Time for heating to equilibrium with constant heat flux

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SUMMARY

The discussion focuses on deriving an equation to describe the heating process of a cylindrical metal subjected to a constant heat flux. The key equation presented is H = kA (dt/dx) = constant, leading to the integration of Hdx = kA dt. This indicates that the temperature of the metal varies linearly with distance until it reaches equilibrium. The goal is to create a temperature-time graph to determine the time required for the metal to achieve thermal equilibrium.

PREREQUISITES
  • Understanding of heat transfer principles
  • Familiarity with differential equations
  • Knowledge of thermal conductivity (k) and heat flux (H)
  • Basic concepts of cylindrical coordinate systems
NEXT STEPS
  • Research the derivation of the heat equation in cylindrical coordinates
  • Learn about thermal equilibrium and its implications in heat transfer
  • Explore numerical methods for solving differential equations related to heat transfer
  • Investigate software tools for simulating heat transfer processes, such as ANSYS or COMSOL Multiphysics
USEFUL FOR

Engineers, physicists, and students involved in thermal analysis, particularly those working with heat transfer in cylindrical geometries.

Komakech
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I have the following scenario and hope one of you can help me. I need to find an equation describing a heating process. A cylindrical metal of known dimensions and properties is heated from one side while the temperature of the other side is kept constant. I need to find the equation describing the temperature rise of the side being heated until it reaches equilibrium, so that from it, one can obtain a temperature time graph and know how long it takes to reach equilibrium.

Or rather does anyone know of an equation that can be used to describe how long a piece of metal being heated with constant heat flux takes to reach equilibrium temperature?
 
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Ok. If a constant amount of heat is supplied, then H=kA dt/dx=constant. Hdx=kA dt. Integrating from 0 to x and 0 to t. kA (t)=H(x). This would make it seem like the temperature varies linearly... with distance? Dunno... sorry can't be of much help...
 

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