Lecture 5 - Beyond 1D conduction (DOBSON) Flashcards
The smaller the delta x and delta y the what?
More realistic approximation
The equation for steady state thermal resistance approach to a multidimensional problem?
q_i + SUM_j ((Tj-Ti)/Rij) = 0 , Ti = temp of a node, qi= heat generated/radiation etc. and Rij = resistance between 2 nodes.
Equation for thermal capacitance for a multidimensional approach?
Ci = rho_ic_iV_i
How to calculate energy at a given time?
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
Equation relating heat flow into / out of the object?
q_i + SUM_j ((Tj^P-Ti^P)/Rij) = Ci(Ti^(P+1)-Ti^(P))/delta_t
What matter emits electromagnetic radiation?
All matter above absolute zero.
What does radiation represent?
A conversion of a body’s thermal energy into electromagnetic energy.
What matter absorbs electromagnetic radiation?
All matter to some degree.
What is a black body?
An object that absorbs all radiation falling on it, at all wavelengths.
What happens when a black body is at uniform temp?
Its emission has a characteristic frequency distribution that depends on the temperature: it’s emission is called black-body radiation.
What is planck’s law of radiation?
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.
What is Wien’s displacement law used for and what is it?
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.
Eqn for total amount of energy emitted by a black body?
Eb=σT^4 where σ= stefan-boltzmann constant (5.67x10^-8 W/m^2K^4), Eb= energy radiated per unit time and area.
Can you draw the graph of central wavelength and energy? What important point can be taken from this?
YES OR NO. Most importantly - radiative heat transfer becomes more important the higher the temp of the system.
What happens to radiation when it is incident on a surface? What is the equation combining these?
DRAW DIAGRAM: some absorbed, some transmitted, some reflected. Equation: rho( fraction reflected) + alpha( fraction absorbed) + tao(fraction transmitted) = 1.
How can the equation with fractions of radiation be simplified?
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.
If an object is placed in a black enclosure and allowed to come to thermal equilibrium we can state:?
EA = qiAα where E = amount of radiation emitted, A=area, qi=flux of incident radiation, α=fraction of radiation absorbed.
If we replace the object in the same black enclosure with an object that is 100% absorbing (BLACK BODY) we can say:?
EbA=qiA (α=1)
Dividing the two equations together gives?
E/Eb= α = ε (emissivity)
What does a larger emissivity mean?
Closer to black body behaviour.
Can you draw the graph relating emissive power to wavelength and emissivity?
YES OR NO
What do we have to remember to consider when we are considering an optical phenomenon?
SHAPE FACTORS, can be looked up for common geometries.
