Everything on MEC203 Flashcards
Gain a good understanding of the basic concepts to enable you to answer the questions.
What is Beta?
It is the volume expansion coefficient. Variation of fluid density with temperature at constant pressure.
What does the Grashof (Gr) number represent?
The natural convection effects in the momentum equation.
What does the Biot number represent?
The ratio of convection at the surface of a body to conduction within the body.
What kind of bodies are most likely to satisfy the condition for lumped system analysis?
Small bodies with large thermal conductivities and low convection coefficients.
What is a thermal boundary layer?
The flow region over the surface in which the temperature difference in the direction normal to the surface is significant.
What does the Nusselt number represent?
The enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the SAME fluid layer.
True or false, the larger the Nusselt number, the more effective the conduction?
FALSE. The larger the Nusselt number, the more effective the convection.
What is the Fourier number?
The ratio:
The rate at which heat is conducted across a body of length L and volume L^3.
—————————–DIVIDE—————————————–
The rate at which heat is stored in a body of L^3.
What does a large Fourier number suggest?
A large propagation of heat through a body.
What is the Biot number?
The ratio of external convection resistance to internal diffusion resistance.
What is FILM temperature?
Tf=0.5*(Ts+Tinfinity)
What is the Rayleigh number?
A dimensionless parameter that measures the instability of a layer of fluid due to differences in temperature and density at the top and bottom of the flow.
Describe the no-slip condition.
It occurs when a fluid in direct contact with a surface sticks to the surface and there isn’t any slip. It is due to the fluid’s viscosity.
What does the friction coefficient represent in fluid flow over a flat plate?
Represents the resistance to fluid flow over a flat plate.
What is turbulent thermal conductivity (kt)?
It accounts for thermal energy transport by turbulent eddies.
Why nondimensionalise the convection equation?
- Reduction in parameters. You go from six to two (Re and Pr)
- Allows you to group a large number of experiments and compare data
Define isothermal.
No change in temperature.
What is the definition of heat flux (q)?
q=-k(dt/dy)
True or false, for an ideal gas, kinematic viscosity is inversely proportional to pressure?
TRUE
True or false, for an ideal gas, thermal conductivity and Prandtl number are independent of pressure.
TRUE
What is the Prantdl Number?
It is a dimensionless number, representing the ratio of momentum diffusivity to thermal diffusivity.
What is the Nusselt number?
The Nusselt number is the ratio of convective to conductive heat transfer across a boundary.
What is the general formula for Nusselt number to find h?
Nu=(hD/k) where k is thermal conductivity and D is diameter.
What is kinematic viscosity?
Dynamic viscosity PER UNIT DENSITY
What is transient?
Time dependant
What is the Biot Number?
It is a dimensionless parameter (heat transfer coefficient). Bi=hL/k.
What is the time constant in lumped system analysis?
b=(hA)/(ρV*c,p)
What is characteristic length?
Lc=V/A
What does fin effectiveness tell you?
It tells your whether more or less heat is extracted from the surface when the fin is present.
What does fin efficiency tell you?
It compares the heat transfer of the actual fin to the heat transfer of the fin if all the fin was at the base temperature.
What does thermal diffusivity represent?
How fast heat diffuses through a material.
What is the formula for thermal diffusivity?
α=k/ρ(c,p)
What is absorptivity?
The fraction of radiation energy incident on a surface that is absorbed by the surface.
What is emissivity?
The ratio of radiation emitted from a surface compared to that emitted from a blackbody.
What is a blackbody?
The idealised surface that emits radiation at the maximum rate
What is the equation for the similarity variable η? When is it used?
η=x/(4αt)^0.5
Used in transient heat conduction in semi-infinite solids.
What is a formula for Prandtl number?
Pr=(kinematic viscosity(ν))/(thermal diffusivity(α))
What is the temperature of a 100% efficient fin?
It is the fin’s base temperature.
What equation do you use for a fully efficient fin?
Qfinmax=hAfin(tb-tinf)
You assume the entirety of the fin is at the same temperature.
Transient lumped system analysis equation?
(T-Tinf)/(Ti-Tinf)=e^(-bt)
What is Rcond and Rconv (convection and conduction resistance)?
Rcond=L/KA
R conv=1/hA
What is Rcyl and Rsph for conduction?
Rcyl=((lnr2/r1)/(2piLk))
Rsph=(r2-r1)/(4pir1r2k)
Define thermal entry length.
The length of the region of flow in which the thermal boundary layer develops and reaches the tube centre.
Equation for average velocity in internal forced convection.
Vavg = (2/R^2)∫u(r)rdr
between 0 and R
Equation for mean temperature in internal forced convection.
Tm = (2/VavgR^2)∫T(r)u(r)rdr
between 0 and R
True or false: The shear stress at the surface of a tube during fully developed turbulent flow is minimum since the shear stress is proportional to the velocity gradient, which is minimum at the tube surface.
FALSE: The shear stress at the surface of a tube during fully developed turbulent flow is maximum since the shear stress is proportional to the velocity gradient, which is maximum at the tube surface.
What is the equation for maximum velocity for fully developed internal laminar flow?
Vmax=2Vavg
What is the actual definition of the Grashof Number?
The ratio of buoyancy forces to viscous forces acting on a fluid.
What force of the Reynolds Number is replaced by buoyancy in the Grashof Number?
Inertial is replaced by buoyancy.
Ideal gas equation?
P=ρRT
In cylinders, what does To and Ti mean?
To = the temperature along the centreline of the cylinder Ti = The initial temperature of the cylinder (spatially uniform)
What is the name of the transient temperature chart?
Heisler chart.
How does the heat transfer across a plate change as the boundary layer thickness increases?
The heat transfer reduces.
What is the most realistic treatment of a fin?
Zero heat loss at the tip with a bit of extra length to account for the tip losses.
What happens when the boundary layer changes from laminar to turbulent?
Heat transfer goes up.
At an insulated boundary…
dT/dx=0
For Nu=C(Re)^m(Pr)^n what happens as velocity increases?
C decreases
m increases
n doesn’t change
What is a typical Prandtl number for engine oil at 400K?
150
Which cannot withstand greater pressure differences, circular or non-circular pipes?
Non-circular pipes.
What is the critical Reynolds number for flow in pipes.
2300 (according to the MEC203 book)
What is the hydrodynamic entrance region?
The region from the pipe inlet to the region where the flow is fully developed.
What is NTU?
Number of Transfer Units. It measures the effectiveness of a heat transfer system.
What does an NTU>5 mean?
The fluid flowing in a tube will reach the surface temperature at the exit REGARDLESS OF THE INLET TEMPERATURE.
Heat transfer in fully developed region of tube?
qs=h(Ts-Tm)
What is the equation used for Fourier number.
т=αt/L^2
What length is used in the Biot number?
The characteristic length.
True or false, a blackbody absorbs the entire radiation incident on it?
TRUE
State Kirchhoff’s law.
The emissivity and absorptivity of a surface at a given temperature and wavelength are equal.
Qabsorbed=αQincident
Qreflected=(1-α)Qincident
What Reynolds numbers signal the transition from laminar to turbulent flow over cylinders and spheres?
210^5 to 210^6
What’s the critical Reynolds number for flow over a flat plate?
5*10^5
Critical radius of insulation for a sphere?
2k/h
Critical radius of insulation for a cylinder?
k/h
Does thermal conductivity k, depend on fluid flow?
No, it is a property of the fluid and is independent of the flow of the fluid.
What page is LBoT useful equations?
p47-48
What is the Fourier number equation?
FourierNo=”alpha”t/L^2
True or false, for a fixed Reynolds number. Velocity entry length is only dependant on velocity and diameter.
True
What type of heat exchanger is the most effective?
Counter flow
If you use the arithmetic temperature difference instead of logarithmic temperature difference (LMTD) for heat exchangers, how will the heat transfer values vary?
Using arithmetic temperature difference will always provide an overestimate of heat transfer. It will always be greater than that predicted by the LMTD.
For heat exchangers, what does the F correction factor depend on?
> Heat exchanger geometry.
>Inlet/outlet temperatures of hot/cold flows
What is the value of F for a condenser/boiler?
1
When can a heat exchanger be classified as compact?
When β is greater than or equal to 700 m^2/m^3. That is the ratio of surface area of heat transfer surface to its volume.
What is the hydraulic diameter for an annular tube?
Dh=Do-Di
Equation for heat transfer through a fin
θ”-(m^2)θ=0
where θ” represents heat conduction
and θ indicates heat convection
What is the solution to the fin conduction equation?
θ=Ae^(mx)+Be^-(mx)
where m=root(hP/kA)
What is spectral blackbody emissive power?
The amount of radiation energy emitted by a blackbody at a temperature T per unit time, per unit surface area and per unit wavelength about the wavelength λ.
True or false. The emissivity of a surface at a specified wavelength, direction and temperature is always equal to the absorptivity for the same conditions.
TRUE
Is the biot number likely to be larger in air or water?
The biot number is much larger in water because the heat transfer coefficient (h) is much larger in water than air. Bi=hL/k
Define radiosity.
The total radiation energy leaving a surface per unit time per unit area.
What were the three crucial pieces of information that Planck had to construct his formula for the energy spectrum of blackbody radiation?
1) Wien’s law accounted for the intensity of radiation at short wavelengths.
2) It failed in infrared. Rubens and Kurlbaum found that wavelength was proportional to temperature.
3) Wein’s displacement law was correct.
What was the focus of Planck’s research as he started his career?
Thermodynamics, particularly the second law. The entropy of an isolated system can never decrease with time.
What are the units for heat transfer coefficient?
W/(m^2)*°C
Kirchhoff’s law for radiation?
αG+τG+εG=G
Radiosity (J) equation?
J=εσT^4 +(1-ε)G
Define view factor.
Radiation energy emitted from one surface to another divided by the total radiation energy emitted in all directions.
What is intensity?
It represents the rate of radiation emission per unit area normal to the direction of emission per unit solid angle.
In radiation. What does G mean?
Incident radiation.
Define graybody.
A body who’s surface properties are independent of wavelength.
When does emissivity equal absorptivity?
When the surface is in thermal equilibrium.
What is the physical meaning of the summation rule?
It represents the conservation of energy. Radiation leaving any surface must be completely received by another surface.
What does diffuse mean?
There is no dependence on the angle of the surface’s exposure.
When is the view factor for a surface to itself not zero?
When it is concave.
What is the summation rule for view factor?
The sum of the view factors from a surface of an enclosure including itself must be equal to unity.
What is the superposition rule for view factor?
The view factor from surface i to surface j is equal to the sum of view factors from surface i to parts of surface j.
What is the main difference between radiosity and emitted energy?
Radiosity includes reflected radiation as well and emitted radiation energy.
Radiation surface resistance?
Ri=(1-Єi)/(AiЄi) where Є is epsilon
What is the end boundary condition for a very long fin tip?
T(L)=Tinfinity
What is fouling factor in heat exchangers?
It is an extra thermal resistance in the heat exchanger that arises due to the accumulation of deposits on the internal surfaces of the heat exchanger.
Can you draw Tm and Ts graph for the thermal entrance region of a pipe?
- One straight line
- One curved and then parallel straight line ABOVE!
- Mark thermal entrance and fully developed region
- This is for constant heat flux
What is the formula for thermal resistance in parallel? Is it the same as electric circuits?
1/Rt = 1/R1 + 1/R2 +…+1/Rn
How do you apply correction factor to find energy transfer in a heat exchanger?
You multiply it with the energy equation for heat exchangers in the formula sheet and LBoT (p50).
What caused Planck to abandon the ideas he had long held dear?
An act of desperation.
In what year did Planck discover the equation for the distribution of radiation emitted by a blackbody?
1900
Who developed the concept of the blackbody?
Kirchhoff
What drove the need for the development of globally agreed set of electrical measurements units?
International competition and the development of electrical technologies like lightbulbs and dynamos.
What drove the need for a unit of luminosity?
The development of increasingly efficient lightbulbs
What was Planck told when he was considering a career in physics?
It was hardly worth doing because there is nothing left to discover.
What was the main disappointment of Helmholtz?
He never prepared his lectures properly
What did the law of conservation of energy not outlaw?
Heat flowing from a cold to a hot body.
What originally stopped planck from trying to derive the exact form of Kirchhoff’s unknown equation?
The lack of experimental data
What crucial guide did Planck have in determing the meaning behind his improvement/correction to Wien’s law?
The formula itself!
What was Planck’s opinion on the atom?
He didn’t believe it. There was no evidence at the time that compelled him to do so.
What is the formula for NTU?
NTU=UA/(ṁcp)min
Who discovered Wien’s Law?
Wilhelm Wien
From the lnP, lnλ graph. What does the area under a temperature curve tell you?
The maximum power emitted by a blackbody at that temperature
What does heat exchanger correction factor depend on?
- Geometry of the heat exchanger
- All four inlet and outlet temperatures
What is the purpose of a correction factor heat exchanger?
It provides the effective LMTD of the heat exchanger compared to the ideal counter-flow heat exchanger
Which has a higher kinematic viscosity, lubricating oil or metal?
Lubricating oil
according to last years past paper
What is a semi-infinite body?
An idealised body with a single exposed surface that extends to infinity in all directions.
What does the NTU not require?
The two outlet temperatures
What is the correction factor for a boiler?
1
