Question

In flow across tube banks, how does the heat transfer coefficient vary with the row number in the flow direction? How does it vary in the transverse direction for a given row number?

Short answer

Answer: In the flow direction, the heat transfer coefficient initially increases with increasing row number due to enhanced turbulence induced by the tubes. However, it eventually reaches a maximum value before starting to decrease as the flow becomes more streamlined. In the transverse direction, the heat transfer coefficient remains relatively constant for a given row number, with possible variations near the tube bank's inlet and outlet.

Step-by-step solution

1. Understand the Concepts

A tube bank is an arrangement of tubes that allows fluid to flow through them for the purpose of heat transfer. Heat transfer coefficient is a measure of the ability of the fluid to take heat away from the tubes. The Nusselt number is a dimensionless number that indicates the relative efficiency of heat transfer through the fluid film.

2. Heat Transfer Coefficient and Row Number in the Flow Direction

In the flow direction, the heat transfer coefficient initially increases as the row number increases, due to enhanced turbulence induced by the tubes. However, the heat transfer coefficient eventually reaches a maximum value and then starts to decrease because the flow becomes more streamlined. The variation of the heat transfer coefficient in the flow direction can be related to the Nusselt number, which is defined as: Nu = h * D / k Where: Nu - Nusselt number h - heat transfer coefficient D - tube diameter k - thermal conductivity of the fluid The Nusselt number increases with increasing Reynolds number up to a point, then starts to decrease when the flow becomes more streamlined. The Reynolds number is defined as: Re = ρ * v * D / μ Where: ρ - fluid density v - flow velocity μ - fluid dynamic viscosity

3. Heat Transfer Coefficient Variation in the Transverse Direction for a Given Row Number

In the transverse direction, the heat transfer coefficient generally remains relatively constant for a given row number. This is because the tubes within a row are typically spaced uniformly, leading to a nearly uniform level of turbulence across the row. However, the value of the heat transfer coefficient may vary in the vicinity of the tube banks' inlet and outlet due to the presence of additional boundaries or transitions in the fluid flow. In conclusion, the heat transfer coefficient varies with row number in the flow direction, increasing at first due to enhanced turbulence induced by the tubes and then decreasing as the flow becomes more streamlined. In the transverse direction, the heat transfer coefficient remains relatively constant for a given row number, with potential variations near the tube bank's inlet and outlet.