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Chem Eng - Y1.S2 > Transport Phen - Heat Transfer > Flashcards

Transport Phen - Heat Transfer Flashcards

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1
Q

What are the 3 types of heat transfer?

A

Conduction
Convection
Radiation

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2
Q

What are the properties of conduction?

A

If a temperature gradient exists in a continuous substance (solid, liquid or gas) heat can flow without any motion of matter

This is due to the transfer of vibrational energy of molecules, and also electrons (important for metals).

Heat conduction can be quantified by Fourier’s law

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3
Q

What is Fourier’s law?

A

Fourier’s law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows.

dq/dA = -k*dT/dx

Where:
q is rate of heat flow in direction normal to surface
A is surface area (m2)
T is temperature (K)
x is distance (m)
k is proportionality constant or thermal conductivity of a substance.

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4
Q

What’s the formula for Fourier’s law?

A

dq/dA = -k*dT/dx

Where:
q is rate of heat flow in direction normal to surface
A is surface area (m2)
T is temperature (K)
x is distance (m)
k is proportionality constant or thermal conductivity of a substance.

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5
Q

What are properties of convection?

A

Convective heat transfer is the flow of heat associated with the movement of a fluid.

It is comprised of two mechanisms:
heat conduction and energy transfer from to the fluid (enthalpy/kinetic energy changes).

Convective heat transfer means the superposition of the energy transport by heat conduction and energy transport by the flowing fluid.

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6
Q

What is k (used in Fourier’s law)?

A

A weak function of temperature; over a small temperature range k may be considered constants (depends also on desired accuracy of results).

Generally k.solid > k.liquid >k.gas insulators entrap air and eliminate convection (some insulators may also reflect radiation rather than absorbing it).

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7
Q

How can heat transfer by convection be calculated?

A

q/A = h(Ts - Tf)

Where:
q is rate of heat flow
A is surface area
h is heat transfer coefficient (W/m2K)
Ts is surface temperature 
Tf is bulk temperature of fluid
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8
Q

What are the types of convection?

A

Natural

Forced

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9
Q

What is natural convection?

A

Convection due to density differences in the fluid occurring due to temperature gradients which generate the fluid’s motion (no external force e.g. a pump or a fan is involved).

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10
Q

What is forced convection?

A

Convection where the flow of the fluid is caused by an external source and is widely independent of density differences.

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11
Q

What are the properties of radiation?

A

It is energy in the form of electromagnetic waves by any matter above 0K.
It can occur in a vacuum.

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12
Q

What is emissive power and how is it determined?

A

It is the energy of thermal radiation emitted in all directions per unit time from each unit area of a surface at any given temperature.

Eb = σTs⁴
Where
σ - Stefan-Boltzmann constant
T - absolute temperature

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13
Q

What is heat flux and how is it determined?

A

The flow of energy per unit of area per unit of time.

E = εσTs⁴
Where
σ - Stefan-Boltzmann constant
T - absolute temperature
ε - emissivity (measures how efficiently a surface emits energy relative to a blackbody)

Real surfaces do not emit in a perfect way therefore an emissivity ε needs to be introduced: 0 < ε < 1

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14
Q

What’s a heat exchanger?What are its requirements?

A

A Heat Exchanger (HX) is a device for the efficient heat transfer from one medium to another

Requirements:
1 - There is two streams S1 and S2
2 - At two different temperatures T1 and T2 (T1 ≠ T2)
3 - No mixing

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15
Q

What are double-pipe heat exchangers?

A

The simplest heat exchanger construction consists basically of two pipes stacked into each other.

E.g. pipe of hot fluid through pipe of cold fluid.
Can be parallel and counter flow.

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16
Q

What’s a shell-and-tube HX?

A

The most common heat exchanger in industry.

It consists of a shell (a large pressure vessel) with a bundle of tubes inside it. One fluid runs through the tubes, and another fluid flows over the tubes (through the shell) to transfer heat between the two fluids.

Baffles are an integral part of the shell and tube heat exchanger design. A baffle is designed to support tube bundles and direct the flow of fluids for maximum efficiency.

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17
Q

What’s a plate HX?

A

A type of heat exchanger that uses metal plates to transfer heat between two fluids.

A plate exchanger consists of a series of parallel plates that are placed one above the other so as to allow the formation of a series of channels for fluids to flow between them.

The space between two adjacent plates forms the channel in which the fluid flows.

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18
Q

Properties of shell-and -tube HX:

A

Good value for money
Heavy
Not used in transport applications

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19
Q

Properties of plate HX:

A

Plate HX cannot take large pressure differences (liquid to liquid operations work best)

Easy to clean

Easy to add / remove plates

Different plate geometries to increase turbulence

Widely used in dairy and food industry because easy to clean and sanitise

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20
Q

What are compact heat exchangers?

A

HX specifically designed to realize a large heat transfer surface area per unit volume.

Compactness and a large area is achieved through thin plate design, fins and special flow conditions e.g. cross flow.

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21
Q

What’s a spiral heat exchanger?

A

HX with two flat surfaces curled into each other.

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22
Q

What are regenerative HX?

A

A type of heat exchanger where heat from the hot fluid is intermittently stored in a thermal storage medium before it is transferred to the cold fluid.

To accomplish this the hot fluid is brought into contact with the heat storage medium, then the fluid is displaced with the cold fluid, which absorbs the heat.

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23
Q

How can Fourier’s law be written to account for thermal resistance?

A

Q = kA* ΔT/L

Where Q = ΔT / R

And R = L/kA

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24
Q

What’s ohms law?

A

V = IR

V proportional to I and R (for constant temp)

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25
Q

How can Newton’s law of cooling (convection heat transfer) be written to consider Herman resistance?

A

Q = hA(Ts - Tf)

Can be written:
Q = (Ts - Tf) / R

R = 1 / hA

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26
Q

How is the radiation heat transfer law written to consider thermal resistance?

A

Q = εσA(Ts⁴ - T𝒻⁴)

Can be written:

(Ts⁴ - T𝒻⁴) / R

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27
Q

How is overall heat transfer calculated?

A

Q = UAΔT

Where U is overall heat transfer coefficient (W/m2K)

U is equal to the inverse of total thermal resistance

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28
Q

How can total thermal resistance of composites be calculated?

A

By finding the sum of conductive, convective and radiative thermal resistances in the system.

R 𝒸ₒₙ = L / kA

R 𝒸ₒₙᵥ = 1 / hAₛ

R ᵣₐ𝒹 = = 1 / h(ᵣₐ𝒹)Aₛ

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29
Q

What does T∞ mean (in terms of heat transfer and heat transfer calculations)?

A

Surrounding temperature

30
Q

How is heat transferred in cylinders?

A

Assuming the inner and outer surfaces of a pipe are exposed to fluids at different temperature. And that temperature inside and outside remain constant over time.

  • No temperature change in axial direction
    (along length of tube)
  • Heat flows only in radial direction (here towards the outside)
31
Q

From Fourier’s law, how can thermal resistance of a sphere and cylinder be found?

A

R cyl = ln (r2 / r1) / 2πLk

R sph = (r2 - r1) / 4πr1r2k

32
Q

How does outer insulation area vary with thickness for pipes?

A

Insulation area increases with thickness.

33
Q

What’s critical thickness (of insulation)

A

The thickness upto which heat flow increases and after which heat flow decreases is termed as critical thickness.
In the case of cylinders and spheres it is called critical radius.

It can be derived the critical radius of insulation depends on the thermal conductivity of the insulation k and the external convection heat transfer coefficient h.

34
Q

What’s assumed when analysing fins?

A

Steady state with no heat generation in the fin.

We assume the thermal conductivity of the material to remain constant.

We also assume the convective heat transfer coefficient to be constant and uniform over the entire fin for the convenience of the analysis.

Usually, the value of h is much
lower at the fin base than it is at the fin tip because the fluid is surrounded by solid surfaces near the base, which disrupts the fluid flow.

35
Q

What’s the fin equation (s.s.)?

A

Rate of heat conduction into the element = (rate of heat conduction from element at x + dx) + (rate of heat convection from the element) which is manipulated to:

d2T/dx2 - hp/kAc(T - Tinf) = 0

OR

d2Ø/dx2 - m2Ø = 0

Where
m2 = hp/hAc

36
Q

What is the boundary condition of an infinitely long fin?

A

For a sufficiently long fin of uniform cross section (Ac = constant), the temperature at the fin tip approaches the environment temperature T∞ and thus θ approaches 0.

θ(L) = T(L) - T inf = 0
L tends to inf

Temperature in this case decreases exponentially from Tb to T inf.

The general solutions in this case consists of a constant multiple of e^-mx

37
Q

What is the boundary condition for negligible heat loss from the fin tip?

(Adiabatic fin tip)

A

Fins are not likely to be so long that their temperature approaches the surrounding temperature at the tip so it’s more realistic for there to be negligible transfer at the tip.

This is because heat transfer from the fin is proportional to surface area and the fin tip surface area in a negligible fraction of the total area.

38
Q

What is the boundary condition for a specified temperature?

T fin tip = T1

A

Temperature at the end of the fin is fixed.

Fin base boundary conditions remain the same.

39
Q

What is the boundary condition for infection from fin tip?

A

Convection occurs at the fin tip.

It has a complex solution.

40
Q

How is fin efficiency determined?

A

= actual heat transfer from fin / ideal heat transfer from fin if entire fin were at base temperature.

41
Q

How is fin effectiveness determined?

A

Ē = heat transfer rate from fin of base area Ab / heat transfer rate from surface of area Ab

(With fin / without fin)

If Ē = 1, addition of fins does not increase heat transfer.
Ē < 1, fin acts as insulation and slows heat transfer
Ē > 1, fin enhances heat transfer

42
Q

What are the general rules for design of fins?

A
  1. The thermal conductivity k of the fin material should be as high as possible. Most fins are made from metals such as copper, aluminum, and iron.
  2. The ratio of the perimeter and the cross-sectional area of the fin p/Ac should be as high as possible i.e. thin plate fins and slender pin fins.
  3. Since the use of fins is most effective in applications with low convection heat transfer coefficient, they are more often used for heat transfer from/to gases.
43
Q

What are the types of fouling?

How can they be avoided?

A
  • Precipitation of solids. Remove solids (including dissolved solids, salts)
  • Corrosion.
    Add corrosion inhibitors
  • Chemical fouling (Reaction products)
    Use ceramic / Plastic coatings
  • Biological fouling (Algae/Microorganisms)
    Add biocides
44
Q

What are the issues of (HX) fouling?

A

Decrease of heat transfer

Labour intensive cleaning necessary

Cleaning and repair causes down-time

45
Q

How’s the resistance of fouling / fouling factor found?

A

Rf / A

Where
Rf is the fouling factor (either on inside, i or outside, o)
A is the area

Rule of thumb: fouling increases with increasing temperature and decreasing fluid velocity

46
Q

What assumptions are made on heat exchangers?

A

Heat exchangers operate for long periods of time with no change in operating conditions.

No heat exchange between the heat exchanger and its surroundings.

Mass flow rate of fluids and temperatures at any inlet and outlet
remain the same.

Specific heat capacity (cp) usually changes with temperature but is
assumed to be constant using an average value.

Axial heat conduction along the tubes is negligible.

Potential (e.g. elevation differences) and kinetic energy changes of
fluids are negligible.

Overall heat transfer coefficient (U) is constant.

47
Q

How can total heat transferred by heat exchangers be calculated when temperature difference along the HX varies? (Depends on type of HX and flow also)

A

By using the log mean temperature difference.

Q = UAdTm

Where Tm = T1 - T2 ….. (cont)

48
Q

What is the symbol for the overall heat transfer coefficient?

A

U

49
Q

What are the (4) types of condensation?

A

Natural/free
Forced
Boiling
Condensation

50
Q

What’s the velocity boundary layer (from no slip condition)?

A

Fluid molecules next to the pipe surface assume zero velocity and will slow molecules that are in further distance to the plate.

Thereby a velocity profile forms that increases with increasing distance to the plate until the velocity V∞ is reached.
The distance between zero velocity and V∞ is defined as the boundary layer.

51
Q

What does the velocity boundary layer (no slip) depend on?

A

Fluid dynamic viscosity
Fluid velocity
Type of fluid flow
Surface properties and geometry

52
Q

How does the temperature boundary layer (no slip) form from convection?

A

Molecules next to the hot plate have the highest temperature. Heat is then transferred within the moving fluid.

The temperature in the temperature boundary layers ranges from Ts at the surface to T∞ at sufficient distance from the hot plate.

Although both the velocity boundary layer and the temperature boundary layer form simultaneously they usually do not have the same values.

53
Q

What does the heat transfer coefficient, h depend on?

A

Fluid dynamic viscosity μ,

Fluid velocity V∞, the type of fluid flow (laminar or turbulent)

Thermal conductivity of the fluid (k)

Density of the fluid

Specific heat capacity of the fluid (cp)

Geometry and the roughness of the solid surface.

54
Q

What’s the Nusselt number, Nu?

A

Nu = hLc/k

It’s the ratio of heat transfer by convection to the heat transfer of conduction.
It represents the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer.

The larger the Nusselt number, the more effective the convection. A Nusselt number of Nu = 1 for a fluid layer represent heat transfer across the layer by pure conduction.

Where:
k is the thermal conductivity of the fluid

Lc is a characteristic length that is defined by the respective heat transfer problem considered (e.g. can be the diameter d in the case of a fluid flowing through a pipe).

55
Q

What’s the Prandtl number?

How’s it calculated?

A

𝑃𝑟 = 𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 / 𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 h𝑒𝑎𝑡 = 𝜐/𝛼

= 𝜇𝑐𝑝/𝑘

Where:
𝜐 (𝜐 = 𝜇/𝜌) is the kinematic viscosity in m2/s

𝛼 (𝛼 = 𝑘/𝜌 ∙ 𝑐𝑝) is the thermal diffusivity in m2/s

mu is the dynamic viscosity in Pa∙s = N∙s/m2

k is the thermal conductivity in W/(m∙K) cp is the specific heat in J/(kg∙K)

56
Q

What’s the Prandtl number?

A

Ratio of molecular diffusivity of momentum to molecular diffusivity of heat

57
Q

What’s the Reynolds number?

A

The ratio of inertia forces to viscous forces.

58
Q

What’s the Dittus-Boelter equation?

A

Nu = 0.023Re^0.8 * Pr^n

59
Q

What’s saturated water?

A

Water at its boiling (saturation) temperature.

60
Q

How is saturation temperature related to saturation pressure?

A

As P increases, T increases

61
Q

What’s dry and wet steam?

A

Dry saturated steam - steam at its saturation temperature

Wet - when there’s a water/steam mixture as water changes to steam

Steam does not obey gas laws.

62
Q

What are the (2) main assumptions for the cooling and heating of thin walled vessels?

A

No temperature gradient within vessel

No storage capacity in the wall (thin walled) and heat capacity cp fluid&raquo_space; cp wall

63
Q

How is the energy from a photon calculated?

A

E = hv = hc/λ

Where 
E is the discrete energy of a photon. 
h is Planck’s constant 
v is the frequency of radiation
c is the speed of light in vacuum
λ is wavelength
64
Q

What are black bodies?

A

Hypothetical surfaces which absorb all incident radiation, regardless of wavelength and direction.

At a specified temperature and wavelength, no surface can emit more energy than a blackbody.

A blackbody emits radiation energy
uniformly in all directions, meaning that it is a diffuse emitter.

65
Q

What does the Stefan-Boltzmann law state?

How is it used to calculated the energy emitted by a blackbody?

A

The emission of thermal radiation is proportional to the fourth power of the absolute temperature.

Eb = σTs^4

66
Q

What’s Planck’s law?

A

Electromagnetic radiation from heated bodies is not emitted as a continuous flow but is made up of discrete units or quanta of energy, the size of which involve a fundamental physical constant (Planck’s constant).

67
Q

What’s the equation for Planck’s law?

A

Eᵦ,λ (λ, T) = C₁ / [λ⁵ *(e^(c₂/λT) - 1)

Where:
C₁ = 2πhc₀²
= 3.74 * 10⁸ Wμm⁴m⁻²

C₂ = hc₀/K
= 1.44 * 10⁴ μmK

68
Q

How does blackbody emissive power/energy emission per unit area vary with wavelength?

A

As wavelength increases, Eb increases, then peaks and decreases.

At any wavelength the amount of radiation increases with increasing temperature.

The curve and its peak shift to the left with temperature increase.
- The peak of the sun is in the visible region of the spectrum.

69
Q

What’s Wein’s displacement law?

A

The wavelength at the peak (of the Eb against λ graph // Wein’s displacement graph) is inversely proportional to absolute temperature.

λ(peak)*T = 0.002898 mK

70
Q

How can emissivity be defined (with regards to black bodies)

A

As the ratio of radiation emitted by the surface of an object to the radiation emitted by a blackbody at the same temperature.

eλ = Eλ / Eb

71
Q

How does the surface radiation emission (emissivity) and emissive power of a real surface differs to that of a black body object (with wavelength)?

A

Emissivity:
As wavelength increases, blackbody emissivity remains constant (at 1).
A real surface fluctuates (about that of a grey surface) but is roughly constant, however it is less than the emissivity of blackbodies.

Emissive power:
As wavelength increases, black body emissive power increases to a max then decreases.
The emissive power of a grey surface increases and decreases but is much lower than that of the blackbody, and real surface emissive power fluctuates about the grey surface curve.

72
Q

What are the (3) requirements of a blackbody?

A

1) They absorb all incident radiation regardless of λ and direction.
2) At a specified temperature and λ, no surface can emit more energy than a blackbody.
3) They emit radiation uniformly in all directions. It’s a diffuse emitter.

Chem Eng - Y1.S2 (10 decks)

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