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Heat Transfer > ALL OF CONDUCTION TO MEMORISE > Flashcards

ALL OF CONDUCTION TO MEMORISE Flashcards

1
Q

what is temp?

A

A measurement of one type of energy that exists in a substance. This can be considered to be the K.E possessed by the atoms and molecules.

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2
Q

If we increase the KE of a noble gas, what happens?

A

Because noble gases are made up of atoms and not molecules it is safe to assume all KE will be used to increase the velocity of the gas atoms.

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3
Q

If we increase the KE of a non atomic gas (made of molecules) what happens?

A

It is possible for some of the KE to be absorbed in making the molecules vibrate and rotate, so not all KE translates to velocity. BUT WE CAN OFTEN IGNORE THIS.

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4
Q

How does a liquid behave differently to a gas?

A

The distance between atoms / molecules is much smaller, it is also less valid to assume elastic interactions between atoms/molecules. (elastic interactions are those which don’t involve loss of KE)

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5
Q

What does increasing temp do to atoms in a solid?

A

Atoms and molecules are tied in place by bonds here so increased temp causes them to vibrate vigorously around their mean positions. If temp is increased further the vibrations can become so large that the bonds break and the solid melts or decomposes.

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6
Q

What is heat?

A

The flow of energy that results from temp gradients

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7
Q

What is Fouriers law and what is its other name?

A

q/A is directly proportional to dt/dx.. the law of heat conduction

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8
Q

Describe conduction on a microscopic scale?

A

Rapidly moving or vibrating atoms / molecules interact with one another transferring some of their KE.

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9
Q

Why are fluids less conductive than solids?

A

Because the large distance between atoms means less likely collisions to occur and so less conduction.

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10
Q

Does conductivity increase or decrease with temp?

A

increase

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11
Q

Draw the pressure vs conductivity graph and describe it?

A
  1. Radiation dominates 2. Pressure increasing causes conductivity to increase due to more particles per unit volume so more collisions 3. At a certain point the mean free path is such that the particles are expected to collide with each other before transferring heat from one surface to another.
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12
Q

How is heat transferred by conduction in a solid?

A

When adjacent atoms vibrate against one another or as electrons move through the the solid between atoms (for conductive solids)

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13
Q

Why is conduction greater in solids?

A

Because the network of relatively fixed spatial relationships between atoms helps to transfer energy between them by vibration.

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14
Q

What is the zeroth law of thermodynamics?

A

If two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

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15
Q

What is the first law of thermodynamics?

A

dU = dQ - dW

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16
Q

What is the second law of thermodynamics?

A

dS>=0

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17
Q

What is the third law of thermodynamics?

A

s=0 when T=0

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18
Q

What assumptions does the Kinetic Theory of Gases rely on?

A
  1. The particles are so small that the overall volume of all the particles added up is negligible compared to the volume of the container.
  2. These particles all have the same mass.
  3. The number of particles is large enough for statistical treatment to be applied.
  4. The particles are in constant rapid and random motion
  5. The particles constantly collide with themselves and the walls of the container. All of these collisions are perfectly elastic.
  6. Except during collisions, the interaction between particles is negligible.
  7. The average KE of the gas particles depends only on the temp of the system.
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19
Q

Eqn describing the KE of a single particle?

A

0.5mv^2=1.5k_bT

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20
Q

How can heat be transferred between 2 solid surfaces via an intermediate fluid?

A

Particles in a fluid can gain KE by colliding with a hot surface. By the opposite action the can lose KE by colliding with a cold surface.

21
Q

What is mean free path?

A

The mean distance a particle will travel before colliding with another particle

22
Q

Eqn for mean free path?

A

lambda = k_bT/(sqrt(2)pid^2P)

23
Q

What does the thermal conductivity of a gas depend on?

A

Temp, pressure and heat capacity (amount of energy each particle is capable of carrying).

24
Q

Eqn for calculating the conductivity of ideal gases?

A

k= nvlambda*c_v/3N_a

25
Q

what are phonons?

A

Normal modes of vibrations which have wave and particle like properties (analogous to photons of light). Phonons propagate through a solid at the speed of sound in that solid but are scattered by boundaries, defects and other phonons in the solid. This scattering limits the transport of heat through the solid.

26
Q

What is the dominant conduction mechanism in solids which conduct electricity?

A

Free-moving electrons rapidly transfer thermal energy. The ‘electron fluid’ of a conductive metallic solid conducts nearly all of the heat flux through the solid.. phonon flux still present but only transfers around 1%

27
Q

How does liquid conduction differ with solid/gas conduction?

A

Has characteristics of both. In general, there is greater particle-particle interaction than in a gas. However bonding is less rigid than in a solid so phonon flux is less.

28
Q

What is steady seat heat conduction?

A

The temp at every point within an object doesn’t change with time. The amount of heat entering any region is the same as the amount leaving + work done by the heat.

29
Q

What is transient heat conduction?

A

Appears after an imposed change in temp at a boundary of an object so that the temps within the system will change in time toward a new equilibrium with the new conditions.

30
Q

What is lumped system analysis and what does it assume?

A

An approximation to simplify otherwise complex differential heat equations: -reduces the thermal system to a number of discrete regions - assumes the temp difference within each region is negligible.

31
Q

How does steady state conduction relate to electrical circuits?

A

Voltage temp difference (dT)
Current heat transfer rate (q)
Resistance thermal resistance (Rth = dx/kA)

32
Q

What are the assumptions of lumped system analysis?

A
  1. The individual discrete regions that the model has been simplified down to are homogeneous (so they have a single thermal resistance value).. complex materials must be broken down.
  2. Thermal variation within a single region is not considered
  3. It is assumed that the model is unchanging with time (purely resistive model (no capacitance) means it is not capable of absorbing energy).
  4. The approach cannot be relied upon for nano or micro scale thermal behaviour.
33
Q

Eqn for thermal resistance of a tube and can you derive it?

A

Rth = ln(r2/r1)/2Pik*L

34
Q

How can convection be added to the lumped system analysis model?

A

N’s Law of cooling: q=hA(dT) => q=(dT)/1/hA == I=V/R

Rth = 1/hA, where A=2Pir*L for a tube

35
Q

Why is the contact between different layers of material not necessarily thermal resistance free?

A

Due to surface roughness (micro/nano scale) preventing perfect contact. So there are pockets of air in the voids.

36
Q

How do you take account of contact resistance?

A

hc –> contact conductance

Rth = 1/hc*A

37
Q

What is the lumped capacitance model and when can it be used?

A

A common approximation in transient conduction. May be used whenever heat conduction within an object is much faster than heat conduction across the boundary of an object. The changing uniform temp within the object or part of a system can then be treated like a capacitate reservoir which absorbs heat until it reaches a steady thermal state in time. NOTE assumption of temp within the part is uniform but changing uniformly with time.

38
Q

What is an example of a lumped capacitance model?

A

N’s law of cooling: states that the temp of a hot or cold object progresses towards the temp of its environment in a simple exponential fashion.

39
Q

What is biot number?

A

A number which tells us whether the assumption of uniform temp within an object is a safe one.

40
Q

What is the eqn for biot number?

A

Bi = h(V/A)/k

41
Q

What does a biot number less than 0.1 indicate ?

A

Bi

42
Q

What does a biot number

A

The thermal resistance to heat transferred into the object is larger than the resistance to heat being diffused completely within the object.

43
Q

Equation used for the lumped capacitance model?

A

(T-T§)/(To-T§) = exp(-(hA/rho.c.V)tao)

44
Q

What is specific heat capacity a function of?

A

The structure of the substance itself.

45
Q

The larger the what the larger the specific heat capacity?

A

The KE is only one of the many DOF which manifests as temp change, and thus the larger the no. of DOF available to the particles of a substance other than KE, the larger the specific heat capacity.

46
Q

In > 1D conduction what do m and n indicate?

A

m - nodal position in x
n - nodal position in y
The smaller the dx and dy the closer the approx to reality.

47
Q

At steady state what is the net heat flow into each node?

A

net heat flow into each node = 0

48
Q

What does Fouriers law become for >1D conduction problems?

A

q=SUM(kdxdT/dy)

Heat Transfer (15 decks)

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