Numerical investigation of natural convection heat transfer in volumetrically heated spherical segments (original) (raw)
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Heat and Mass Transfer, 2007
This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water solution 50%). The simulations are performed at two different Rayleigh numbers (5 · 10 6 and 5 · 10 7 ) and six different Prandtl numbers (3 · 10 5 ≥Pr≥ 50). Heat conduction through the cavity glass walls is also considered. The propsed correlations of the averaged heat transfer coefficient (Nu) showed that it is dependant on the initial Ra and almost independent on P r. The instantaneous flow patterns, temperature contours and time evolution of volume averaged temperature and heat transfer coefficient are presented and analyzed.
The Canadian Journal of Chemical Engineering, 1963
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 · 10 4 \ Ra \ 5 · 10 5 ) for different annulus gap widths (L/D o = 0.23, 0.3, and 0.37) and different inclination of the annulus (a = 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 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 a. The prediction of the correlation has been compared with the present and previous data and fair agreement was found.
The International Conference on Applied Mechanics and Mechanical Engineering
Two-dimensional steady laminar natural convection in a differentially heated cavity filled with water and has various aspect ratios due to buoyancy force effect is analyzed numerically. The governing mass, momentum and energy equations are considered and a finite volume algorithm is used to capture the numerical solution. The left vertical side wall of the cavity is linearly heated while the right vertical one is maintained at constant cold temperature. The bottom wall is maintained at constant hot temperature while the top wall is considered thermally insulated. The Rayleigh number is varied from 10 3 to 10 6 , while the cavity aspect ratio (W/H) is varied as 0.5, 1.0 and 2.0 respectively. Results are presented in the form of streamline and isotherm contours. The results of the present work explain that the natural convection phenomenon is significantly influenced by changing the cavity aspect ratio, so that when the aspect ratio is high the convection effect is week and vice versa. Also, it is found that non-uniform heating in the left vertical sidewall of the cavity plays a major role to improve the heat transfer rates. For uniform and nonuniform heating of the bottom wall and left vertical sidewall respectively, the local Nusselt number at these walls increases from its minimum value at the left edge of these walls toward maximum value at the right edge. While, the average Nusselt number for both left side and bottom walls increases with increasing of Rayleigh number.
Heat transfer from a moving fluid sphere with internal heat generation
Thermal Science, 2014
In this work, we solve numerically the unsteady conduction-convection equation including heat generation inside a fluid sphere. The results of a numerical study in which the Nusselt numbers from a spherical fluid volume were computed for different ranges of Reynolds number (0
International Communications in Heat and Mass Transfer, 2007
Combined convection heat transfer in a vertical circular cylinder has been experimentally studied for assisting, thermally developing and thermally fully developed laminar air flows under constant wall heat flux boundary conditions for Reynolds number range from 400 to 1600, and the heat flux is varied from 60 Wm − 2 to 400 Wm − 2 . This paper has examined the effect of the cylinder inclination angle on the mixed convection heat transfer process. The experimental setup consists of aluminum cylinder as test section with 30 mm inside diameter and 900 mm heated length (L / D = 30). The hydrodynamically developed condition has been achieved by using aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths. The entrance sections included two long calming sections, one with length of 1800 mm (L / D = 60), another one with length of 2400 mm (L / D = 80) and two short calming sections with lengths of 600 mm (L / D = 20), 1200 mm (L / D = 40). The results present the surface temperature distribution along the cylinder length, the local and average Nusselt number distribution with the dimensionless axial distance Z + . The results have clearly shown that the surface temperature values decrease as the cylinder inclination angle moves from θ = 90°vertical cylinder to θ = 0°horizontal cylinder. The results have demonstrated that an increase in the Nusselt number values as the heat flux increases and as the angle of cylinder inclination moves from θ = 90°vertical cylinder to θ = 0°horizontal cylinder. The mixed convection regime has been bounded by the convenient selection of Re number range and the heat flux range, so that the obtained Richardson numbers (Ri) varied approximately from 0.1 to 10. The average heat transfer results have been correlated with an empirical correlation by dimensionless groups as Log P Nu against Log P Ra= P Re, and compared with available literature and with laminar forced convection and showed satisfactory agreement.
Transient natural convection heat transfer in a large-diameter cylinder
Experimental Thermal and Fluid Science, 1988
The transient two-dimensional laminar natural convection of water, enclosed in rectangular cavities with wall temperature maintained at 0°C is studied analytically. This investigation is carried out in order to study the inversion of flow patterns caused by the maximum density of water at 4°C. Numerical solutions are obtained for cases involving different aspect ratios and initial water temperatures varying between 4 and 21°C. Solutions of the governing coupled system ofpartial differential equations are obtained using an alternating direction implicit finite difference method. The results are presented graphically in the form of stream function and isotherm contour plots. The heat transfer through each wall is evaluated in order to study the effect of the density inversion on the cooling process. It is established numerically that one of the consequences of the nonlinearity of the water is to change the maximum heat transfer from the top wall of the cavity to the bottom one.
2020
In the current study, the effect of an inner heated circular cylinder placed inside a cooled square enclosure on the heat transfer and fluid flow is numerically studied. The main parameters that were investigated are the position of the inner cylinder which was varied both in the vertical and diagonal directions from -0.2 to +0.2 and the aspect ratio which was from 0.05 to 0.25. The Rayleigh number and the Prandtl number were kept constant at 10 and 0.7, respectively. However, for the comparison study, three Prandtl numbers were examined 10, 10, and 10. The numerical study is conducted using (FORTRAN 90) code which is built to perform the calculations for the Navier-Stokes equation of the stream-vorticity expression using finite-difference approach that relates with the non-orthogonal body-fitted coordinate system. The results revealed that the highest local Nu number was achieved at the top surface of the cylinder when the cylinder is moved both in the vertical and diagonal directi...
Computational Analysis of Natural Convection in Spherical Annulus Using FEV
HEAT transfer by natural convection from a body to its finite enclosure is of importance in nuclear reactor technology, electronic instrumentation packaging, aircraft cabin design, the analysis of fluid suspension gyrocompasses, and numerous other practical situations. The steady natural convection heat transfer of fluids between two concentric isothermal spheres is investigated computationally with the help of FEV in ANSYS 14.5. The inner wall is subjected to a higher temperature and outer is at room temperature. The steady behavior of the flow field and its subsequent effect on the temperature distribution for different Rayleigh numbers and radius ratios are analyzed.
Journal of Heat Transfer, 1992
The phenomenon of natural convection in a square cavity filled with a copper-water nanofluid is investigated numerically. The studied domain is a square cavity with hot and cold isothermal walls at x = 0 and x = L, respectively, while the other walls are adiabatic. The fins are considered perfectly conductive with different lengths (L f) and positioned at different locations. We examined the situation for Rayleigh numbers ranging between 10 4 and 10 6. The governing equations are expressed in the vorticity, stream function, and temperature formulation. The system of equations was solved by the finite difference method, using the upwind scheme. The computation code thus developed was used to analyze the effect of the different locations of the fins on the thermal performances. The obtained results were validated by comparing with those of a previously published work and with those obtained using COMSOL Multiphysics. It has been found that adding fins on the cold and adiabatic walls results in an increase in the average Nusselt number, while it decreases when the fin is located on the hot wall. That is to say, placing the fins on the cold and adiabatic walls increases the thermal performances of the transfer.
Numerical analysis of natural convection between a heated cube and its spherical enclosure
International Journal of Thermal Sciences, 2020
Three-dimensional numerical simulations were conducted for the natural convection phenomena which occurs between an inner hot body and its outer enclosure. The physical model considered here is that a body of cubical shape is located at the center of an isothermal cooled spherical enclosure. Therefore, the fluid flow inside the enclosure results from the temperature difference between the cooled spherical enclosure and the heated cube. The governing equations are solved using a second-order accurate finite volume approach on a staggered grid system and multi-grid acceleration. Three different fluids, an air (Pr = 0.71), a water (Pr = 6.2) and the other a dielectric liquid (Pr = 25) are employed encompassing descriptive Rayleigh numbers Ra that range three orders of magnitude from 10 4 to 10 7. The conducted benchmark study leads to excellent accordance with previous findings. Detailed three-dimensional flow and thermal structures in the enclosure were analyzed using the distribution of iso-contours of temperature, iso-surfaces of the standard velocity vector and streamtraces for different Rayleigh numbers. The variation of the local and the surface-averaged Nusselt numbers at the inner hot cube wall are also presented to exhibit the overall heat transfer characteristics inside the enclosure. At the end, monomial correlations are presented for the quantification of the heat transfer that emanates from the heated cube and the spherical enclosure in harmony with the various Rayleigh number. It was found that the thermal and flow fields eventually reach steady state for Rayleigh numbers ranging from 10 4 to 10 7. Results indicate also that the heat transfer is increasing significantly by increasing Rayleigh numbers and optimal heat transfer rate is obtained for high Rayleigh number set to 10 7 .