. Depending on the value of the Lewis number, the flow pattern is either stable and symmetric, periodic and oscillatory, or unsymmetric and random.

The purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.

The discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.

It is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.

To the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.

This paper presents the hydrodynamic and thermal behavior of fluid that surrounds an isothermal circular cylinder in a square cavity. Simulations were carried out for four aspect ratios (defined by L/D), i.e. 2.0, 3.0, 4.0, 5.0. An incompressible flow of Newtonian fluid is considered. Prandtl number is assumed constant and equal to 1. Effect of eccentric positions (ε=−0.5 and 0.5) of the cylinder with respect to the cavity was carried out at L/D=2.0. Predicted results for eccentric cases are compared with concentric (ε=0.0) case. Grashof number is based on the diameter of the cylinder and ranges from 10 to 10⁶. The control volume based finite volume method is used to discretize the governing equations in cylindrical coordinate. SIMPLE algorithm is used. A collocated variable arrangement is considered and SIP solver is employed to solve the system of equations. Parametric results are presented in the form of streamlines and isothermal lines for both eccentric and concentric positions. Heat transfer distribution along the perimeter of the cylinder is presented in the form of local Nusselt number. Predicted results show good agreement with the results described by Cesini et al. (1999).

Studies numerically natural convection in a saturated porous medium bounded by two horizontal, isothermal eccentric cylinders by solving the governing two‐dimensional Darcy‐Boussinesq equations on a very fine grid for different values of the eccentricity ε. For a radius ratio of 2 and ε < 0.5, both a bicellular and a tetracellular flow patterns remain stable for moderate Rayleigh numbers. For ε ≥ 0.5, the transition from one flow regime to the other occurs with one of the solutions losing stability. Suggests that in a real situation, insulation is more efficient if the eccentricity is set to the maximum value for which the four‐cell flow pattern is physically realizable than to the value that minimizes the heat transfer when the flow pattern is bicellular. The net gain with respect to a concentric insulation can be of the order of 10 per cent.

The flow between eccentric rotating cylinders when either the outer or inner cylinder is stationary is analysed both for the creeping flow approximation and for the case when inertial effects are not negligible. Numerical solutions are obtained using a finite difference ADI scheme and a fine orthogonal bipolar coordinate grid. When the centres of the two cylinders are far enough, a two‐dimensional recirculation zone appears in the region where the gap spacing is greatest. On increasing the eccentricity, the recirculation zone becomes bigger and the separation and reattachment points move towards the region of narrowest gap. Further increase of the eccentricity results in the formation of a saddle point between the cylinders at the region of narrowest gap. As the Reynolds numbers increases, inertial effects modify slightly the recirculation region; the separation point moves upstream and the reattachment point moves downstream when either the inner or the outer cylinder rotate.

The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters.

The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders.

As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases.

The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal boundary conditions with one cylinder heated isothermally while the other cylinder is kept at the inlet fluid temperature.

A finite‐difference algorithm has been developed to solve the bipolar boundary‐layer equations for the conjugate laminar free convection heat transfer in vertical eccentric annuli.

Numerical results are presented for a fluid of Prandtl number, Pr=0.7 in eccentric annuli. The geometry parameters of NR₂ and E (the fluid‐annulus radius ratio and the eccentricity, respectively) have considerable effects on the results.

Applications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.

The paper presents results that are not available in the literature for the problem of conjugate laminar free convection in open‐ended vertical eccentric annular channels. Geometry effects having been investigated by considering fluid annuli having radii ratios NR₂=0.1 and 0.3, 0.5 and 0.7 and four values of the eccentricity E=0.1, 0.3, 0.5 and 0.7. Moreover, practical ranges of the solid‐fluid conductivity ratio (KR) and the wall thicknesses that are commonly available in pipe standards have been investigated. Such results are very much needed for design purposes of heat transfer equipment.

The purpose of this paper is to investigate the effect of narrow gap on the fluid flow and heat transfer through an eccentric annular region is numerically. Flow through an eccentric annular geometry is a model problem of practical interest.

The approach involves standard finite volume-based SIMPLE scheme. The numerical simulations cover the practically relevant Reynolds number range of 104-106.

In the narrow gap region, temperature shoot up was observed due to flow maldistribution with an attendant reduction in the heat removal from the wall surfaces. CFD analysis is presented with the aid of, streamlines, isotherms, axial velocity contours, etc. The engineering parameters of interest such as, Nusselt number, wall shear stress, etc., is presented to study the effect of eccentricity and radius ratio.

The present investigation is a simplified model for the rod bundle heat transfer studies. However, the detailed study of sectorial mass flux distribution is a useful precursor to the thermal hydraulics of rod bundles.

For nuclear reactor fuel rods, the effect of eccentricity is going to be detrimental and might lead to the condition of critical heat flux. A thorough sub-channel analysis is very useful.

Nuclear safety standards require answers to a wide a range of what-if type hypothetical scenarios to enable preparedness. This study is a highly simplified model and a first step in that direction.

The narrow gap region has been systematically investigated for the first time. A detailed sectorial analysis reveals that, flow maldistribution and the attendant temperature shoot up in the narrow gap region is detrimental to the safe operation.