Question

Water flows through a tube of length L with a mean inlet temperature (Ti). The tube is held at a uniform surface temperature (Ts) greater than Ti. Which temperature profile best represents the mean temperature of the water as it flows through the tube?

A) Constant temperature along the tube length, with the mean temperature between Ti and Ts.
B) Temperature decreasing exponentially from Ts at the inlet to Ti at the outlet.
C) Gradual increase in temperature from Ti at the inlet to Ts at the outlet.
D) Uniform temperature maintained throughout at Ti.

Answer 1

Option C, indicating a gradual increase in temperature from Ti at the inlet to Ts at the outlet, best represents the mean temperature profile of the water as it flows through a heated tube.

Step-by-step explanation:

The question pertains to the temperature profile of water flowing through a tube with a uniform surface temperature higher than the water's inlet temperature. Given that the surface temperature of the tube (Ts) is greater than the inlet temperature (Ti), it is logical to predict that the mean temperature of the water will increase as it flows through the tube. The correct temperature profile would be option C, which indicates a gradual increase in temperature from Ti at the inlet to Ts at the outlet. This increase occurs because as water flows through the tube, heat is transferred from the hotter surface of the tube to the cooler water, thus increasing the water's temperature. The mean temperature can't remain constant nor can it decrease if the tube's temperature is higher than the water's inlet temperature, and it will not instantly rise to Ts because the transfer of heat takes time and is subject to convective heat transfer processes.