Lecture 3 - Lumped System Analysis (DOBSON)

Question 1

What is lumped system analysis and why is it useful?

Answer 1

This approximation is useful to simplify otherwise complex differential heat equations. Reduces the thermal system to a no. of distinct regions. Assumes the temp difference inside each region is negligible.

Question 2

Can you draw the graph of temp vs distance for brick-insulation-blocks as part of a wall? And also the flow diagram?

Answer 2

YES OR NO

T1 -> Fbr -> T2 -> Fi -> T3 -> Fbl -> T4

Question 3

What would a better represntation of the temp variation in the wall system?

Answer 3

Temp variation within the discrete regions. DRAW GRAPH.

Question 4

How can the maths of DC electrical conduction be applied to hear currents?

Answer 4

Thermal Resistances -> electrical resistances
Temperature -> voltage
Heat flux -> electrical current

Question 5

Fouriers law?

Answer 5

q= kA dT/dx = dT/dx/kA

Question 6

what does dx/kA represent?

Answer 6

A description of how well the particle conducts heat as a result of its size, shape and material therefore:
dx/kA = Rth and q = dT/Rth, which is equivalent to ohms law. (q= I, dT = V, Rth = R).

Question 7

What are the assumptions and approximations of this method?

Answer 7

The individual discrete regions that the model has been simplified down to are homogeneous:
- complex materials (e.g. composites) need to be simplified to produce a single thermal resistance value.
- thermal variations within a single region are not considered.
It is assumed that the model is unchanging with time:
- this is due to the fact that, as a purely resistive model (no capacitance), no part of the model is capable of absorbing energy.
The approach can not be relied upon to model micro and nano scale thermal behaviour.

Question 8

How can we consider conduction through a plane?

Answer 8

By integrating fourier’s law to give:- q= (-kA/deltax)(T2-T1)
q = heat transfer rate
delta x = thickness of plane
k = thermal conductivity
A = area of plane
T2 - T1 = thermal difference across the plane

Question 9

Can you write the expression from conduction through a plane in a form analogous to an electrical circuit?

Answer 9

HEAT FLOW = THERMAL POTENTIAL DIFFERENCE / THERMAL RESISTANCE