Question

# Heat Transfer,

Why the ratio of (thermal resistance of conduction)/(thermal resistance of convection) must be less than .1 for a system to lumped.

 

Answer 1

Biot Number :

It is the ratio of internal resistance of body which is conduction resistance to external resistance which is heat convection. It is key parameter for applying Lumped System Analysis & is similar to Nusselt Number.

Lumped System :

In heat transfer, some bodies are observed to behave like “Lump” whose interior temperature remains essentially uniform at all time during heat transfer(isothermal/uniform temp. distribution). So, lumped System is only applicable if temperature distribution is uniform at all time.

Significance of Biot Number in Lumped System Analysis :

In Lumped System Analysis, body temp. is uniformly distributed i.e. isothermal . So, when thermal resistance of body to heat conduction is zero otherwords, Bi = 0, lumped system analysis is exact & Bi > 0, lumped system analysis is approximated. But 15 % uncertanity in convection heat transfer co effecient, h in most cases is considered normal & expected. Thus it is generally accepted that lumped system is applicable if Bi <= 0.1