Heat Transfer

Deals with specifics of one form of energy transfer (heat transfer)

Heat Transfer

Thermal energy transfer over space and time

Heat Transfer (Driving Force)

Energy can enter and leave a system by heat transfer Q, which is caused by a temperature difference (Delta T) between the system and surroundings.

If $T_A$ > $T_B$ heat is transferred out of the system (Q is -)
Q is + if the case is the other way around.

Heat (Process, not a property, quantified across a boundary):
$q=\frac{Q}{m}$

Modes of Heat Transfer

Three modes of heat transfer (May occur simultaneously):

• Conduction (molecular diffusion)
• Convection (bulk fluid motion)
• Radiation (electromagnetic waves)
  

Heat Transfer (Driving Force)

Energy can enter and leave a system by heat transfer Q, which is caused by a temperature difference (Delta T) between the system and surroundings.

If T_A > T_B heat is transferred out of the system (Q is -)
Q is + if the case is the other way around.
Heat (Process, not a property, quantified across a boundary):
$q=\frac{Q}{m}$

Modes of Heat Transfer

Three modes of heat transfer (May occur simultaneously):

• Conduction (molecular diffusion)
• Convection (bulk fluid motion)
• Radiation (electromagnetic waves)

Heat Added

$\Delta U=Q-W$

Isothermal processes

If the current process is isothermal, then…

$$\Delta U=0$$

But funny enough…

$$\Delta Q\ne 0$$

So for isothermal processes, you can have heat transfer but no change in internal energy

---

Post-Midterm Content

We mainly deal with thermal energy transfer over space and time.

Intro to Conduction

Conduction

Heat transfer due to molecular motion (diffusion) from more energetic molecules to less energetic ones

Due to:

• Intermolecular collisions
• Lattice vibrations
• Free electron motion in solids Governed by Fourier’s Law in any direction in: $Q_n^{\prime }=-k\frac{\delta T}{\delta n}$
  Where:
• Q” = Our heat flux (heat flowing through an area) [w/m^2]
• k = Thermal conductivity [w/m*K]

E.g Conduction through a plane wall (1-D)
$Q_x^{\prime }=-k\frac{dT}{dx}=-k\left(\frac{T_2-T_1}{L}\right)$

Intro to Convection

• Heat transfer from one location to another due to movement of a fluid
• Governed by Newtons law of cooling in units of [w/m^2] and [w] respectively $Q_s^{\prime }=h\left(x\right)\left(T_s-T_{\infty }\right)$
  $Q_s^{\prime }=\overline{h}A\left(T_s-T_{\infty }\right)$ h depends on flow patterns of fluid properties

Intro to Radiation

• All matter emits electromagnetic radiation due to spontaneous fluctuations in quantum energy states
• The energy of these emissions depend on the absolute temperature of the substance
• A blackbody is an idealized object (ideal absorber and emitter)
  

Blackbody emissive power
$E_b=\sigma T_s^4$
Where $\sigma =5.67\cdot 10^{-8}$

Real surfaces emit less radiation
$E=ϵ\sigma T_s^4$
Where $0<ϵ<1$ and that is the emissivity

Surfaces also absorb irradiation from other surfaces so the net radiation leaving the surface is

$Q^{{}^{\prime }}=ϵE_b=-\alpha G$
Where:

• Alpha = Absorptivity 0 < alpha < 1
• G = Irradiation [w/m^2]

Kirchoff’s (thermal) law
$ϵ=\alpha$
$Q_{net}^{\prime }=ϵ\sigma \left(T_s^4-T_{surr}^4\right)$
$Q_{net}^{\prime }=h_{rad}\left(T_s^{}-T_{surr}^{}\right)$
Where $h_{rad}$ is ($T_s$, $T_{surr}$)

More on Modes of Heat Transfer

Includes Thermal Circuits and Conduction and Convection and Radiation.

Conduction and convection happens through Heat Transfer Fins which makes them very effective for heat transfer.

For transient problems, the temperature of a body changes over time but it is often useful to treat the whole body as one uniform temperature at any given time using the Transient Heat Transfer.