Undefined log-mean temperature in heat exchanger design

In summary, the conversation discusses the design of a heat exchanger for cooling electronic components in a UAV. The known parameters include a heat load of 910 W, a cross-flow air to liquid heat exchanger, and specific properties for both the cold side and hot side. The problem arises when trying to calculate the log-mean temperature due to a negative fraction. The issue may be with the temperatures of the hot side, which were assumed based on the temperature of the cabin of the UAV. The conversation ends with a question about the outlet air temperature being 4.87 °C, which may seem odd given the outside air temperature of -34.5 °C and the inlet hot fluid temperature of -17.5 °C.
  • #1
mastermechanic
108
15
For a course project, I need to design a heat exchanger to cool electronic components in an UAV. The heat exchanger will be cross-flow air to liquid. The cold side (air side) properties are evaluated at an altitude of 7620 m and -34.5 °C. For the hot side ethylene glycol - water solution with a 60:40 ratio will be used.

Known Parameters

Heat Load: 910 W

Cold Side Hot Side

Mass Flow Rate: 0.023 kg/s Mass Flow Rate: 0.1 kg/s
Specific Heat: 1.005 kJ/kg.K Specific Heat: 3.626 kJ/kg.K
Inlet Temp: - 34.5 °C Inlet Temp: -17.5 °C (from Q = m.c.dt)
Outlet Temp: 4.87 °C (from Q = m.c.dt) Outlet Temp: -20 °CThe problem arises when I try to calculate log-mean temperature,

T_lm = [ (T_h_1 - T_c_2) - (T_h_2 - T_c_1) ] / ln[ (T_h_1 - T_c_2) / (T_h_2 - T_c_1)]

But since (T_h_1 - T_c_2) = ( -17.5 - 4.87) = -22.37 °C and (T_h_2 - T_c_1) = (-20 - (-34.5)) = 14.5 °C

The fraction inside the ln function becomes negative. Where is the problem? I am sure about the temperatures of the air side, therefore, the problem is probably due the temperatures of the hot side.

Although, the air outside is - 34.5°C the cabin of the UAV must be warmer. Considering the radiation from electronics and engine we assumed the cabin temperature as - 20°C and calculated inlet temp. from Q= m.c.dt. I need your help at this point.
 
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  • #2
mastermechanic said:
Inlet Temp: - 34.5 °C Inlet Temp: -17.5 °C (from Q = m.c.dt)
Outlet Temp: 4.87 °C (from Q = m.c.dt) Outlet Temp: -20 °C
4.87 C
 
  • #3
256bits said:
4.87 C

Sorry, I didn't understand what you meant. What's wrong with 4.87?
 
  • #4
mastermechanic said:
Sorry, I didn't understand what you meant. What's wrong with 4.87?
Outside air temperature = -34.5 C inlet Cold Air
Cabin temperature = -17.5 C Inlet Hot Fluid

Does it not seem odd that the outlet air temperature will heat up to 4.87 C?
 
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1. What is the concept of undefined log-mean temperature in heat exchanger design?

The log-mean temperature is a concept used in heat exchanger design to determine the average temperature difference between the hot and cold fluids. It is calculated using the logarithmic mean of the temperature differences at the inlet and outlet of the heat exchanger.

2. Why is the log-mean temperature sometimes undefined in heat exchanger design?

The log-mean temperature can be undefined when the temperature difference between the hot and cold fluids is very small, or when the heat transfer coefficient is very low. This can happen in certain types of heat exchangers, such as plate heat exchangers, or in situations where there is a large temperature cross between the hot and cold fluids.

3. How does the undefined log-mean temperature affect heat exchanger performance?

If the log-mean temperature is undefined, it means that the heat exchanger is operating at very low efficiency. This can result in a lower heat transfer rate and reduced overall performance of the heat exchanger. It is important to consider the log-mean temperature in heat exchanger design to ensure optimal performance.

4. Can the log-mean temperature be approximated in cases where it is undefined?

Yes, there are several methods for approximating the log-mean temperature in cases where it is undefined. These methods include the arithmetic mean temperature difference method, the geometric mean temperature difference method, and the modified logarithmic mean temperature difference method. These methods can provide a reasonable estimate of the log-mean temperature in situations where it is undefined.

5. How can the undefined log-mean temperature be avoided in heat exchanger design?

The undefined log-mean temperature can be avoided by carefully selecting the type of heat exchanger and considering design factors such as the temperature difference between the hot and cold fluids, the heat transfer coefficient, and the flow rates. It is also important to properly size and design the heat exchanger to ensure efficient heat transfer and avoid the log-mean temperature becoming undefined.

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