Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder

In this work, the natural convection in a concentric annulus between a cold outer square cylinder and a heated inner circular cylinder is simulated using the differential quadrature (DQ) method. The vorticity‐stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation. It is shown in this paper that the outer square boundary can be approximated by a super elliptic function. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression, and all the geometrical parameters can be computed exactly. Numerical results for Rayleigh numbers range from 104 to 106 and aspect ratios between 1.67 and 5.0 are presented, which are in a good agreement with available data in the literature. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of flow and thermal fields. The present study suggests that a critical aspect ratio may exist at high Rayleigh number to distinguish the flow and thermal patterns. Copyright © 2002 John Wiley & Sons, Ltd.     

Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli

The influence of various Prandtl numbers on the laminar convection flow between concentric and vertically eccentric cylinders is studied numerically. To overcome the difficulties associated with the complex physical domains a numerical transformation method is used to map this region on a rectangle. Although two independent computer programs which are based on different formulations of the governing equations were used, nearly identical results were obtained. Local heat transfer results are presented for a wide range of Rayleigh numbers for the first time. Local heat transfer rates are found to depend on the Prandtl number in addition to the Rayleigh number dependence.     

Experimental investigation of natural convection heat transfer between two oblate concentric and eccentric hemi-spheroids with different elliptical ratios

In this paper, natural convection between a pair of oblate hemi-spheroids with different elliptical ratios was depicted experimentally. The experimental tests study the effects of the orientation modes (horizontal, inclined, vertical, inclined revolved and vertical revolved) as well as the vertical eccentricity on the natural convection between each pair. Correlations among Nusselt number, Rayleigh number, elliptical ratio and eccentricity were deduced. A notable increase in the natural convection could be satisfied through the gaps among successive layers of hemi-spheroids having higher elliptical ratio rather than hemi-spherical ones. The positive vertical eccentricity shows remarked increase in natural convection rather than both concentric and negative eccentric cases. Also, the inclination of the minor axis of hemi-spheroids while keeping the major axis parallel to the horizontal plane produces a stronger upward plume rather than different inclination modes.     

Experimental investigation of heat transfer and flow pattern from heated horizontal rectangular fin array under natural convection

This paper presents results of the experimental study conducted on heated horizontal rectangular fin array under natural convection. The temperature mapping and the prediction of the flow patterns over the fin array with variable fin spacing is carried out. Dimensionless fin spacing to height (S/H) ratio is varied from 0.05 to 0.3 and length to height ratio (L/H) = 5 is kept constant. The heater input to the fin array assembly is varied from 25 to 100 W. The single chimney flow pattern is observed from 8 to 12 mm fin spacing. The end flow is choked below 6 mm fin spacing. The single chimney flow pattern changes to sliding or end flow choking at 6 mm fin spacing. The average heat transfer coefficient (h_a) is very small (2.52–5.78 W/m² K) at 100 W for S = 5–12 mm. The h_a is very small (1.12–1.8 W/m² K) at 100 W for 2–4 mm fin spacing due to choked fin array end condition. The end flow is not sufficient to reach up to central portion of fin array and in the middle portion there is an unsteady down and up flow pattern resulting in sliding chimney. The central bottom portion of fin array channel does not contribute much in heat dissipation for S = 2–4 mm. The h_a has significantly improved at higher spacing as compared to lower spacing region. The single chimney flow pattern is preferred from heat transfer point of view. The optimum spacing is confirmed in the range of 8–10 mm. The average heat transfer results are compared with previous literature and showed similar trend and satisfactory agreement. An empirical equation has been proposed to correlate the average Nusselt number as a function of Grashof number and fin spacing to height ratio. The average error for this equation is ?0.32 %.     

Natural convection heat transfer from a long heated vertical cylinder to an adjacent air gap of concentric and eccentric conditions

In this work, the natural convection heat transfer from a long vertical electrically heated cylinder to an adjacent air gap is experimentally studied. The aspect and diameter ratios of the cylinder are 55.56 and 6.33, respectively. The experimental measurements were obtained for a concentric condition and six eccentricities from 0.1 to 0.92 at five different heat fluxes. The surface temperature of the heated rod is measured at different heights, and the Nusselt number is calculated at the temperature measurement locations. A correlation is suggested to determine the Nusselt number based on the variation of the eccentric ratio values. The experimental results show a good agreement with other studies.     

A numerical simulation of combined radiation and natural convection heat transfer in a square enclosure heated by a centric circular cylinder

A numerical simulation of combined natural convection and radiation in a square enclosure heated by a centric circular cylinder and filled with absorbing-emitting medium is presented. The ideal gas law and the discrete ordinates method are used to model the density changes due to temperature differences and the radiation heat transfer correspondingly. The influence of Rayleigh number, optical thickness and temperature difference on flow and temperature fields along with the natural convection, radiation and total Nusselt number at the source surfaces is studied. The results reveal that the radiation heat transfer as well as the optical thickness of the fluid has a distinct effect on the fluid flow phenomena, especially at high Rayleigh number. The heat transfer and so the Nusselt number decreases with increase in optical thickness, while increases greatly with increase in temperature difference. The variation in radiation heat transfer with optical thickness and temperature difference is much more obvious as comparison with convection heat transfer.     

Conjugate natural convection between horizontal concentric cylinders filled with a porous medium

A conjugate problem of natural convection between two horizontal concentric, isothermal cylinders filled with a fluid-saturated porous medium is studied. The flow field and energy equations are solved under the conditions of equality in temperature but with jump in heat flux at the fluid-solid interface. Numerical results by a finite-difference technique are presented for a large variation in the parameters entering the problem. A comparison of the solution with non-conjugate problem is also given.Das konjugierte Problem der freien Konvektion zwischen zwei horizontalen, konzentrischen, isothermen Zylindern, die mit einem fluid-gesättigten porösen Medium gefüllt sind, wurde hier untersucht.Das Strömungsfeld und die Energiegleichung sind unter den Bedingungen gelöst worden, daß die Temperatur gleich ist, aber ein Wärmeflußsprung am Übergang von der Flüssigkeits- zur Festphase stattfindet. Die numerischen Ergebnisse werden mit dem Finite-Differenzen-Verfahren für viele Parametervariationen dargestellt. Zudem wurde ein Lösungsvergleich mit einem nicht konjugierten Problem gegeben.     

Visualization of natural convection heat transfer on horizontal cylinders

Natural convection heat transfer phenomena on horizontal cylinders were investigated experimentally in order to explore the applicability of analogy experimental method using the copper electroplating system and to visualize the local heat transfer depending on the angular position and the diameter of the horizontal cylinder. The diameters of the cylinders are varied from 0.01 to 0.15 m, which correspond to the Rayleigh numbers of 1.73 × 10⁷–5.69 × 10¹¹. The measured mass transfer coefficients show good agreements with the existing heat transfer correlations. The patterns of copper plated on the aluminum cathodes for various Rayleigh numbers reveal and visualize the local heat transfer depending on the angular position and show good agreement with the works of Kitamura et al. The hydrogen bubbles produced at higher applied potential visualize the plumes appeared on top region of the cylinders.     

Conjugate natural convection heat transfer between two fluids separated by a horizontal wall: steady-state analysis

The conjugate heat transfer across a thin horizontal wall separating two fluids at different temperatures is investigated both numerically and asymptotically. The solution for large Rayleigh numbers is shown to depend on two nondimensional parameters;α/ε ², withα being the ratio of the thermal resistance of the boundary layer in the hot medium to the thermal resistance of the wall andε the aspect ratio of the plate, andβ, the ratio of the thermal resistances of the boundary layers in the two media. The overall Nusselt number is an increasing function ofα/ε ² taking a finite maximum value forα/ε ² → ∞ and tending to zero forα/ε ² → 0.     

Experimental investigation of natural convection heat transfer in horizontal and inclined annular fluid layers

In the present study, an experimental investigation of heat transfer and fluid flow characteristics of buoyancy-driven flow in horizontal and inclined annuli bounded by concentric tubes has been carried out. The annulus inner surface is maintained at high temperature by applying heat flux to the inner tube while the annulus outer surface is maintained at low temperature by circulating cooling water at high mass flow rate around the outer tube. The experiments were carried out at a wide range of Rayleigh number (5 × 10⁴ < Ra < 5 × 10⁵) for different annulus gap widths (L/D _o = 0.23, 0.3, and 0.37) and different inclination of the annulus (α = 0°, 30° and 60°). The results showed that: (1) increasing the annulus gap width strongly increases the heat transfer rate, (2) the heat transfer rate slightly decreases with increasing the inclination of the annulus from the horizontal, and (3) increasing Ra increases the heat transfer rate for any L/D _o and at any inclination. Correlations of the heat transfer enhancement due to buoyancy driven flow in an annulus has been developed in terms of Ra, L/D _o and α. The prediction of the correlation has been compared with the present and previous data and fair agreement was found.     

Adverse and favorable mixed convection heat transfer in a two-side heated square channel

Experimental heat transfer measurements and analysis for mixed convection in a vertical square channel are presented. Water flow directions are selected such that buoyancy assists or opposes the bulk flow pressure gradient. Unlike most previous experiments with symmetrically heated circular tubes, the present configuration uses an asymmetric heating condition (two sides heated and two sides insulated) and shows significant increase in the Nusselt number for both assisted and opposed flow conditions. Observed heat transfer coefficient distributions are different from the symmetrically heated channels; and this difference in heat transfer coefficient is attributed to the formation of buoyancy driven large-scale flow structures. In general, opposed flow shows higher heat transfer coefficients, and the Nusselt number ratio is observed to increase as Gr/Re or Gr/Re² ratios increase for both assisted and opposed flow conditions. A correlation based on the buoyancy parameter predicts the heat transfer pattern well in both assisted and opposed mixed convection. The range of Reynolds numbers discussed (Re=400–10,000) is of importance for direct numerical simulations and the details provided here can serve as the benchmark data required for complicated buoyancy affected turbulence simulations.     

Laminar fluid convection between concentric and eccentric heated horizontal rotating cylinders for low-Prandtl-number fluids

Numerical experiments are performed to study rotational effects on the mixed convection of low-Prandtlnumber fluids enclosed between the annuli of concentric and eccentric horizontal cylinders. The inner cylinder is assumed to be heated and rotating. The rotational Reynolds number considered is in the range where the effect of Taylor vortices is negligible. The Prandtl number of the fluid considered is in the range 0·01–1·0. The Rayleigh number considered is up to 10⁶. A non-uniform mesh transformation technique coupled with the introduction of ‘false transient’ parameters to the vorticity and streamfunction-vorticity expressions was used to solve the governing set of equations. Results show that when the inner cylinder is made to rotate, the multicellular flow patterns observed in stationary cylindrical annuli subside in a manner depending on the Prandtl number of the fluids. Eventually the flow tends toward a uniform flow similar to that of a solid body rotation. For a fixed Rayleigh number and with a Prandtl number of the order of 1·0, when the inner cylinder is made to rotate, the mean Nusselt number is observed to decrease throughout the flow. For lower Prandtl number of the order 0·1–0·01 the mean Nusselt number remained fairly constant when the inner cylinder was made to rotate. The mean Nusselt numbers obtained were also compared with available data from other investigators.     

Computation of conjugate natural convection heat transfer from a rectangular fin on a partially heated horizontal base

In this study, a numerical investigation has been carried out to reveal the mechanism of fluid flow and heat transfer from a vertical rectangular fin attached to a partially heated horizontal base. The problem is a conjugate conduction-convection heat transfer problem with open boundaries. The governing equations for the problem are the conservation of mass, momentum and energy equations for the fluid and the heat conduction equation for the fin. The control volume technique based on the SIMPLEC algorithm with a nonstaggerred grid arrangement is employed to solve the governing equations. The effect of the heated base, on the mechanism of the fluid flow and heat transfer, is numerically investigated. Temperature distribution and flow patterns around the fin are plotted to support the discussion. Results are obtained for air at laminar and steady flow. Received on 15 May 1997     

Laminar natural convection of Cu-water nanofluid in concentric annuli with radial fins attached to the inner cylinder

Laminar natural convection of Cu-water nano-fluid between two horizontal concentric cylinders with radial fins attached to the inner cylinder is studied numerically. The inner and outer cylinders are maintained at constant temperature. The governing equations in the polar two-dimensional space with the respective boundary conditions are solved using the finite volume method. The hybrid-scheme is used to discretize the convection terms. In order to couple the velocity field and the pressure in the momentum equations, the well known semi-implicit method for pressure linked equation reformed algorithm is adopted. Using the developed code, a parametric study is undertaken, and the effects of the Rayleigh number, Number of fins, length of the fins and the volume fraction of nano-particles on the fluid flow and heat transfer inside the annuli are investigated. In this study, two cases with different number of fins are considered. It is observed from the results that the average Nusselt number increases with increasing both the Rayleigh number and the volume fraction of the nano-particles. Moreover, the average Nusselt number decreases by increasing the fins’ length and the number of fins. Heat transfer rate increases by increasing the fins’ length at all Rayleigh numbers, but it increases by increasing the number of fins at high Rayleigh numbers.     

最大偏心圆环空间自然对流传热的数值分析

采用正切圆坐标变换 ,对不同直径比以及上、下、侧面三种偏心位置 ,偏心率达到最大值± 1的变壁温水平圆柱环形封闭空间内空气的自然对流传热进行了数学模拟 ,求出的二维空间温度分布与实验拍摄相应的温度干涉条纹图片吻合良好。计算结果同时给出流线分布及内、外壁面的局部传热系数、热流量。并与现有的偏心率小于 1的有关资料作对比分析。数值计算的范围是 :2 .0× 1 0 2 ≤ Ra≤ 3 .0× 1 0 5,1 .3≤ Do/Di≤ 3 .8,Pr=0 .70 6,|ε|=1 .     

Experimental study of steady and transient natural convection heat transfer of mercury

An experimental investigation of transient and steady-state natural convection in a narrow vertical rectangular channel following a step-change in uniform wall-heat-flux is presented. The construction and instrumentation for two test sections are described. These test sections formed a rectangular channel 15.2×2.54×25.4 cm and consisted of: 1) both 15.2×25.4 cm faces heated uniformly by constant radiant heat flux with mercury as the fluid, and 2) the same boundary conditions as 1 but lead was used to thermally model the mercury. Initially the fluid was stagnant and at a uniform temperature. The transient was initiated by suddenly increasing the wall-heat-flux from zero to some constant, preselected value using radiant heating. Temperature-time histories were measured during the transient and steady-state regimes at several locations on the wall and in the fluid. Transient and steady-state heat transfer results are reported. The results show that when the wall-heat-flux on both faces is sufficiently large, the primary mechanism for energy transport in the fluid is molecular conduction. For lower values of imposed heat flux, natural convection, as well as conduction, contributed to the energy transfer.     

A numerical and experimental study of natural convective heat transfer from an inclined isothermal square cylinder with an exposed top surface

Natural convective heat transfer from an isothermal inclined cylinder with a square cross-section which have an exposed top surface and is, in general, inclined at an angle to the vertical has been numerically and experimentally studied. The cylinder is mounted on a flat adiabatic base plate, the cylinder being normal to the base plate. The numerical solution has been obtained by solving the dimensionless governing equations subject to the boundary conditions using the commercial cfd solver, FLUENT. The flow has been assumed to be symmetrical about the vertical center-plane through the cylinder. Results have only been obtained for Prandtl number of 0.7. Values of inclination angle between 0° and 180° and a wide range of Rayleigh number and the dimensionless cylinder width, W = w/h, have been considered. The effects of Dimensionless widths, Rayleigh numbers, and inclination angles on the mean Nusselt number for the entire cylinder and for the mean Nusselt numbers for the various surfaces that make up the cylinder have been examined. Empirical equations for the heat transfer rates from the entire cylinder have been derived.     

Free convection heat transfer from a horizontal fin attached cylinder between confined nearly adiabatic walls

Steady state two-dimensional free convection heat transfer from a horizontal, isothermal fin attached cylinder, located between nearly two adiabatic walls is studied experimentally using a Mach–Zehnder interferometer. Effects of the walls inclination angel (θ) on heat transfer from the cylinder is investigated for Rayleigh number ranging from 1000 to 15,500. Two cylinders with different diameters of D = 10 and 20 mm are used to cover wide Rayleigh range. Results indicate that, heat transfer phenomena differ for different Rayleigh number. For Rayleigh numbers lower than 5500, heat transfer rate from cylinder surface is lower than the heat transfer from a single cylinder. In this range by the use of walls, heat transfer from the cylinder decreases slightly and walls’ inclination does not change heat transfer rate from the cylinder surface. For Rayleigh number ranging from 5500 to 15,500, amount of heat transfer from the cylinder surface is less than that of a single cylinder. However, by adding nearly adiabatic walls to experimental model heat transfer mechanism differs and chimney effect between fin and walls increases the heat transfer rate from the cylinder surface. By increasing the walls inclination angel from 0° to 20°, the chimney effect between walls and fin diminishes and heat transfer rate from the cylinder surface is approaching to the heat transfer rate of fin attached cylinder without adiabatic walls.     

Direct contact heat transfer between two immiscible liquids flowing in a horizontal concentric annulus

Direct contact heat transfer between water and a heat transfer oil was investigated under non-boiling conditions in co-current turbulent flow through a horizontal concentric annulus. The ratio of the inner pipe diameter to the outer pipe diameter (aspect ratio) κ = 0.730−0.816; total liquid velocity (mixture velocity) V_T = 0.42−1.1 m/s; inlet oil temperature T_oi = 38−94°C; oil volume fraction in the flowing mixture φ_o = 0.25−0.75 were varied and their effects on the overall volumetric heat transfer coefficient U_v were determined at constant interfacial tension of 48 dynes/cm.

It was found that, in each concentric pipe set, the overall volumetric heat transfer coefficient increased with increasing dispersed phase volume fraction at each constant mixture velocity and reached a maximum at around φ_o = φ_w ≈ 0.5. The maximum U_v values increased with increasing total liquid velocity and decreasing aspect ratio of the annulus. The volumetric heat transfer coefficient was also found to increase with increasing inlet oil temperature and increasing total liquid velocity but to decrease with length along the test section keeping all other parameters constant. Empirical expressions for the volumetric heat transfer coefficient were obtained within the ranges of the experimental parameters.     

Experimental study on turbulent natural convection heat transfer in water with sub-millimeter-bubble injection

Using thermocouples and a particle tracking velocimetry technique, temperature and velocity measurements are conducted to investigate flow and heat transfer characteristics of turbulent natural convection from a vertical heated plate in water with sub-millimeter-bubble injection. Hydrogen-bubbles generated by the electrolysis of water are used as the sub-millimeter-bubbles. In the turbulent region, the heat transfer deterioration occurs for a bubble flow rate Q = 33 mm³/s, while the heat transfer enhancement occurs for Q = 56 mm³/s. Temperature and velocity measurements suggest that the former is caused by a delay of the transition due to the bubble-induced upward flow. On the other hand, the latter is mainly due to two factors: one is the enhancement of the rotation of eddies in the outer layer, and the other is the increase in the gradient of the streamwise liquid velocity at the heated wall. These are caused by bubbles, which are located in the inner layer, rising at high speed.