Numerical Study of Heated Tube Arrays in the Laminar Free Convection Heat Transfer

Laminar free convection heat transfer from a heated cylinder and tube arrays is studied numerically to obtain the local and average Nusselt numbers. To verify the numerical simulations, the Nusselt numbers for a single cylinder were compared to other authors for the Rayleigh numbers of 103 and 104. Furthermore, the vertically arranged heated tube arrays 4 × 1 and 4 × 2 with the tube ratio spacing SV/D = 2 were considered, and obtained average Nusselt numbers were compared to the existing correlating equations. A good agreement of the average Nusselt numbers for the single cylinder and the bottom tube of the 4 × 1 tube array is proved. On the other hand, the bottom tubes of the 4 × 2 tube array affect each other, and the Nusselt numbers have a different course compared to the single cylinder. The temperature fields for the tube array 4 × 4 in basic, concave, and convex configurations are studied, and new correlating equations were determined. The simulations were done for the Rayleigh numbers in the range of 1.3 × 104 to 3.7 × 104 with a tube ratio spacing S/D of 2, 2.5, and 3. On the basis of the results, the average Nusselt numbers increase with the Rayleigh numbers and tube spacing increasing. The average Nusselt number and total heat flux density for the convex configuration increase compared to the base one; on the other hand, the average Nusselt number decreases for the concave one. The results are applicable to the tube heaters constructional design in order to heat the ambient air effectively.

Dimensionless Correlating-Equations for Predicting the Optimal Tilting Angle of Water-Filled Square and Shallow Enclosures Differentially Heated at Sides

Laminar natural convection heat transfer inside water-filled, tilted square and shallow cavities heated at one side and cooled at the opposite side, is studied numerically. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. Simulations are performed using the Rayleigh number based on the length of the heated and cooled sides, the height-to-width aspect ratio of the enclosure, and the positive tilting angle with respect to the gravity vector (which corresponds to configurations with the heated wall facing upwards), as independent variables. It is found that the heat transfer performance has a peak at an optimal tilting angle which increases as the Rayleigh number is decreased and the aspect ratio is increased. On the basis of the results obtained, a set of dimensionless correlations is developed.

Correlating Equations for Laminar Free Convection From Misaligned Horizontal Cylinders in Interacting Flow Fields

Steady laminar free convection in air from a pair of misaligned, parallel horizontal cylinders, i.e., a pair of parallel cylinders with their axes set in a plane inclined with respect to the gravity vector, is studied numerically. A specifically developed computer code based on the SIMPLE-C algorithm is used for the solution of the dimensionless mass, momentum, and energy transfer governing equations. Results are presented for different values of the center-to-center cylinder spacing from 1.4 up to 10 diameters, the tilting angle of the two-cylinder array from 0degto90deg, and the Rayleigh number based on the cylinder diameter in the range between 103 and 107. It is found that the heat transfer rates at both cylinder surfaces may in principle be traced back to the combined contributions of the so-called plume effect and chimney effect, which are the mutual interactions occurring in the vertical and horizontal alignments, respectively. In addition, at any misalignment angle, an optimum spacing between the cylinders for the maximum heat transfer rate, which decreases with increasing the Rayleigh number, does exist. Heat transfer dimensionless correlating equations are proposed for any individual cylinder and for the pair of cylinders as a whole.