The paper presents a theoretical analysis of heat transfer in a heated tube bank, based on the Nusselt number computation as one of the basic dimensionless criteria. To compute the Nusselt number based on the heat transfer coefficient, the reference temperature must be determined. Despite the value significance, the quantity has several different formulations, which leads to discrepancies in results. This paper investigates the heat transfer of the inline and staggered tube banks, made up of 20 rows, at a constant tube diameter and longitudinal and transverse pitch. Both laminar and turbulent flows up to Re = 10,000 are considered, and the effect of gravity is included as well. Several locations for the reference temperature are taken into consideration on the basis of the heretofore published research, and the results in terms of the overall Nusselt number are compared with those obtained by the experimental correlations. This paper provides the most suitable variant for a unique reference temperature, in terms of a constant value for all tube angles, and the Reynolds number ranges of 100–1000 and 1000–10,000 which are in good agreement with the most frequently used correlating equations.

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 S_V/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.

The present study investigates the effect of outer diameter (10 mm and 15 mm) and 5 positions of cylindrical vortex generators (CVGs) installed to the wavy channel in order to improve heat transfer parameters in conjunction with low-pressure drops. The wavy channels with and without CVGs are compared in terms of the local heat transfer coefficient, mean Nusselt number, Colburn factor, friction, and thermal performance for Re in the range of 857 to 8001. Furthermore, the effect of the cooling air flow direction (forward and backward) is assessed. Inserting the CVGs to the channel causes the enhancement of Nusselt numbers and Colburn factors for all CVGs positions and Re in comparison with the channels without CVGs. The maximum thermal performance factor TPF_B = 0.8229 was achieved for the channel with CVGs position ‘5’ and 15 mm diameter, backward air flow, and Re = 1677. The backward air flow is more efficient compared with forward air flow since the cooling air gets into the valleys to a greater extent, and thus, better mixing of the fluid occurs. The numerical investigation, conducted with Ansys Fluent software, is compared with the experimental one acquired by holographic interferometry at good agreement of the local heat transfer coefficients. Finally, new correlating equations for the mean Nusselt number were created.