Heat transfer equation - formulation

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SUMMARY

The discussion centers on the formulation of the heat transfer equation for a device heated internally by Joule's heat. The equation presented is dQ = CdT1 + γ(dT2)dt, where dQ represents the heat added, C is the heat capacity, γ is the heat loss coefficient, and dt is the time differential. The user seeks clarification on the term dT2, questioning whether it refers to the temperature differential of the device or the difference between the device's instantaneous temperature and the surrounding temperature. Understanding the correct interpretation of dT2 is crucial for accurately calculating heat loss.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the concepts of heat capacity and heat loss coefficients.
  • Basic knowledge of differential equations and their application in physical systems.
  • Experience with Joule heating and its effects on temperature variations.
NEXT STEPS
  • Research the derivation and application of the heat transfer equation in thermodynamics.
  • Study the concept of heat loss coefficients and their calculation methods.
  • Learn about differential calculus as applied to temperature changes over time.
  • Explore experimental methods for measuring heat capacity and heat loss in materials.
USEFUL FOR

This discussion is beneficial for thermal engineers, physicists, and researchers involved in heat transfer analysis and device thermal management.

rammer
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Hi, I have a device which is heated from inside by constant heat (let's say by Joule's heat - UIt). Some heat causes temperature rise of the device, some is lost into surroundings through device's surface. I measured how temperature of the device varies with time and I want to calculate constants like heat capacity of the device and heat loss coefficient.

But I'm not sure whether my equation is correct:

dQ = CdT1 + γ(dT2)dt

dQ=UIdt
C - heat capacity of the device
γ - heat loss coefficient
dt - time differential
dT1 - temperature differential (of the device per dt)

I'm confused about last expression in the equation: What does dT in the expression γ(dT2)dt mean? Is it the same as dT1 or is it rather instantaneous temperature of the device minus temperature of surroundings?
 
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Anyone? I just need in what form/terms we express heat loss...
 

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