Question

Air at 40ᵒC and an average velocity of 2.5 m/s enters and flows through a thin copper tube that is submerged in a lake. The lake water average temperature is 15ᵒC and the convective heat transfer coefficient of the water is 1200 W/(m2⋅K). How long must the tube be such that air leaves the tube at 20ᵒC ? The tube diameter is 0.1 m.

Answer 1

The question asks for a calculation of the required length of a tube to cool air via convection. To solve it, the principles of heat transfer by convection are applied, but the question lacks enough information, such as specific heat capacity and mass flow rate of air, to provide an accurate answer.

Step-by-step explanation:

The student's question involves a calculation pertaining to heat transfer by convection. Since the air in the tube is being cooled by the surrounding water in the lake, we must apply principles of thermodynamics to find the necessary length of the copper tube. The given data includes the inlet and outlet temperatures of the air, the velocity of the air flow, convective heat transfer coefficient of the water, and the diameter of the tube. To answer the question, we would use the formula for convective heat transfer Q = hAΔT, where Q is the heat transfer rate, h is the convective heat transfer coefficient, A is the surface area, and ΔT is the temperature difference. This heat transfer will relate to the change in air temperature along the tube's length. However, the question does not provide enough information to calculate this, as it is missing the specific heat capacity of air and the mass flow rate. Therefore, an accurate answer cannot be provided without these additional inputs.