Is flowing water hoter than water in a container ?

Sometime, especially in winter, we find the temperature of flowing water is higher than the water in a container. You may notice the phenomenon like this, when you washing your hair, you think the temperature of flowing water is just perfect. But you then find it too cold after you had wetted your hair. So you put your hand into the basin, the temperature seems decreased.

Let me have a brief research on this interesting phenomenon. Is the temperature decreased rapidly during its way to basin?www.zhangpeng.info

In my opinion, this phenomenon causes by three reasons.

First, your hand-skin temperature is lower than your skin on head, so your skin will cheat you.

Second, the heat transfer efficiency is much higher in a forced convection than natural convection.

Third, the temperature decreased during its way to basin due to convection and radiation.

Based on biology, your skin feels the temperature by compare the difference between your skin and surroundings. It’s to say, if your skin temperature is same to the surrounding, you may just have no feeling about the temperature. For example, you can’t feel hot if you skin temperature is the same as evioriment though it’s 70 degree now. So, when your hand-skin is cold than your skin on your head, it will feel warmer at a same temperature. And in cold days, our hands are usually colder than our head. This is one reason why you feel the temperature is higher by testing with your hands. But, after testing once time, your hand is warmed by hot water. That’s to say you will feel temperate goes down after wetted your hair.

Second, I’ll calculate the heat transfer in a forced convection.

According to Newton equation:

Q=h(Tw-Tf)
Where:
Q. Heat transfer during the whole process
h. Convection coefficient
Tw. Surface temperature
Tf. Fluid temperature

In a forced convection, ‘h’ can be much higher than a natural convection. Usually, ‘h’ in a forced convection can be 10 times in a natural convection.

When you put your hand under flowing water, the Q is high, in other words, the heat transfer is high. And the temperature of your skin increase rapidly. So you think the water temperature is suitable. But put your hand in basin, the ‘Q’ is lower; your skin may tell you the temperature is lower than the flowing water.

Third, the temperature decreased during its way to basin due to convection and radiation. It’s to say, the temperature is surely lower in the basin.

On its way to basin, there are convection and radiation. The convection is a forced convection. According the above discuss, result on temperature decrease is obviously.

And base on black body radiation equation:

Q=δ(T_f^4-T_0^4)
Where
Q. Heat transfer during the whole process
T_f. Temperature of water
T_0. Temperature of the environment

We know during its way to the basin, water will lose some heat because of radiation and the temperature decrease.

So, the real situation is that the temperature in your basin decreased when the water flow out of water pipe.

Above all, my conclusion about this interest phenomenon on some degree is misleading by your feeling but it’s a fact that the temperature is lower in your basin.

How to make this process better?

There are three ways to improve. First, warmer your hands before you prepare water. Second, turn down the valve to let the water flow slowly so the convection reduced. Third, just put you basin near outlet to decrease the heat transfer during its way to your basin.

There also a simple solution, remember next time when you want to wash your hair in winter, prepare your water hotter than perfect.