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

Abstract

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.

The Effect of Inclination on Natural Convective Heat Transfer from a Slender Cuboid

“…The model was previously validated by Kalendar and Oosthuizen [29] who compared numerical, correlation equation, and experimental results for constant temperature boundary conditions and found that they exhibited fairly good agreement. Further validation was carried out using the correlation equation and experimental results obtained by Ali [30] for a square cylinder in air with constant heat flux boundary conditions of w/h = 0.08 and at angles of 60 • (30 • from the horizontal) and 45 • where the bottom and top surfaces were adiabatic.…”

“…The equations governing the solution domain shown in Figure 3 were solved using ANSYS-FLUENT software in terms of dimensionless parameters; taking the height, h, of the slender cuboid as the normalizing scale of length, for the temperature scales; taking q w h/k as the constant wall heat flux boundary condition; and T H -T F as the constant wall temperature boundary condition, with T F being temperature of the undisturbed fluid far from the slender cuboid. The solution procedures and the governing equations were adopted from our previous studies (see Kalendar and Oosthuizen [28,29]). The flow was assumed steady, laminar, and symmetrical around the vertical center-plane, and the properties of the fluid were assumed constant except for the change in density with temperature which was handled using the Boussinesq approach.…”

“…Ra = 1 × 10 4 The variations in the mean Nusselt number of individual heated surfaces of the slender cuboid, (Nuleft, Nuright, Nufront), versus dimensionless width, W, at different positions, φ, and heat flux Rayleigh numbers, Ra*, are presented in Figures 7-9, respectively. The rate of heat transfer from the heated top surface of the slender cuboid, being very small compared to that of other surfaces (see Kalendar and Oosthuizen [29]), will not be considered The variations in the mean Nusselt number of individual heated surfaces of the slender cuboid, (Nu left , Nu right , Nu front ), versus dimensionless width, W, at different positions, ϕ, and heat flux Rayleigh numbers, Ra*, are presented in Figures 7-9, respectively. The rate of heat transfer from the heated top surface of the slender cuboid, being very small compared to that of other surfaces (see Kalendar and Oosthuizen [29]), will not be considered in our discussions.…”

“…A correlation equation was established for the vertical side surfaces and the top of the square cylinders. Kalendar and Oosthuizen [28,29] investigated the effects of dimensionless parameter w/h ratios in the range 0.25 to 1, Rayleigh numbers in the range 1 × 10 3 to 1 × 10 7 , and inclination angles in the range 0 • to 180 • on the mean Nusselt numbers for different surfaces of square cylinders in the laminar flow region. A correlation equation was developed for the rate of heat transfer from the entire cylinder.…”

Free Convection Heat Transfer from Different Objects

“…They have used that method to determine the heat transfer from inclined cylinders. Numerical and experimental investigation on free convection heat transfer was reported by Kalendar and Oosthuizen [23] using inclined isothermal square cylinders. Those cylinders had been exposed to the top surface.…”