Experimental study on heat and fluid flow in LNG tank heated from the bottom and the sidewalls

Heat and fluid flow in a layer heated from the bottom and the sidewalls simulating an underground LNG tank is experimentally studied under high Rayleigh number (7.5×10¹⁰<Ra<1.5×10¹³) conditions by electrochemical mass transfer technique. The experiment yielded the following results. When sidewalls are heated, the heat transfer along the bottom surface is reduced. Heat transfer along sidewalls is independent of bottom heating, and is modeled by an equation for laminar natural convection flow even for Ra>10⁹. Convective flow pattern in the tank is visualized by the Schlieren technique. The results, combined with local mass transfer measurement, show that Sh of the bottom surface is reduced in the area where impinging downward flow exists. It is caused by the suppression of thermal plume formation by the downward flow. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 417–430, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20031     

Fluid flow and heat transfer of opposing mixed convection adjacent to upward‐facing,inclined heated plates

Opposing mixed convective flows of air induced over uniformly heated, upward‐facing, inclined plates were investigated experimentally. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers, Re_L=7.2×10² to 1×10⁴ and Ra_L^*=5×10⁶ to 8×10⁸, and the inclination angles from θ=15 to 75^° from horizontal. The flow fields over plates were visualized with smoke. The results showed that a separation of forced boundary layer flow occurs first at the trailing edge, and then the separation point shifts toward upstream with increasing the wall heat flux, and finally, reaches to the leading edge of the plates. It was also found that the separations at the trailing and leading edges are correlated well with the non‐dimensional parameter as (Gr_θ^*/Re_L^2.5)=0.35 and 1.0, respectively. The local heat transfer coefficients of the inclined plates were also measured and the results showed that the above separation retards the heat transfer significantly from that of the forced convection. It was also revealed that the heat transfer by forced, natural, and combined convections can be classified with the above parameter as (Gr_θ^*/Re_L^2.5)<0.2,(Gr_θ^*)/Re_L^2.5)>3, and 0.2<(Gr_θ^*/Re_L^2.5)<3, respectively. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(3): 127– 142, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20151     

Investigation of natural convection in convergent vertical channels

Using air as the working fluid, natural convection heat transfer in a uniform wall temperature convergent vertical channel has been investigated numerically. The investigation encompassed half angles of convergence between 0° (parallel-walled channel) and 10° and the solutions were performed for (S/L) Ra_s range of 1 to 2 × 10⁴. In order to find a correlation format which will merge the convergent channel results for low Rayleigh number ranges (Ra′ < 10²) with those for the parallel-walled channel ones, the minimum (S_min), mean (S_avg), and maximum (S_max) interval spacing between channel walls were used as characteristic dimensions. It was found that merging was best achieved by the use of maximum interval spacing (S_max) as the characteristic dimension. These numerical findings agree with those for high Rayleigh number ranges (RA′ > 10²) reported in the literature.     

An Experimental and Numerical Study of Natural Convection Heat Transfer in Horizontal Annuli between Eccentric Cylinders

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Heatlines based natural convection analysis in tilted isosceles triangular enclosures with linearly heated inclined walls: effect of various orientations

Natural convection in isosceles triangular enclosures with various configurations (case 1 — inverted, case 2 — straight and case 3 — tilted) is studied via heatline analysis for linear heating of inclined walls. Detailed analysis and comparison for various base angles (φ = 45°, 60°) of triangular enclosures have been carried out for a range of fluids (Pr = 0.015 − 1000) within Ra = 10³ − 10⁵ using Galerkin finite element method. The heat flow distributions indicate conduction dominant heat transfer at low Ra (Ra = 10³) for case 1 and case 2 whereas in case 3, convective heat flow is observed due to high buoyancy force. As Ra increases, enhanced thermal mixing is observed at the core of the cavity. Wall to wall heat transfer occurs at walls AB and AC due to linear heating boundary condition in all the cases. Although the distributions of fluid flow and heat flow are qualitatively similar for φ = 45° and 60°, the intensity of fluid flow and heat flow decreases as φ increases. Strength of fluid flow and heat flow circulation cells is found to be higher in case 3 for identical parameters. Results show that upper side wall (AC) for case 3 exhibits higher heat transfer rates whereas heat transfer rates for walls AB and AC are the same for case 1 and case 2. Also Nu_AB is higher for case 2 followed by case 1 and case 3 at the middle portion of wall AB. Thus to achieve high heat transfer from fluid to wall at the central region, case 2 and case 3 configurations may be recommended at high Ra (Ra = 10⁵) and Pr, irrespective of φ.     

Non-Darcy effects in buoyancy driven flows in an enclosure filled with vertically layered porous media

Natural convection in an enclosure filled with two layers of porous media is investigated numerically. Constant heat flux is imposed on the left vertical wall and the right wall is assumed to be at a low temperature. The focus of the work is on the validity of the Darcy model when various combinations of fluid Rayleigh number, Darcy number and permeability ratios are considered for fixed values of the modified Rayleigh numbers. It is found that the boundary effects (Brinkman term) have significant importance at higher modified Rayleigh numbers (Rayleigh number based on permeability, Ra_m). Calculations are performed for a modified Rayleigh number up to 10⁵. The results showed that, for the investigated range of parameters, the flow structure and heat transfer could be different than what Darcy model predicts. Two circulations are predicted for Ra_f=1×10⁸, for two different cases, Da=1×10⁻³, K_r=1000 and Da=1×10⁻⁴, K_r=100 (K_r=K₁/K₂). For K_r>1, increasing permeability ratio decreases flow penetration from layer 1 to layer 2 while reverse is true for K_r<1. For low Ra_m (Ra_m?10³) and K_r=1000, the heat transfer is conductive in the right layer, while this is true for the left layer for K_r=0.001. It is possible to obtain no-slip velocity boundary conditions both at the walls and at the interface between the porous layers even for very low permeability.     

Heat transfer enhancement for combined convection flow of nanofluids in a vertical rectangular duct considering radiation effects

In this paper, combined convective heat transfer and nanofluids flow characteristics in a vertical rectangular duct are numerically investigated. This investigation covers Rayleigh numbers in the range of 2 × 10⁶ ≤ Ra ≤ 2 × 10⁷ and Reynolds numbers in the range of 200 ≤ Re ≤ 1000. Pure water and five different types of nanofluids such as Ag, Au, CuO, diamond, and SiO₂ with a volume fraction range of 0.5% ≤ φ ≤ 3% are used. The three‐dimensional steady, laminar flow, and heat transfer governing equations are solved using finite volume method (FVM). The effects of Rayleigh number, Reynolds number, nanofluids type, nanoparticle volume fraction of nano‐ fluids, and effect of radiation on the thermal and flow fields are examined. It is found that the heat transfer is enhanced using nanofluids by 47% when compared with water. The Nusselt number increases as the Reynolds number and Rayleigh number increase and aspect ratio decreases. A SiO₂ nanofluid has the highest Nusselt number and highest wall shear stress while the Au nanofluid has the lowest Nusselt number and lowest wall shear stress. The results also revealed that the wall shear stress increases as Reynolds number increases, aspect ratio decreases, and nanoparticle volume fraction increases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20354     

Natural convection in a triangular cavity filled with air under the effect of external air stream cooling

Natural convection in a triangular cavity filled with air is investigated numerically. In this paper, the cavity is exposed to air stream cooling exerted on its sides and it is heated by a fixed heat flux from the base. The air inside the cavity is assumed to be laminar and obeying Boussinesq approximation. The governing equations are solved numerically using the finite volume technique with SIMPLE algorithm. The results are achieved with a range of Rayleigh number (10⁴ < Ra < 10⁷), free stream Reynolds number (10³ < Re_∞ < 1.5 × 10⁴), four aspect ratios (AR = 0.25, 0.5, 0.866, and 1) and five inclination angles (? = 0°, 30°, 45°, 60°, 90°). The influence of these parameters is displayed on the stream function, isotherms lines, local and average Nusselt numbers. The results reveal that the heat transfer rate increases as Rayleigh number, free stream Reynolds number and AR increase. The highest heat transfer rate is obtained at ? = 0° while the lowest one is obtained at ? = 90°. Furthermore, as the AR augments, the local and average Nusselt numbers are enhanced and the stream function is formed of two symmetric counter‐rotating vortices.     

Fluid flow and heat transfer of natural convection around large horizontal cylinders: Experiments with air

Natural convective flows of air around large horizontal cylinders were investigated experimentally. The main concerns were the turbulent transition mechanisms and the heat transfer characteristics of turbulent flows. The cylinders were heated with uniform heat flux and their diameters were varied from 200 to 1200 mm to enable experiments over a wide range of modified Rayleigh numbers, Ra_D^* = 1.0 × 10⁸ to 5.5 × 10¹¹. The flow fields around the cylinders were visualized with smoke to investigate the turbulent transition mechanisms. The results show that three‐dimensional flow separations occur first at the trailing edge of the cylinder when Ra_D^* exceeds 3.5 × 10⁹, and the separation points shift upstream with increasing Rayleigh numbers. These separations become a trigger to the turbulent transition and transitional and turbulent flows appear downstream of the separations at higher Rayleigh numbers. However, they occupy a relatively small portion of the cylinder surfaces even at the maximum Rayleigh numbers of the present experiments. The local heat transfer coefficients were also measured. The results show that the coefficients are increased significantly in the transitional and turbulent regions compared with the laminar coefficients. Moreover, the present results for air were compared with previous results for water and the effects of Prandtl number on the flow and heat transfer were discussed. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 293–305, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10080     

Simulation of turbulent natural convection in a porous cylindrical annulus using a macroscopic two-equation model

This work presents numerical computations for laminar and turbulent natural convection within a horizontal cylindrical annulus filled with a fluid saturated porous medium. Computations covered the range 25 < Ra_m < 500 and 3.2 × 10⁻⁴ > Da > 3.2 × 10⁻⁶ and made use of the finite volume method. The inner and outer walls are maintained at constant but different temperatures. The macroscopic k–ε turbulence model with wall function is used to handle turbulent flows in porous media. First, the turbulence model is switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra_m. Subsequently, the turbulence model is included and calculations start at high Ra_m, merging to the laminar branch for a reducing Ra_m. This convergence of results as Ra_m decreases can be seen as an estimate of the so-called laminarization phenomenon. Here, a critical Rayleigh number was not identified and results indicated that when the porosity, Prandtl number, conductivity ratio between the fluid and the solid matrix and Ra_m are kept fixed, the lower the Darcy number, the higher is the difference of the average Nusselt number given by the laminar and turbulent models.     

Heat transfer of combined forced and natural convection from horizontal cylinder to air

Experimental investigations have been carried out for combined convective flows of air induced around uniformly heated, horizontal cylinders. Three cases of aiding, opposing, and cross flows were examined. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers of Re_d=50 to 900 and Ra_d^*=5×10⁴ to 3×10⁶. The flow fields around the cylinders were visualized with smoke. The results showed that separation points gradually shift from those of the forced convection to the top edge of the cylinder with increasing wall heat fluxes. The local heat transfer coefficients of the cylinders were also measured. Although the local coefficients show complex variations with the forced flow velocities and the wall heat fluxes, the overall coefficients become higher than those estimated from pure forced and natural convections throughout the cases of aiding, opposing, and cross flows. Moreover, it was confirmed that the overall Nusselt numbers as well as the separation points can be predicted with the non‐dimensional parameter (Gr_d^*/Nu_dRe_d²). © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 474–488, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20180     

MAXIMAL HEAT TRANSFER DENSITY IN VERTICAL MORPHING CHANNELS WITH NATURAL CONVECTION

In this article we show numerically that the entire flow geometry of a vertical diverging or converging channel with laminar natural convection can be optimized for maximal heat transfer rate density (total heat transfer rate per unit of flow system volume). The geometry is free to change in three ways: (1) the spacing between the walls, (2) the distribution of heating along the walls, and (3) the angle between the two walls. Numerical simulations cover the Rayleigh number range 10⁵ ≤ Ra_H ≤ 10⁷, where H is the channel height. Nonuniform wall heating is modeled as an isothermal patch of varying height H ₀ (≤H) on each wall, which is placed either at the bottom (entrance) end of the channel, or at the top (exit) end. The results confirm that the use of upper unheated sections enhances the chimney effect and the heat transfer. The new aspect is that the heat transfer rate density decreases because the unheated sections increase the total volume. It is shown that for maximal heat transfer rate density it is better to place the H ₀ sections at the channel entrance. It is also shown that the optimal angle between the two walls is approximately zero when Ra _H is large, i.e., for maximal heat transfer rate density the walls should be parallel or nearly parallel. Finally, the optimized spacing (1) developed in the presence of (2) and (3) as additional degrees of freedom is of the same order of magnitude as the optimal spacing reported earlier for parallel isothermal walls, i.e., in the absence of features (2) and (3). The robustness of the optimized flow architecture is discussed. Additional degrees of freedom and global objectives that may be incorporated in this constructal approach are the curvature of the facing walls and the mechanical strength and stiffness of the confining walls.     

Natural convection slip flow in a vertical microchannel heated at uniform heat flux

Numerical solutions for steady state developing natural convection flow in air, in vertical parallel-plate microchannels are accomplished. An asymmetric heating is considered and the walls are assumed to be at uniform heat flux. A first-order model is used for slip and jump boundary conditions and an analytical solution for the fully developed flow is also given. Results are performed for air, for the heat flux ratio in the 0.0–1.0 range, for Rayleigh, Ra, and Knudsen, Kn, numbers from 10^?1 to 8 × 10³ and from 0.0 to 0.10, respectively. The maximum mass flow rate is always obtained for the highest considered Kn value, whereas the average Nusselt number, Nu, increases for lower Ra (<10) and decreases for Ra > 100. Wall temperature profiles have the lowest values for highest considered Kn value at lower Ra, whereas for the developing flow, they present opposite trends. For developing flow, velocity profiles for asymmetric and symmetric heating are completely different. In developing flow velocity profiles along the wall present the highest increases for asymmetric heating and the highest considered Kn value.     

Experimental study of natural convection heat transfer in a semicircular enclosure

An experimental study of natural convection heat transfer in a differentially heated semicircular enclosure was carried out. The flat surface was heated and the radial surface was cooled isothermally. The effects of angle of enclosure inclination on the heat transfer across semicircular regions of several radii were measured for Rayleigh numbers Ra_R ranging from 6.72 × 10⁶ to 2.33 × 10⁸, using water as the working fluid. The angle of inclination varied from −90 degrees to 90 degrees with radii R of 50, 40, and 30 mm. The flow patterns were sketched from the results of a visualization experiment using aluminum powder. The temperature measurements in the enclosure were carried out using liquid crystals and thermocouples. The results indicate that different flow patterns were encountered as the angle of inclination varied, and the heat transfer rate was largely dependent on the flow pattern. In particular, enhanced heat transfer rates can be obtained when plume-like flow occurs along both hot and cold walls in the case of an upward-facing hot wall. Heat transfer for the inclined enclosure can be predicted using the equation for a vertical enclosure presented in this paper. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 131–142, 1997     

Entropy generation in Poiseuille–Benard channel flow

The issue of entropy generation in Poiseuille–Benard channel flow is analyzed by solving numerically the mass, momentum and energy equations with the use of the classic Boussinesq incompressible approximation. The numerical scheme is based on Control Volume Finite Element Method with the SIMPLER algorithm for pressure–velocity coupling. Results are obtained for Rayleigh numbers Ra and irreversibility φ ranging from 10³ to 5×10⁴ and from 10⁻⁴ to 10 respectively. Variations of entropy generation and the Bejan number as a function of Ra and φ are studied. The limit value φ_l for which entropy generation due to heat transfer is equal to entropy due to fluid friction is evaluated. It has been found that φ_l is a decreasing function of the Rayleigh number Ra. φ_l varies from 0.0015 to 0.096 when Ra decrease from 5×10⁴ to 10³. Stream lines and entropy generation maps are plotted at six times over one period at Ra =10⁴ and φ=10⁻³. It has been found that the maximum entropy generation is localized at areas where heat exchanged between the walls and the flow is maximum. No significant entropy production is seen in the main flow.     

Natural Convection Heat Transfer From a Hot Rectangular and a Square Corrugated Plate to a Cold Flat Plate

IntroductionReduction of heat loss from the absorber plate of asolar collector through the cover plates improvescollector efficiency. Therefore, the natllral convectionheat loss across air layers bounded by tWo parallel platesis of special interest to the designers of solar collectors.Most of the investigations on heat transfer in aconfined space have been cAned out with parallel platesin horizontal and inclined positions. Hollands, et al.[l]experimentally investigated the heat trallsferchara…     

Experimental Investigation of Local Heat Transfer and Skin Friction in Tube Coils

Local heat transfer and skin friction around the tube perimeter of coils were studied in airflow. The heat transfer experiments were performed with two different coils D/d = 23 and 15.6, and skin friction experiments were performed with three different coils D/d = 25, 13.3 and 6.67 In the wide range of Re number from 4×103 till 105 . Variation of the local heat transfer around the perimeter and along the tube was defined. The behavior of the shear stresses at the wall and of the flow modes were studied. Investigations of the heat transfer indicated that with the increase of D/d the difference between heat transfer in the initial thermal section and the stabilized heat transfer increases. Investigations of the shear stress and its fluctuations indicated that, in large-curvature coils, the transition from laminar-vortex flow to turbulent flow around the tube perimeter takes place at different values of Re. In the region of the external generatrix of the bend, the transition occurs at smaller Re, whereas a     

Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.     

Numerical modeling of heat and mass transfer characteristics during the forced convection drying of a square cylinder under strong blockage

Two-dimensional analysis of heat and mass transfer during drying of a square cylinder (SC) for confined flow with a strong blockage ratio (β?=?0.8) was performed using the alternating direction implicit (ADI)-based software. The influence of Reynolds number (Re?=?10–50) and moisture diffusivity number (D?=?1?×?10^?5???1?×?10^?8?m²/s) on the heat and mass transfer mechanisms was investigated. The convective heat transfer coefficients on SC surfaces were obtained using a commercial software package. The moisture content distributions inside a SC under transient conditions were calculated using the ADI method. The calculations showed that a higher Reynolds number enhances the overall mean Nusselt number and heat transfer coefficient value. The largest mean Nusselt number and heat transfer coefficient values were obtained at the front face of the SC, which makes the greatest contribution to the overall mean Nusselt number and heat transfer coefficient values for all surfaces of the SC. The effect of Reynolds number on the overall drying time was also investigated. Low Reynolds number and moisture diffusivity values lead to an increase in the overall drying time (Δt_od). For Re?=?10, the Δt_od values are 502.19?→?220288?s and for Re?=?50, the Δt_od values are 126.14?→?70353.21?s for a moisture diffusivity range of D?=?1?×?10^?5???1?×?10^?8?m²/s. Δt_od-Re?=?10/Δt_od-Re?=?50 ratios are 3.98–3.89 and 3.13 for a moisture diffusivity range of D?=?1?×?10^?5???1?×?10^?8?m²/s. Δt_od-D2/Δt_od-D1 is 7.47 for Re?=?10, and Δt_od-D3/Δt_od-D2 is 7.63 for Re?=?50, whereas Δt_od-D3/Δt_od-D1 is 438.66 for Re?=?10, and Δt_od-D3/Δt_od-D1 is 557.74 for Re?=?50. Additionally, iso-moisture contours of SC were presented and relations for Nusselt number and mass transfer coefficient values were derived.     

Free convective mass transfer at down-facing horizontal surfaces with free or collared edges

Free convective mass transfer at down-facing horizontal surfaces was experimentally studied using the electrochemical technique with emphasis on the influence of the edge condition. It was found that the mass transfer rate is significantly lower for collared surfaces which was explained in terms of the different fluid flow conditions at the disc edge. The previous literature was critically reviewed and reported correlations were compared with those found for the present case, which, for discs with free edges, was found to be Sh_d = 2.08 Ra_d^0.178 for Ra_d in the range 7 × 10³ to 1 × 10¹¹.