IB Thermofluids ALL

What makes a process reversible

Both the system and the environment must be able to return to original state

What does it mean if a process is reversible and adiabatic

It is isentropic

What is b (equation)

Available energy, h-T_oS. T_o is the environment temperature.

Explain what b=h-TS looks like on a TS diagram

The full area under a curve is h. ToS is the area of the rectangle that touches the lowers temperature on the curve. b is the remaining area above this rectangle

What is Qdot in a throttle

Zero, too fast for heat transfer

What does a Joule cycle look like (TS diagram)

Two isobar lines curving up and right. Lines between them go L to R as S increases in the compressor and turbine. Vertical dotted lines go 1 to 2 and 3 to 4 to show 2s and 4s, ideal changes if isentropic

What is thermal efficiency/ first law efficiency

W(net) / Q(in)

What is loss of available power in an exhaust

ToS, this is Q(out) to the environment. Remember to use lowest temp of cycle, not temp at exhaust

How to relate compressor work and turbine work

They are physically connected so are the same

When is a throttle isenthalpic

Always (so use SFEE)

What does a Rankine cycle look like (TS)

Upside down u for phases. Starts on lhs line, up and LEFT for compressor, zigzag up along isobar (heat addition), down to turbine output which may be on phase line or inside u

What is the rational efficiency/ second law efficiency

W(net) / delta(b)

When doing a Rankine cycle what property do you use for calculations

Enthalpy, q’s are all changes in h because pressure is not constant (cv not cp)

What does a Carnot cycle look like

A rectangle inside the L-V u on a TS diagram

Why do reheats improve the Rankine cycle

It improves the quality of heat transfer, change in available energy b is higher because entropy changes are lower at higher temperatures (isobars get steeper)

What is a T-x diagram

Temperature against fraction of heat transferred in a steam power plant

What is the best way to deal with a weird funky heat cycle

Draw a TS diagram, make a table of p,T,h

What is special about a Carnot cycle

It is reversible

What is COP(R)

Refrigerator coefficient of performance, Q(cold) / shaft work

What is COP(P)

Heat pump coefficient of performance, Q(hot) / shaft work

What is specific humidity omega

Mass of vapour / mass of air

What is the equation for specific humidity

0.622 x partial vapour pressure / (pressure - partial vapour pressure)

What is relative humidity phi

Vapour partial pressure / saturated vapour pressure

What is the dew point

When Pv = Pvsat

What is the method for writing combustion equations with excess air

Fuel plus gap goes to co2 plus h2o plus gap. First gap is lambda(x h2o plus 79/21x n2). Ignoring lambda, balance oxygens. In terms of lambda, add the leftover air to the rhs gap. Use the air to fuel ratio, which uses Mr’s in terms of lambda. Calculate lambda using the AFR and complete the equation

What is the equivalence ratio phi

1/lambda where lambda is the stoichometry of the combustion equation (lambda is one for the perfect amount of air)

How do combustion questions differ if they are lean (not enough oxygen)

You also have CO as a product and you need simultaneous equations balancing C and O to find the stoichiometry

What does combustion being wet or dry mean

If it is wet, (products above 100C) water plays a part in gas calculations. If it is dry(colder) water does not

What equation may be used in combustion calculations

The SFEE. Use the molar enthalpies table to do an energy balance

What is the mean free path

The distance a particle is expected to travel before colliding

What is Poiseville flow

Pressure driven pipe flow, sideways u shape

What is the relevance of a flow having no curl

There is no vorticity so Bernoulli can be applied along AND across streamlines

Explain the material derivative D/Dt

It is dv/dt plus v dot del (v). The whole thing is the acceleration of something in a field, the dv/dt is the gradient of speed of the field, the dot del bit is movement relative to the field

What is the pressure gradient of a curved streamline

Lower on concave side, higher on convex side

How does curl relate to angular momentum

Curl = 2 x omega

What is the equation for fluid shear

Mu(viscosity) x dv(x)/dy

What is couette flow

Linear velocity gradient between plates due to imposed velocity of one plate

What is hydrostatic pressure

The one due to g

Why is making dimensionless variables useful

They should be the same for the real thing and a model

What is Buckingham’s pi theorem

Number of dimensionless variables = number of variables - number of dimensions

How do you make dimensionless variables

By cancelling through one dimension on each pass

What is the overarching method for pipe flows

Go from start to end via different routes and equate the pressure changes

What is static pressure

Atmospheric pressure

What is dynamic pressure

½ rho v²

What is stagnation pressure

Pressure where we neglect g, so just static plus dynamic

What is the pressure loss in a pipe

4Cf x L/D x (wall shear)/(dynamic pressure)

What is kinematic viscosity

Viscosity divided by density

Can you use the SFME if there’s a wibble wobble

Yes as long as flow is steady coming in and out of the control volume

What is the rough boundary layer thickness equation

4.64 / root(Re)

What are the three mechanisms of heat transfer

Conduction convection radiation

What is Fourier’s law for heat conduction

Qdot/A = - lambda dT/dx

What is the thermal resistance for going through a material

L / (lambda x A)

How do you do heat transfer through multiple materials

Adding resistances in series

What is thermal resistance of boundaries

1 / hA

What is the thermal resistance for radial through

Ln(r2/r1) / (2 pi L lambda)

What is thermal diffusivity

lambda / (rho c)

How does thermal diffusivity alpha relate to a characteristic time for diffusion

X² / a

What is the fourier number

The ratio of time and a characteristic diffusion time

When is a lumped heat capacity analysis valid

When the biot number hs/lambda is less than 0.1 (s =V/A)

What is the heat exchanger equation which uses the overall heat transfer coefficient

Qdot= UA(delta)T

What is the maximum possible heat exchange in a heat exchanger

(mdot c)_min times the biggest temperature difference

How is the effectiveness of a heat exchanger defined

Qdot real / Qdot max

What is the film temperature

The mean temperature of the wall and environment

What does it mean if the Prandtl number is 1

The momentum diffusivity equals the thermal diffusivity

What does a high Grashof number mean

A turbulent convective boundary layer

What is the time constant for heating up a sphere

Tau = rho x c x d / 6h

What temperature do you use for convection calcs

The film temperature

What is beta regarding convection

1/v dv/dT where v is specific volume and T is temp (it is 1/T for a perfect gas)

What is the maximum rate a body can radiate energy at

Sigma x T^4

What is absorptivity equal to

Emissivity

What is irradition

Radiation incident on a surface per unit time

What is radiosity J

Radiation leaving a surface per unit time

What is the equivalent resistor between sigma T^4 and J

1-e/eA where e is emissivity

What is shape factor reciprocity

A1F12 = A2F21

What is the resistor between J1 and J2

1/A1F12

What do shape factors add to

Unity

What does a radiation resistor network between two surfaces look like

3 in series- out, across, in.

1-e1/A1e1

1/A1F12

1-e2/A2e2

What can a large enclosure be modelled as

A black body

How do you do sums with a radiation sheild

Add resistors for absorption and emission (ie 2 × 1-e/eA

Reflectivity plus transmissivity plus absorptivity equals

1