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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).

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.

The purpose of this paper is to investigate the effects of geometrical parameters, eccentricity and perforated fins on natural convection heat transfer in a finned horizontal annulus using three-dimensional lattice Boltzmann flux solver.

Three-dimensional lattice Boltzmann flux solver is used in the present study for simulating conjugate heat transfer within an annulus. D3Q15 and D3Q7 models are used to solve the fluid flow and temperature field, respectively. The finite volume method is used to discretize mass, momentum and energy equations. The Chapman–Enskog expansion analysis is used to establish the connection between the lattice Boltzmann equation local solution and macroscopic fluxes. To improve the accuracy of the lattice Boltzmann method for curved boundaries, lattice Boltzmann equation local solution at each cell interface is considered to be independent of each other.

It is found that the maximum heat transfer rate occurs at low fin spacing especially by increasing the fin height and decreasing the internal-cylindrical distance. The effect of inner cylinder eccentricity is not much considerable (up to 5.2% enhancement) while the impact of fin eccentricity is more remarkable. Negative fin eccentricity further enhances the heat transfer rate compared to a positive fin eccentricity and the maximum heat transfer enhancement of 91.7% is obtained. The influence of using perforated fins is more considerable at low fin spacing although some heat transfer enhancements are observed at higher fin spacing.

The originality of this paper is to study three-dimensional natural convection in a finned-horizontal annulus using three-dimensional lattice Boltzmann flux solver, as well as to apply symmetry and periodic boundary conditions and to analyze the effect of eccentric annular fins (for the first time for air) and perforated annular fins (for the first time so far) on the heat transfer rate.

Conjugate laminar forced convection heat transfer in the entry region of eccentric annuli is numerically investigated. Heat transfer parameters are presented for a fluid of Pr = 0.7 flowing in an annulus of radius ratio 0.5 for four values of dimensionless eccentricity ranging from 0.1 to 0.7. Solid‐fluid conductivity ratio (KR) is varied to cover the range for practical cases with commonly encountered inner and outer tube thickness. Boundary conditions applied are isothermal heating of the inner surface of the core tube, while the outer surface of the external tube is maintained at the inlet fluid temperature. Limits for KR above which the conjugation can be neglected are obtained.

The paper utilizes a boundary‐layer model in bipolar coordinates to study the developing laminar free convection in vertical open‐ended eccentric annuli with one of the boundaries uniformly heated while the other boundary is cooled and kept isothermal at the ambient temperature. This model has been solved numerically using finite‐difference techniques. Results not available in the literature are presented for a fluid of Prandtl number 0.7 in an annulus of radius ratio 0.5 for three values of the dimensionless eccentricity, namely, 0.1, 0.5 and 0.7. These results include the developing velocity profiles and the pressure along the annulus, the channel heights required to naturally induce different flow rates and the variation of the total heat absorbed by the fluid with the channel height.

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 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.

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 work is to highlight the effects of partial unipolar injection on electro-thermo-convection (ETC) in dielectric liquid contained between two eccentric cylinders.

A finite volume method was used to solve governing equations. The study is performed for different parameters, such as radius ratio (0.2 ≤ Γ ≤ 0.6), dimensionless electric Rayleigh number (0 ≤ T ≤ 900), eccentricity (−0.4 ≤ e ≤ 0.4) and thermal Rayleigh number (10 ≤ Ra ≤ 5.105).

It is found that heat transfer increases with increase in dimensionless electric Rayleigh number and eccentricity ratio.

The originality of this work is to analyze the ETC in dielectric liquid subjected to partial unipolar injection between two eccentric cylinders

The purpose of this paper is to numerically study the double-diffusive natural convection within an eccentric horizontal cylindrical annulus filled with a Newtonian fluid. The annulus walls are maintained at uniform temperatures and concentrations so as to induce aiding thermal and mass buoyancy forces within the fluid. For that, this simulation span a moderate range of thermal Rayleigh number (100Ra_T100,000), Lewis (0.1Le10), buoyancy ratio (0N5) and Prandtl number (Pr=0.71) to examine their effects on flow motion and heat and mass transfers.

A finite volume method in conjunction with the successive under-relaxation algorithm has been developed to solve the bipolar equations. These are written in dimensionless form in terms of vorticity, stream function, temperature and concentration. Beforehand, the implemented computer code has been validated through already published findings in the literature. The isotherms, streamlines and iso-concentrations are exhibited for various values of Rayleigh and Lewis numbers, and buoyancy ratio. In addition, heat and mass transfer rates in the annulus are translated in terms of Nusslet and Sherwood numbers along the enclosure’s sides.

It is observed that, for the range of parameters considered here, the results show that the average Sherwood number increases with, while the average Nusselt number slightly dips as the Lewis number increases. It is also found that, under the convective mode, the local Nusselt number (or Sherwood) increases with the buoyancy ratio. Likewise, according to Lewis number’s value, the flow pattern is either symmetric and stable or asymmetric and random. Besides that, the heat transfer is transiting from a conductive mode to a convective mode with increasing the thermal Rayleigh number, and the flow structure and the rates of heat and mass transfer are significantly influenced by this parameter.

The range of the Rayleigh number considered here covers only the laminar case, with some constant parameters, namely the Prandtl number (Pr = 0.71), and the tilt angle (α=90°). The analysis here is only valid for steady, two-dimensional, laminar and aiding flow within an eccentric horizontal cylindrical annulus. This motivates further investigations involving other relevant parameters as N (opposite flows), Ra, Pr, Le, the eccentricity, the tilt angle, etc.

An original framework for handling the double-diffusive natural convection within annuli is available, based on the bipolar equations. In addition, the achievement of this work could help researchers design thermal systems supported by annulus passages. Applications of the results can be of value in various arrangements such as storage of liquefied gases, electronic cable cooling systems, nuclear reactors, underground disposal of nuclear wastes, manifolds of solar energy collectors, etc.

Given the geometry concerned, the bipolar coordinates have been used to set the inner and outer walls boundary conditions properly without interpolation. In addition, since studies on double-diffusive natural convection in annuli are lacking, the obtained results may be of interest to handle other configurations (e.g., elliptical-shaped speakers) with other boundary conditions.