Lecture 4 - Advanced 1D Conduction (DOBSON) Flashcards
What is the thermal resistance equation for heat flow inside a cylinder?
Rth = ln(r_o/r_i)/2Pik*L
If the surface of a cylinder is undergoing natural convection, what does the thermal resistance become?
Rth= 1/2Pir_oLh
Why is it often not the case that when two materials are brought together their contacting surface temperatures are the same?
Normally considered to be due to surface roughness, preventing a perfect contact.
How can we calculate the surface contact thermal resistance?
Rth = 1?h_c*A, where h_c is the contact conductance coefficient.
When can a lumped capacitance model be used?
Whenever heat conduction within an object is much faster than heat conduction across the boundary of the object. The changing uniform temp within the object or part of a system, can then be treated like a capacitate reservoir which absorbs heat until it reaches a steady thermal state in time.
Example of a lumped capacitance model?
Newton’s law of cooling: the temp of a hot (or cold) object will progress toward the temp of its environment in a simple exponential fashion.
Most important assumption with lumped system analysis?
The temp within the part is uniform
What does the Biot number do?
Allows us to asses whether it is safe to assume the temp within a part is uniform.
What is the limit for Biot number?
If Bi < 0.1 , surface convection/conduction is small enough compared to internal conduction: internal temp distributions should be uniform.
Equation for Biot number?
Bi = h(V/A)/k
When is the Biot number <1?
When the thermal resistance to heat transferred into the object is larger than the resistance to heat being diffused within the object. Must be <1 for usefully accurate approximation and heat transfer analysis.
If the Biot number is not small enough what can we do?
Break the system down into a sufficient number of sections so that Bi becomes small enough (since Bi depends on characteristic length).
What is heat capacity?
The amount of heat required to change a substance’s temp by a given amount (J/K).
What is specific heat capacity?
The heat capacity per unit mass of a material (J/kgK)
What does doubling the amount of substance do to the heat capacity?
Doubles it
