Mixed convection model for predicting the Nusselt number of oscillating vertical plates
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Natural convection heat transfer was experimentally investigated in a staggered array of heated cylinders, oriented horizontally within a rectangular isothermal enclosure. The test conditions were characteristic of a spent-fuel assembly during transport or horizontal dry storage. The assembly was configured with a pitch-to-diameter ratio of 1.33 and backfilled with pressurized helium or nitrogen. The backfill pressure was varied between 1 and 5 atm, while the assembly power was varied between 1 and 5 W per heater rod. The resulting data are presented in the form of Nusselt-Rayleigh number correlations, where the Nusselt number has been corrected for thermal radiation using a numerical technique. The staggered-array data are compared to previous data for a similar-pitch aligned rod array (a simulated boiling water reactor fuel assembly) to determine if convective heat transfer is enhanced or hindered in a staggered configuration. For the overall array, both the staggered and aligned configurations yield Nusselt-Rayleigh curves with a three-regime trend, which suggests distinct conduction and convection regimes separated by a transition regime. For lower Rayleigh numbers (<106), representative of the conduction regime, the aligned-array Nusselt number is 10 to 12% higher than the corresponding staggered-array value. However, in the convection regime at higher Rayleigh numbers, the staggered-array Nusselt number slightly exceeds the aligned- array Nusselt number. This is attributed to the fact that the staggered array begins to transition into the convection regime at lower Rayleigh number than the aligned array. For both configurations, the slope of the Nusselt-Rayleigh curve in the convection regime suggests turbulent flow conditions.
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Two-dimensional laminar natural convection in an inclined square enclosure with uniform internal heat generation is studied here. The steady-state solutions are obtained for inclination angles of 45°, 30° and 15° and at Rayleigh number of 1.5 × 105. For these cases, the two counter-rotating rolls of fluid are present in the cavity. Streamlines, isotherms and heat transfer for these results are compared with the existing experimental results and are found to be in reasonably good agreement. It is found that the location of maximum non-dimensional temperature in the inclined cavity is higher than that for pure conduction case. The maximum non-dimensional temperature in the cavity decreases as the Rayleigh number increases. For Ra > 5 × 104, the maximum non-dimensional temperature in inclined cavity is almost independent of the inclination angle. It is also observed that the local Nusselt number at the top wall is greater than the pure conduction solution, whereas that for bottom wall it is lower than the Nusselt number for pure conduction. The effect of Rayleigh number and inclination angle on the local Nusselt number and modified local Nusselt number are also studied. For horizontal cavity, at Rayleigh number greater than or equal to 5 × 104, periodic solutions are obtained. In this case, two unstable secondary rolls are present near the center of top wall, in addition to the primary rolls. The secondary rolls are dissipated and recreated during one period of oscillation.
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Numerical study natural convection heat transfer inside a differentially heated square cavity with adiabatic horizontal walls and vertical isothermal walls is investigated. Two perfectly conductive thin fins are attached to the isothermal walls. To solve the governing differential mass, momentum and energy equations a finite volume code based on Pantenkar’s simpler method is developed and utilized. The results are presented in form of streamlines, isotherms as well as Nusselt number for Rayleigh number ranging from 104 up to 107. It is shown that the mean Nusselt number is affected by the position of the fins and length of the fins as well as the Rayleigh number. It is also observed that maximum Nusselt number occurs about the middle of the enclosure where Lf is grater the 0.5. In addition the Nusselt number stays constant and does not varies with width of the cavity (lf) when Lf is equal to 0.5 and Rayleigh number is equal to 104 and 107 as well as when Lf is equal to 0.6 and low Rayleigh numbers.
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Numerical simulations were conducted to determine local and average natural convection Nusselt numbers for uniformly heated horizontal plates with convection occurring simultaneously from upper and lower surfaces. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 86 to 1.9 × 108. Upper surface Nusselt numbers were found to be smaller than corresponding lower surface Nusselt numbers. The local Nusselt number was largest at the plate edge and decreased towards the plate center for both surfaces. This variation followed approximately a minus 1/3-power law variation with the non-dimensionalized x coordinate on the upper surface for modified Rayleigh numbers greater than 104, and a minus 1/9-power law variation on the lower surface for all modified Rayleigh numbers. Comparative simulations were also performed for upward and downward facing uniformly heated plates (single sided convection). For these cases, Nusselt numbers on the upward facing plates were larger than for downward facing plates.
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This paper is based on the numerical investigation of natural convection of two vertical enclosure of square and triangular cavity with air filled. The vertical cavity consist of adiabatic and hot and cold wall with wide range of Rayleigh number from 103 to 106 with aspect ratio from 1 to 10 at the interval of 2.5. Flow patterns and isotherm plots were used to display the results, and for every case, local and mean Nusselt values were also produced. The results show that an increase in Rayleigh numbers greatly increases heat transfer, natural convection intensity, and average Nusselt number at a particular aspect ratio. Keyword: ANN (average Nusselt number), AR (aspect ratio), LNN (local Nusselt number), Nu (Nusselt number), Pr (Prandtl number), Ra (Rayleigh number).
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Natural convection in a steady state of incompressible air inside a cavity’s porous with a heated low wall of a sinusoidal profile is investigated numerically in this paper. The upper horizontal wall is kept cold while the two sides are thermally insulated. The proposed physical model was developed and studied with two-dimensional conditions, using the finite element method and adapting the Darcy-Brinkman model. This paper examines the laminar natural convection in a square porous cavity for different Rayleigh numbers (10 ≤ Ra ≤ 104), aspect ratios (0.25 ≤ AR ≤ 1.0), and sinusoidal temperature amplitude (0.25 ≤ λ ≤ 1.0). Moreover, the variation effect of Ra, AR, and λ on isotherms, streamlines, and the mean and local Nusselt numbers has been presented and analyzed. The results showed that an increase in the sinusoidal thermal amplitude, mean Nusselt number, and AR reduced somewhat the Rayleigh number. This provided a solution in which the mean Nusselt number increased by increasing the sinusoidal thermal amplitude and the Rayleigh number. On the other hand, it decreases slightly by increasing the AR. In addition, the convection transfer mechanism is the main mode when the Rayleigh number is high. Thus, it was found that the Darcy number also has an effect on heat transmission. The obtained results were compared with those found in the literature and were found to be in good accordance.
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In this work, we study numerically the natural convection of nanofluids (NF) in an inclined flat bottom flask; it is one of laboratory flasks used in organic chemistry synthesis. The main reason of this study is to enhance the thermal properties of the reaction medium inside the flat bottom flask and to ameliorate the rate of chemical reactions using nanofluids. The flat bottom wall is maintained at a constant high temperature Th. While the top, left and right walls of the cavity are maintained at a low temperature TL. The NF comprises Cu and Al2O3 nanoparticles (NP) suspended in pure water. The governing equations are solved numerically using the finite-volume approach and formulated using the Boussinesq approximation. In this simulation we examined the effects of the NP volume fraction (φ) from 0% to 5%, the Rayleigh number from 103 to 106, the various inclination angles of enclosure (γ=0°,5°,10°, 15°) and the NF type (Cu and Al2O3) on the flow streamlines, isotherm distribution and Nusselt number. The obtained results show that the addition of Cu and Al2O3 NP increases the mean Nusselt number which enhances the heat transfer in the flat bottom flask and causes significant changes in the flow pattern. In addition, the mean Nusselt number is increase with increasing the Rayleigh number and the volume fraction and the best results have obtained from the Cu nanofluide. Also, as the inclination angle increases the mean Nusselt number decreases and the highest value of Nusselt number was obtained for a vertical enclosure (γ=0°). The obtained streamlines are mostly symmetric and their values are generally increase by increasing the Rayleigh number and volume fractions of NPs. Besides, the obtained isotherms are generally follow the geometry of the flat bottom flask.
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