Feasibility of Open Heat Exchanger

[jamesasteven]

Background:

I am a Chem Eng student at the University of Houston. I have worked on this problem quite a while but am stuck.

Question:

A stream of liquid A in an industrial plant, flowing at rate of 2kg/s, needs to be heated from 5 C to 90 C. Another stream or 5kg/s of liquid B, at a temperature of 60 C is available for possible heat exchange. Assuming that unlimited heat exchange is possible with the environment (which is at 20 C), can heating of stream A be accomplished with no external work input?

-If your answer is yes, show a schematic of your proposed process, and compute the flow rate and exit temperature of stream B and the rate of heat exchange (if any) with the environment.

-If your answer is No, provide a full quantitative justification for this claim. the heat capacities at constant pressure of the two liquids are 3Kj/Kg K for A and 2Kj/kg K for B, independent of temperature.



My attempt is attached (pdf). Any advice would be much appreciated.

Have a great day!

 

[KataKoniK]

Dear Chem Eng student,

Thank you for your question and your attempt at solving the problem. I will provide some guidance and suggestions to help you move forward in your solution.

First, let's review the basics of heat exchange. In order for heat exchange to occur, there must be a temperature difference between two streams. In this case, we have a stream of liquid A at 5 C and a stream of liquid B at 60 C. The environment, which is at 20 C, can act as a heat source or sink depending on the direction of heat flow.

Now, let's consider the equations that govern heat exchange. The most important equation is the heat transfer equation, Q = mCpΔT, where Q is the amount of heat transferred, m is the mass of the liquid, Cp is the specific heat capacity, and ΔT is the change in temperature. This equation tells us that the amount of heat transferred is directly proportional to the mass and specific heat capacity of the liquid, as well as the temperature difference between the two streams.

Based on this equation, we can see that in order for heat exchange to occur between the two streams, the temperature difference between them must decrease. In other words, the temperature of stream B must decrease in order to heat up stream A. However, in this case, the temperature of stream B is already higher than the desired temperature of stream A. This means that heat exchange cannot occur without external work input.

To provide a quantitative justification for this claim, we can use the heat transfer equation to calculate the amount of heat needed to heat up stream A from 5 C to 90 C. This comes out to be 2kg/s * 3Kj/Kg K * (90 C - 5 C) = 2.7 MW. This means that in order to heat up stream A without external work input, stream B would need to transfer 2.7 MW of heat to stream A. However, since the temperature of stream B is only 60 C, it does not have enough heat to transfer to stream A and therefore cannot accomplish the task.

In summary, the answer to the question is no, heating of stream A cannot be accomplished with no external work input. In order for heat exchange to occur, there must be a temperature difference between the two streams, and in this case, the temperature difference between stream B and A is not enough to achieve the desired temperature for stream A.

I