Heat Transfer question regarding counterflow heat exchange.

[watsup1993]

Homework Statement

A counterflow, concentric tube heat exchanger is used to cool the lubricating oil for large industrial gas turbine engine. The flow rate of cooling water through the inner tube (Di = 25 mm) is 0.2 kg/s, while the flow rate of oil through the outer annulus (Do = 45 mm) is 0.1 kg/s. The oil and water enter at temperatures of 100 and 300 C, respectively. How long must the tube be made if the outlet temperature of oil is to be 600C ?

Homework Equations

Not sure

3. The Attempt at a Solution [/b

Not sure again, sorry

 

[SteamKing]

Your question is confusing. Oil enters the exchanger at 100 C and you want cool it so that it exits at 600 C, by using 'cool' water that starts at 300 C. Notice something funny about this setup?

 

[watsup1993]

Sorry, I meant 30*C, and at the end also 60*C

 

[Chestermiller]

You are given enough information to calculate the outlet temperature of the water. To do this, you need to assume a typical heat capacity for the oil (you already know the heat capacity of water, I presume). Use the information you have to get the outlet temperature of the water. You also already have enough information to calculate the heat load of the heat exchanger. Calculate the heat load. Then show us your results. We'll help you figure out what to do next.

chet

P.S. Welcome to Physics Forums.

 

[paranormal]

.

I would approach this question by first identifying the key variables and equations that are relevant to heat transfer in a counterflow heat exchanger. From the given information, we know the flow rates and inlet temperatures of both the cooling water and lubricating oil. Additionally, we are given the desired outlet temperature of the oil.

To solve for the required length of the tube, we can use the heat transfer equation for a counterflow heat exchanger:

Q = m*Cp*(Tin - Tout)

Where Q is the heat transfer rate, m is the mass flow rate, Cp is the specific heat capacity, Tin is the inlet temperature, and Tout is the outlet temperature.

We can rearrange this equation to solve for the length of the tube, represented by L:

L = Q / (m*Cp*(Tin - Tout))

To calculate Q, we need to know the heat transfer coefficient, which can be determined by the overall heat transfer coefficient (U) and the surface area of the heat exchanger (A):

Q = U*A*(Tin - Tout)

We can estimate the overall heat transfer coefficient using the Nusselt number (Nu) and the thermal conductivity (k) of the fluids:

U = Nu * k / Do

Where Do is the outer diameter of the tube.

Now, we can substitute all of these values into the equation for L and solve for the required length of the tube.

L = (U*A*(Tin - Tout)) / (m*Cp*(Tin - Tout))

We can also use this equation to determine the outlet temperature of the oil if a different length of tube is used. By rearranging the equation, we can solve for Tout:

Tout = Tin - Q / (m*Cp*L)

In conclusion, as a scientist, I would use the above equations and calculations to determine the required length of the tube in order to achieve an outlet temperature of 600C for the lubricating oil. Additionally, I would also consider factors such as the materials and design of the heat exchanger, as well as any potential heat losses, in order to ensure the most accurate and efficient solution.