Lecture 5 - Beyond 1D conduction (DOBSON)

Question 1

The smaller the delta x and delta y the what?

Answer 1

More realistic approximation

Question 2

The equation for steady state thermal resistance approach to a multidimensional problem?

Answer 2

q_i + SUM_j ((Tj-Ti)/Rij) = 0 , Ti = temp of a node, qi= heat generated/radiation etc. and Rij = resistance between 2 nodes.

Question 3

Equation for thermal capacitance for a multidimensional approach?

Answer 3

Ci = rho_ic_iV_i

Question 4

How to calculate energy at a given time?

Answer 4

deltaE/delta_t=Ci(Ti^(P+1)-Ti^(P))/delta_t, where E is internal energy, P is a time increment and t is time

Question 5

Equation relating heat flow into / out of the object?

Answer 5

q_i + SUM_j ((Tj^P-Ti^P)/Rij) = Ci(Ti^(P+1)-Ti^(P))/delta_t

Question 6

What matter emits electromagnetic radiation?

Answer 6

All matter above absolute zero.

Question 7

What does radiation represent?

Answer 7

A conversion of a body’s thermal energy into electromagnetic energy.

Question 8

What matter absorbs electromagnetic radiation?

Answer 8

All matter to some degree.

Question 9

What is a black body?

Answer 9

An object that absorbs all radiation falling on it, at all wavelengths.

Question 10

What happens when a black body is at uniform temp?

Answer 10

Its emission has a characteristic frequency distribution that depends on the temperature: it’s emission is called black-body radiation.

Question 11

What is planck’s law of radiation?

Answer 11

A way to calculate the intensity of radiation as a function of wavelength and temp: B_λ(T)=(2hc^2/λ^5)(1/e^(hc/λk_bT)-1).
Where B = spectral radiance, T=abs temp, λ=wavelength, c=speed of light, k_b=Boltzmann constant, h=planck constant.

Question 12

What is Wien’s displacement law used for and what is it?

Answer 12

If we are only interested in the value for peak wavelength. λ=b/T where λ= peak wavelength, T= abs temp, b=Wien’s displacement constant.

Question 13

Eqn for total amount of energy emitted by a black body?

Answer 13

Eb=σT^4 where σ= stefan-boltzmann constant (5.67x10^-8 W/m^2K^4), Eb= energy radiated per unit time and area.

Question 14

Can you draw the graph of central wavelength and energy? What important point can be taken from this?

Answer 14

YES OR NO. Most importantly - radiative heat transfer becomes more important the higher the temp of the system.

Question 15

What happens to radiation when it is incident on a surface? What is the equation combining these?

Answer 15

DRAW DIAGRAM: some absorbed, some transmitted, some reflected. Equation: rho( fraction reflected) + alpha( fraction absorbed) + tao(fraction transmitted) = 1.

Question 16

How can the equation with fractions of radiation be simplified?

Answer 16

Thermal radiation is normally in the infrared, a wavelength at which very few materials are transparent. Therefore in most situations we can say: rho + alpha = 1.

Question 17

If an object is placed in a black enclosure and allowed to come to thermal equilibrium we can state:?

Answer 17

EA = qiAα where E = amount of radiation emitted, A=area, qi=flux of incident radiation, α=fraction of radiation absorbed.

Question 18

If we replace the object in the same black enclosure with an object that is 100% absorbing (BLACK BODY) we can say:?

Answer 18

EbA=qiA (α=1)

Question 19

Dividing the two equations together gives?

Answer 19

E/Eb= α = ε (emissivity)

Question 20

What does a larger emissivity mean?

Answer 20

Closer to black body behaviour.

Question 21

Can you draw the graph relating emissive power to wavelength and emissivity?

Answer 21

YES OR NO

Question 22

What do we have to remember to consider when we are considering an optical phenomenon?

Answer 22

SHAPE FACTORS, can be looked up for common geometries.