Calculating Thermal Energy of Hot Air Flow

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Discussion Overview

The discussion revolves around calculating the thermal energy of hot air, specifically the exhaust air from a chimney, with a focus on the temperature and flow rate parameters. Participants explore the theoretical and practical aspects of thermal energy calculations in this context.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant inquires about the method to calculate thermal energy for hot air at 250°C with a flow rate of 11,000 m³/h.
  • Another participant suggests using the mass flow rate multiplied by specific internal energy, noting that mass flow rate is derived from volumetric flow rate and density, which depend on pressure and temperature.
  • A third participant adds that the temperature difference should be considered, implying it is between the hot air and the outside air temperature.
  • The original poster seeks clarification on the temperature difference, indicating they want to calculate the thermal energy of air at 200°C without heating it further.
  • One participant reiterates the need to multiply mass flow rate by specific internal energy, emphasizing that specific internal energy is a function of temperature for ideal gases and that the exhaust temperature should be used.
  • Another participant introduces the first law of thermodynamics for open systems, suggesting a formula involving heat transfer based on intake and exhaust temperatures, but acknowledges that this may not align with the original poster's intent.

Areas of Agreement / Disagreement

Participants present multiple approaches and interpretations regarding the calculation of thermal energy, indicating that there is no consensus on the specific method or parameters to be used.

Contextual Notes

Participants mention dependencies on temperature, pressure, and specific heat capacities, but do not resolve the implications of these factors on the calculations.

wat681
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haw can i calculate the thermal energy (watt or BTU ) of the hot air (or the exhaust air of the chimney) according to the following :

Temp. : 250 C
hot air flow rate : 11 000 m3/h


thanks
 
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You need to multiply the mass flow rate by the specific internal energy.

Mass flow rate equals the volumetric flow rate times the density, which is a function of pressure and temperature. Specific internal energy is a function of pressure and temperature, or just a function of temperature for an ideal gas.
 
You alsoneed to subtract the temp of the outside air.
 
thanks for reply
i got the following formula for the thermal energy :

Flow rate (m3/h) * Density (Kg/m3) * specific energy (KJ/Kg K) * temp. deference (K)

my question , what is the temperature deference ? is it between the hot air and the atmosphere temperature ?
because i don't want to heat this air i Have the hot air at 200 C and want to calculate the thermal energy of it


thanks
 
If you just want the thermal energy of the exhaust, do what I originally said. You need to multiply the mass flow rate by the specific internal energy [kJ/kg], which is just a function of the temperature for an ideal gas (u=2.5*R*T for a diatomic gas). The temperature you should use is the exhaust temperature.

Now, on the other hand, if you are looking for the heat from combustion, you can apply the first law for an open system and find the Q=m_dot*(h_out-h_in)=m_dot*c_p*(T_out-T_in), where T_in would be the intake temperature, and T_out would be the exhaust temperature and this is likely the temperature difference russ was referring to. But it sounds like that is not what you are looking for, so just refer to my original response.
 

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