Why this special case occurs in an exchange of heat

[Andres Padilla]

Homework Statement

Hello. First of all sorry about this question, it has to do a little with heat transfer from engineering. This situation is not real, I was working in a proyect and this doubt came to me.

I have a heat exchanger of parallel tubes. Water flows in a tube and oil flows in another one. The initial conditions are shown in the picture. I will write them here:
Water
To= 18°C
Tf= 26°C
m=0.25 kg/s
cp= 4.18 kJ/kg°C
Oil
To: 0°C
m= 0.1 kg/s
Cp= 1.79 kJ/kg°C

Homework Equations

Q= m.cp (Tf-to)

The Attempt at a Solution

I found the heat transfer from the water to the oil

Qw= (0.25)(4.18)(26-18)=8.36
This is the same heat that comes into the oil.

So
8.36=(0.1)(1.79)(Tf-0)
Tf= 46.7°C

This result does not make sense to me, because I find impossible that the oil has increased its temperature more than water. I thought that the maximum possible temperature than the oil can reach is the same 26°C of water ( Assuming an infinite length in the heat exchanger)

In the picture I put a axis with the temperatures.

Could anyone explain me why, according with the calculations, I got Tf= 46.7°C for the oil?

 

[haruspex]

To= 18°C
Tf= 26°C

I assume you meant the other way around. Heat is being transferred from the water to the oil, right?

impossible that the oil has increased its temperature more than water

Quite so. It won't happen. The best arrangement in a heat exchanger is that the flows are opposite, i.e. the incoming cool fluid is adjacent to the exiting warm fluid, etc. In this way, the oil might get close to 26C, but never quite there.

 

[Let'sthink]

I think some information, some data, is missing here. How can the temperature of oil and water both increase. Is there a heating coil in oil tube? I think it must be there. The higher temperature rise of oil is there because specific heat of oil is smaller and also oil is moving at a slower rate so it remains in contact with water and also remains exposed to the radiation of heater coil, which is at much higher temperature inside oil. I think water has been used here to check the increase of temperature of oil to its boiling point.

 

[Andres Padilla]

I wrote incorrectly one part, I am sorry! The water comes in with 26°C and comes out 18°C.

 

[Andres Padilla]

I assume you meant the other way around. Heat is being transferred from the water to the oil, right?

Quite so. It won't happen. The best arrangement in a heat exchanger is that the flows are opposite, i.e. the incoming cool fluid is adjacent to the exiting warm fluid, etc. In this way, the oil might get close to 26C, but never quite there.

Yes, I know the best arrangement is with the counterflow heat exchanger. I agree with you, the oil will get closer to 26°C, but how can I prove that with calculations? Because according with calculations, I will get the 46.7°C

 

[haruspex]

Yes, I know the best arrangement is with the counterflow heat exchanger. I agree with you, the oil will get closer to 26°C, but how can I prove that with calculations? Because according with calculations, I will get the 46.7°C

It is a case of garbage in, garbage out.
Assuming you meant T₀ for the water is 26C (please confirm), you have specified a result (final temperature of the water as 18C) that simply will not happen.
Instead of specifying T_f for the water as 18C try setting the water and oil to have the same final temperature.