Transport Phen - Heat Transfer Flashcards
What are the 3 types of heat transfer?
Conduction
Convection
Radiation
What are the properties of conduction?
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
What is Fourier’s law?
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.
What’s the formula for Fourier’s law?
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.
What are properties of convection?
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.
What is k (used in Fourier’s law)?
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).
How can heat transfer by convection be calculated?
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
What are the types of convection?
Natural
Forced
What is natural convection?
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).
What is forced convection?
Convection where the flow of the fluid is caused by an external source and is widely independent of density differences.
What are the properties of radiation?
It is energy in the form of electromagnetic waves by any matter above 0K.
It can occur in a vacuum.
What is emissive power and how is it determined?
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
What is heat flux and how is it determined?
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
What’s a heat exchanger?What are its requirements?
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
What are double-pipe heat exchangers?
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.
What’s a shell-and-tube HX?
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.
What’s a plate HX?
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.
Properties of shell-and -tube HX:
Good value for money
Heavy
Not used in transport applications
Properties of plate HX:
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
What are compact heat exchangers?
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.
What’s a spiral heat exchanger?
HX with two flat surfaces curled into each other.
What are regenerative HX?
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.
How can Fourier’s law be written to account for thermal resistance?
Q = kA* ΔT/L
Where Q = ΔT / R
And R = L/kA
What’s ohms law?
V = IR
V proportional to I and R (for constant temp)
How can Newton’s law of cooling (convection heat transfer) be written to consider Herman resistance?
Q = hA(Ts - Tf)
Can be written:
Q = (Ts - Tf) / R
R = 1 / hA
How is the radiation heat transfer law written to consider thermal resistance?
Q = εσA(Ts⁴ - T𝒻⁴)
Can be written:
(Ts⁴ - T𝒻⁴) / R
How is overall heat transfer calculated?
Q = UAΔT
Where U is overall heat transfer coefficient (W/m2K)
U is equal to the inverse of total thermal resistance
How can total thermal resistance of composites be calculated?
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