Undefined log-mean temperature in heat exchanger design

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Discussion Overview

The discussion revolves around the calculation of the log-mean temperature difference in the design of a heat exchanger for cooling electronic components in a UAV. The focus is on the parameters and assumptions related to the temperatures of the cold air and hot fluid sides, as well as the implications of these values on the calculations.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a heat exchanger design scenario, detailing the properties of the cold air and hot ethylene glycol-water solution, and raises a question about the calculation of the log-mean temperature difference.
  • The calculation for the log-mean temperature difference yields a negative value inside the logarithm, which prompts the participant to question the temperatures used for the hot side.
  • There is uncertainty expressed regarding the assumed cabin temperature of -20 °C and its impact on the outlet temperature of the cold air side, which is calculated to be 4.87 °C.
  • Another participant seeks clarification on the significance of the outlet temperature of 4.87 °C, indicating confusion about its plausibility given the inlet temperatures.
  • Further comments reiterate the concern about the outlet temperature of 4.87 °C, questioning whether it is reasonable for the outlet air temperature to increase from -34.5 °C to 4.87 °C.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the calculated outlet temperature and the assumptions made regarding the inlet temperatures. There is no consensus on the correctness of the temperatures or the implications for the heat exchanger design.

Contextual Notes

Participants have not resolved the assumptions regarding the cabin temperature and its effect on the heat exchanger calculations. The discussion highlights potential limitations in the assumptions made about the thermal properties and conditions of the system.

mastermechanic
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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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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
 
256bits said:
4.87 C

Sorry, I didn't understand what you meant. What's wrong with 4.87?
 
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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