Question

heat transfer question, show equations, assumptions, calculations and steps clearly. will give thumbs up rating if solved correctly in 50 minutes

part a:

What is the Lumped Capacitance Method, what does it assume, and for which criteria is it valid?

part b:

When part of a system is perfectly insulated, how do we translate this mathematically as a boundary condition?

part c:

State three important assumptions that must be respected for the thermal resistance concept to be valid in a plane wall.

Answer 1

Lumped capacitance it is a method to solve unsteady state problem.

It assumes that the temperature of the solid in
question is spatially uniform at any given instant during a transient process. It implies that temperature gradients within the solid are negligible.
The second major assumption of the lumped capacitance method is that that resistance to
conduction within the solid is small compared to the resistance to heat transfer between the solid and it's surroundings.

Validity: Biot number Bi=(h*L)/k

When Bi << 1, the resistance to conduction within the solid is much less than the
resistance to convection across the fluid boundary layer. This means that the assumption
of a uniform temperature distribution is reasonable.

Part b:

When part of a system is perfectly insulated, then temperature gradient is zero. Mathematically it will be represented as

Part c

three important assumptions that must be respected for the thermal resistance concept to be valid in a plane wall.

1 Heat transfer through the wall is steady since
2 Heat transfer through the wall is one-dimensional
3 Thermal conductivity is constant.