TP2 - Heat Transfer Flashcards
What’s natural convection?
When fluid motion is caused by buoyancy forces, which are induced by differences in density due to variation of temperature of the fluid
What’s buoyancy force?
The upwards force exerted by a fluid on a body, completely or partially immersed on it, and it is equal to the weight of the fluid displaced by this body
FB = fluid density * g * body volume
Thus net force = weight - buoyancy force
What’s the Grashof number?
A dimensionless number measuring the relative magnitudes of the buoyancy force and the opposing viscous force acting on a fluid.
Gr = buoyancy forces / viscous forces
Gr = [𝑔𝛽 (Τ𝑠 − 𝑇∞ )𝐿𝑐^3] / 𝑣2
Where:
𝑣: kinematic viscosity of the fluid, [𝑚2/𝑠
𝐿𝑐: characteristic length of the geometry, [𝑚]
𝛵𝑠 : surface temperature (K)
𝑇∞: temperature away from the surface (K)
𝛽𝑖𝑑𝑒𝑎𝑙, 𝑔𝑎𝑠 : Volume expansion coef. for ideal gases [1/K]
What’s the Rayleigh number?
The product of Grashof number and Prandtl number
Ra = Gr*Pr
Gr = [𝑔𝛽 (Τ𝑠 − 𝑇∞ )𝐿𝑐^3] / 𝑣a
Where
a - thermal diffusivity
𝑣: kinematic viscosity of the fluid, [𝑚2/𝑠
𝐿𝑐: characteristic length of the geometry, [𝑚]
𝛵𝑠 : surface temperature (K)
𝑇∞: temperature away from the surface (K)
𝛽𝑖𝑑𝑒𝑎𝑙, 𝑔𝑎𝑠 : Volume expansion coef. for ideal gases [1/K]
What’s the equation for the Prandtl number?
Pr = v / a = mu* Cp/k
v: kinematic viscosity of the fluid, [𝑚2/𝑠]
𝐿𝑐: characteristic length of the geometry, [𝑚]
𝛵𝑠 : surface temperature (K)
𝑇∞: temperature away from the surface (K)
𝜇: dynamic viscosity [kg/m·s] or [N·s/𝑚2]
α: thermal diffusivity [𝑚2/s]
How’s Nusselt number calculated?
Nu = hLc/k
Nu = C(GrPr)^n = CRa^n
What’s forced convection?
Fluid motion is generated by an external source (like a pump, fan, suction device, etc.) => More efficient; Higher heat transfer rates than natural convection
Heat transfer is complicated because:
- involves fluid motion
- depends on the thermophysical properties of the fluid (μ, k, ρ, cp)
- the geometry and roughness of the solid surface
- type of flow (laminar, turbulent)
The higher the fluid velocity, the higher the convection heat transfer
What are the velocity and temperature boundary layers / profiles like?
(Basic forced convection)
Velocity - The fluid layer adjacent to the surface sticks onto the surface
⇒ 𝒗𝒔 = 𝟎 (no-slip condition)
⇒ retards the fluid layers above
⇒ responsible for the velocity profile
Temperature
The fluid layer adjacent to the surface obtains the temperature of the solid
⇒ T𝑠 = 𝑇𝑓 (no-temperature jump condition)
⇒ pure conduction ( motionless fluid)
What’s drag force?
A body which is forced to move within a fluid experiences some resistance. The force that the fluid exerts on the body is called drag force.
Types of forces:
- wall shear/friction forces (viscous effects while fluid flows)
- pressure forces (depend on the shape of the body)
Plate aligned parallel to the flow -> shear only Plate perpendicular -> pressure only
What are the types of forces exerted on fluids in forced convection?
Types of forces:
- wall shear/friction forces (viscous effects while fluid flows)
- pressure forces (depend on the shape of the body)
Plate aligned parallel to the flow -> shear only Plate perpendicular -> pressure only
How is drag force calculated?
D = 0.5CrhoV^2A
How are fluid velocity, plate length and kinematic viscosity used to calculate Re?
R.E. = V*L/v
How does forced convection flow for parallel flow over isothermally heated plates?
There are three regions of flow: laminar, transition and turbulent.
How does forced convection flow for flow across cylinders and spheres?
Flow exhibits a complex flow pattern; both pressure and frictional drag forces are significant
- Low velocities Re <1: fluid wraps up the cylinder
- Higher velocities Re = 10: boundary layer detaches from the surface and moves to the back
- Higher velocities 103
What happens during forced convection in internal flow?
Internal flow: Liquid is within a confined space = > the boundary layer growth has a limit
Velocity:
• The fluid layer adjacent to the walls has 𝑣𝑠 = 0 (no-slip condition on top/bottom walls)
- We are interested in the V.avg
- There is shear stress and friction on the pipe walls
Which type/shape of pipe can withstand the largest pressure differences, inside and out, without undoing significant distortion?
Circular pipes
How do velocity and temperature profiles vary over a heated, vertical plate?
In general, the fluid velocity is very low and hence the heat transfer rate is slow.
The velocity on the surface edge and far away from it, is zero.
The temperature is maximum on the edge but decreases as the fluid flows away from the surface on the surface edge and far away from it, is zero.
Moving away from the plate: (Hot) fluid travels upwards. Velocity increases then decreases and temperature decreases.
The opposite takes place for a cold plate, and the fluid moves down.
How is the volume expansion coefficient (beta) calculated for an ideal gas?
β = 1 / T
What does the Grashof number show?
Gr represents the natural convection effects in a momentum equation.
Determines the type of the flow (vertical plate: turbulent >109, laminar < 109)
Gr = buoyancy forces / viscous forces
What is the characteristic length, Lc, for a vertical plane?
It is equal to the vertical length, L.
The width is irrelevant.
What is the characteristic length, Lc, for a inclined plane?
It is equal to the tilted length, L.
The width is irrelevant.
What is the characteristic length, Lc, for a horizontal cylinder or sphere?
D, diameter
What is the characteristic length, Lc, for a vertical cylinder?
L, length/height of the cylinder
What plate orientation allows the most effective heat transfer?
When the plate surface is facing the oncoming fluid flow, so that the plate does not act as a barrier.
How is film average temperature calculated?
Tf = (𝑇𝑠 + 𝑇∞)/2
What’s the equation for heat transfer by convection?
Q = ℎ𝐴(𝑇𝑠 − 𝑇∞)
What’s the equation for heat transfer by radiation?
Q = ε𝜎A(𝑇𝑠⁴ − 𝑇∞⁴)
How is heat transferred in the absence of buoyancy forces?
Heat transfer between a hot surface and the fluid will occur due to conduction, and not natural convection.
Its rate would be much lower.
What is Fourier’s law of conduction equation?
Q = -kAdT/dx
What are finned surfaces also known as?
Heat sinks
Energy is first transferred from the hot plate to the heat sinks by conduction, and then to the surrounding air via convection.
How does fin size/length effect convection between fins?
Long surface fins: channel flow fully develops and, if the fins are close enough, the channels merge boundary layers from both sides.
Short surface fins or fins with large spacings between experience natural convection from 2 independent plates. There is no merging of channel flows.
How does fin spacing effect heat sink design?
Closely packed fins will allow greater surface area for heat transfer, however heat transfer coefficient will decrease (due to extra resistance from additional fins)
Widely spaced fins will allow higher heat transfer coefficients but have a smaller surface area.
Thus an optimum fin spacing is used to maximise natural convection.
What is the critical length, Lc, for parallel vertical fins?
It is usually fin spacing, S, however plate length L can be used also.
Ra.s gives the Rayleigh number for the fin whilst Ra gives the Rayleigh number for the plate
How is optimum fin spacing calculated (when fin thickness t<
S opt = 2.714*(S³L/Ra.s)¹/⁴
= 2.714*L/Ra¹/⁴
What is the Nusselt number, using optimum fin spacing.
Nu = h*S opt/k = 1.307 = constant
How is total heat transfer rate calculated for a finned surface?
𝑄 = ℎ2𝑛𝐿𝐻(𝑇𝑠-𝑇∞) = ℎ2𝑛𝐴(𝑇𝑠-𝑇∞)
where A is the surface area of 1 fin, n is the total number of fins, and this must be multiplied by 2 to consider both sides of the fin.
Total heat transfer area = 2nA
How does fluid move within a vertical enclosure?
Fluid by the hot surface rises and that by the cold surface moves down, so air can circulate.
How does fluid move within a horizontal enclosure?
If the hot surface is at the top, and cold at the bottom, then no convection currents form as the light/hot fluid is above the heavy/cold fluid.
If the Nusselt number is 1, heat transfer will only be by pure conduction.
If the cold surface is on top, and hot is at the bottom, heat is initially transferred by pure conduction.
Once buoyant forces overcome fluid resistance (Ra>1708), natural convection and air circulation begin
How does fluid move within a horizontal enclosure when the hot plate is on top?
If the hot surface is at the top, and cold at the bottom, then no convection currents form as the light/hot fluid is above the heavy/cold fluid.
If the Nusselt number is 1, heat transfer will only be by pure conduction.
How does fluid move within a horizontal enclosure when the hot plate is on the bottom?
If the cold surface is on top, and hot is at the bottom, heat is initially transferred by pure conduction.
Once buoyant forces overcome fluid resistance (Ra>1708), natural convection and air circulation begin
How is the Rayleigh number calculated for enclosures?
Ra = Prg𝛽(T1 - T2)Lc³/v²
Lc is the distance between hot and cold plates.
Fluid properties are chosen considering the average fluid temperature.
How is heat transferred in an enclosure calculated?
Convection:
Q = hA(T1 - T2) = (kNu/Lc)A(T1 - T2)
Conduction:
Q = (k/Lc)*A(T1 - T2)
If Nu = 1, heat is only transferred by conduction
How is the Nusselt number calculated, considering the Rayleigh number?
When 10⁴ < Ra < 4*10⁵:
Nu = 0.195Ra¹/⁴
When 10⁵< Ra < 4*10⁷:
Nu = 0.068Ra¹/³
How are critical length and heat transfer calculated for concentric horizontal cylinders?
Lc = (Do - Di)/2
Q = (2pik/ln(Do/Di))/(Ti - To)
How is total heat transfer rate between plates calculated (considering radiation)?
Qt = Q conv + Q rad
The heat transfer coefficients for natural convections are typically low (compared to forced convection), therefore radiation should be taken into account for the overall heat transferred.
How is heat transfer by radiation found?
Q = 𝜎𝜀A(T₁⁴ - T₂⁴)
What is forced convection and why is it more complicated?
Fluid motion is generated by an external source (like a pump, fan, suction device, etc.)
More efficient; Higher heat transfer rates than natural convection
Heat transfer is complicated because:
- involves fluid motion - depends on the thermophysical properties of the fluid (μ, k, ρ, cp)
- the geometry and roughness of the solid surface
- type of flow (laminar, turbulent)
The higher the fluid velocity, the higher the convection heat transfer
𝑄′ = ℎ𝐴𝑠 𝑇1 − 𝑇2
How do velocity and temperature profiles vary for forced convection and external flow?
Velocity:
The fluid layer adjacent to the surface sticks onto the surface
- 𝒗 = 𝟎 (no-slip condition)
- retards the fluid layers above
- responsible for the velocity profile
Temperature:
The fluid layer adjacent to the surface obtains the temperature of the solid
- T𝑠 = 𝑇𝑓 (no-temperature jump condition)
- pure conduction (motionless fluid)
What is drag force, and what resistive forces are exerted on the fluid?
A body which is forced to move within a fluid experiences some resistance. The force that the fluid exerts on the body is called drag force.
Types of forces:
- wall shear/friction forces (viscous effects while fluid flows)
- pressure forces (depend on the shape of the body)
Plate aligned parallel to the flow -> shear only Plate perpendicular -> pressure only
How is drag force calculated?
𝐷 = 1/2𝐶𝜌𝑽2𝐴𝑓
Where:
C - drag coefficient
- combines the wall shear and (geometric) pressure drag
- depends on velocity, viscosity, shape and size
- determined experimentally
Af is frontal area
How is Re calculated for forced convection parallel flow over isothermally heated plates?
Re = V*L/v
Where:
V is fluid velocity
L is plate length
v is kinematic viscosity
What are the 3 regions of flow for parallel fluid flow over isothermally heated plates (forced convection)?
Laminar
Transition
Turbulent
How does fluid flow around cylinders and spheres during forced convection?
Flow exhibits a complex flow pattern; both pressure and frictional drag forces are significant.
Low velocities Re <1: fluid wraps up the cylinder
Higher velocities Re = 10: boundary layer detaches from the surface and moves to the back
Use in heat exchangers design which involves external and internal flow of liquids
Higher velocities 103
How is Re calculated for flow across cylinders and spheres (forced convection - external flow)?
Re = V*D/v
Where:
V is fluid velocity
D is external diameter
v is kinematic viscosity
What is internal flow?
How does the velocity vary?
Liquid is within a confined space - the boundary layer growth has a limit
Velocity
• The fluid layer adjacent to the walls has 𝑣𝑠 = 0 (no-slip condition on top/bottom walls)
• We are interested in the Vavg
• There is shear stress and friction on the pipe wall
What shape of pipe can withstand high pressures?
Circular pipes withstand large pressure differences between inside and outside without going significant distortion, whereas non-circular pipes cannot.
What is the critical length, Lc, for non-circular pipes?
Lc = Dh = 4*Ac/P wet
How does the velocity boundary layer develop (for forced convection undergoing internal, laminar flow)?
Velocity profile develops across the ‘hydrodynamic entrance region’. (Lh,laminar=0.05 Re D)
Beyond this is the ‘hydrodynamically fully developed region’.
How does the temperature boundary layer develop (for forced convection undergoing internal, laminar flow)?
It develops/increases along the thermal entrance region (Lt,laminar=0.05 Re Pr D).
Beyond this is the thermally fully developed region.
Dimensionless temperature profile (Ts-T)/(Ts-T∞)=const.
What happens if the length of hydrodynamic entrance region (L h,laminar) is greater than the tube length?
Fluid will not be thermally developed.
How is Q calculated for forced convection and internal flow (general and considering thermal conditions)?
Q = mcdT
Q = hAsdT lm
Where As is pidL and Tm is log mean temperature difference
How is long mean temperature difference calculated when considering forced convection in internal flow (and Q = hAT)?
T lm = (ΔTo - ΔTi)/ln(ΔTo/ΔTi)
Where:
ΔTo = Ts - To
ΔTi = Ts - Ti
For combined flow, what does Gr / Re^2 show?
If Gr / Re^2 »_space; 1
Inertia forces are negligible and natural convection dominates
If Gr / Re^2 «_space;1
Buoyancy forces are negligible and forced convection is considered
What’s fully developed flow?
When temperature and velocity profiles/flows are both fully developed.
When does boiling occur and what is it’s mechanism?
When the temperature of a fluid at a specified pressure is raised to the saturation temperature T at that pressure, boiling occurs.
Heat transfer in boiling is done via convection, as they involve fluid motion, such as the bubbles rising to the top.
How does boiling compress to other forms of convection?
It depends on latent heat of vaporisation, h.gf and surface tension, σ.
In phase change, T is constant and latent heat of vaporisation is transferred.
Heat transfer coefficients are bigger than those involved in single phase heat transfers.
Where do boiling and evaporation occur?
Boiling - at solid-liquid interface when T solid > T sat
Evaporation - at liquid-vapour interface when P vap < P sat
How is boiling heat flux, from soling surfaces to liquid, calculated?
Q’’ boiling = h*(Ts - T sat) = hΔΤ excess
Ts - surface temp
T sat - sat temp of fluid for given P
ΔΤ excess - temp excess of surface above saturation temp
What’s pool boiling?
No bulk fluid flow
Motion only related to natural convection currents and bubbles raising under buoyancy effects
Subcooled, when T bulk < T sat
Bubbles form near the heated bulk sat.
surface, but disappear before reaching the top, releasing the heat to the colder bulk.
Saturated, when T =T Bubbles rise to the top bulk sat.
What’s flow boiling?
Fluid is forced to move by external means (i.e. by pump).
Heat transfer due to forced convection.
What are the four stages of the boiling curve?
Natural convection boiling
Nuclear boiling
Transition boiling
Film boiling
What happens in natural convection boiling, stage 1 of the boiling curve?
Natural convection (O-A):
- No bubbles.
- Liquid at saturation temperature and the heating element at slightly
higher temperature. - Natural convection currents developed
What happens in nucleate boiling, stage 2 of the boiling curve?
Nucleate boiling (A-C):
- Nuclei of bubbles form.
- At the start they collapse in the bulk and as temperature increases they
rise to the top where they brake and release their vapour content.
At the start ΔT and h increase. As bubbles start forming around the
surface, h reduces, but is balanced by ΔT => Q’’ continues to increase.
The bubbles act as insulation, making it harder for heat to be transferred and h is reduced.
The heat flux reaches its maximum value (Critical heat flux, 𝑄’’max)
What happens in transition boiling, stage 3 of the boiling curve?
Transition boiling (unstable regime) (C-D):
A large fraction of the heater is covered by a vapour film => acts as an insulator.
- surface becomes ‘’vapour-locked’’
- thermal conductivity of vapour «_space;liquid
h and 𝑄’’𝑏𝑜𝑖𝑙𝑖𝑛𝑔 decrease to Q’’min (Leindenfrost point)
What happens in film boiling, stage 4 of the boiling curve?
The heater surface is completely covered by a vapour film.
- initially low heat transfer via conduction
- for high ΔΤexcess => Heat transfer via conduction and radiation
How is boiling heat flux calculated?
Q’’b = h(Ts - T sat) = hΔΤ excess
Q’’b = Q’b / A
How is evaporation rate calculated?
Q eva = m*hfg
What are re-boilers?
Heat exchangers used to provide latent heat of vaporization to a liquid coming from the bottom of a distillation column and convert it to vapour, which returns to the column for further separation
They act as an additional theoretical tray for the distillation column
Their design depends on the application. Usually: shell and tube type heat exchangers.
Heating liquids: Steam, hot oil or DOWTHERM (mixture of biphenyl (C12H10) and diphenyl oxide (C12H10O))
Operate at the nucleate boiling regime
For sizing: Usually Q’’max is taken into account
Flux depends on nucleation => materials, fluid properties, ΔΤ
What are the (2) main types of re-boiler?
Kettle
Thermosyphon
Properties of kettle reboilers:
Are very simple and reliable.
Often used for light hydro-carbon (propane, butane) separations.
Consist of a tube bundle (where the steam enters as a vapour and leaves as a liquid) placed within an oversized shell (where the distillation bottoms flow).
Tube bundle has baffles to allow liquid movement and reduce the potential for vapour blanketing
Can handle process flow fluctuations and high heat fluxes better than other reboiler designs.
They may require pumping of the column bottoms liquid in to the kettle or there may be sufficient liquid head to deliver the liquid in to the reboiler
Expensive
Properties of thermosyphon reboilers:
Exploits the difference in density between the liquid feed and the two-phase product => natural circulation of the boiling fluid
No pumping required
Less expensive to operate
There is no pool boiling; the bottom liquid partially vaporizes -The velocity of the liquid entering the tube is ~ 1m/s
Types: Horizontal (boiling fluid on the shell side ), Vertical (boiling fluid on the tube side), Circulating
Adv and disadv of vertical thermosyphon reboilers:
+ High heat transfer rates possible
+ Compact / simple piping
+ Low residence time
+ Low Goulding tendency
- hard to clean/maintain
- additional column skirt height needed
- poor performance with high viscosity fluids
When does condensation occur?
When T vapour reduces below its saturation temperature.
What are the 2 distinct types of condensation?
Film condensation
Dropwise condensation
What’s film condensation?
The condensate wets the surface and forms a liquid film which slides down under gravity.
The film acts as a liquid wall ( -> conduction heat transfer), offering resistance to heat transfer.
The latent heat, hfg released during the vapor-liquid phase change, must pass through this film first before it reaches the solid surface and get transferred onto the other side.
Requires clean, smooth, homogenous surface.
Not efficient heat transfer
What’s dropwise condensation?
When the condensate forms many droplets of varying diameters.
The droplets coalesce and detach once they reach a certain size => surface is clear and re- exposed to vapour => latent heat transferred
It’s 10x more efficient than film condensation / preferred to film condensation.
Requires nucleation sites (pits, scratches, dust, rough surface) for the droplet formation
How can dropwise condensation (and thus better heat transfer) be promoted?
The vapour must not wet the surface.
Surfaces are treated with suitable dropwise promoters which can enhance “dropwise” condensation.
These promoters:
- increase surface hydrophobicity => achieve high surface-liquid contact angle
- act as impurity which will provide nuclei for the formation of drops
For the design of HE film condensation is assumed, as dropwise condensation doesn’t last long
What is required for condensation to occur?
T s < T sat
How does film condensation form on a vertical plate?
Ts < T sat
Liquid starts forming at the top of the plate and flows down due to gravity.
Latent heat, h fg, is released and transferred to the plate.
As condensation continues, thickness of the film δ, increases in flow direction.
Due to increase in δ in flow direction, are will increase
Velocity:
- is zero on the surface (‘’no-slip’’ condition)
- maximum on the liquid-vapour interface
Temperature:
- decreases gradually from T -> T as it
approaches the surface
sat s
How does h fg* differ from h fg?
(h fg suggests latent heat)
In theory, the latent heat, hfg, represents the heat released instantaneously during the condensate formation.
In reality, the condensate releases continuously heat through the condensate.
hfg is replaced by the modified latent heat of vaporization hfg*
h 𝑓𝑔 ∗ = h 𝑓𝑔 + 0.68 𝑐𝑝𝑙(T𝑠𝑎𝑡 - T𝑠)
where cpl is specific heat of liquid
How does Re change with horizontal and vertical plate film condensation?
As condensation continues, thickness of the film δ, increases in flow direction.
Due to increase in δ in flow direction, are will increase
laminar, 0
How is average heat transfer coefficient in condensate (empirical) calculated?
Large equation given.
h vert (coefficient for vertical plate) and h h,n (coefficient for horizontal plate per tier/number of rows) are different
How is heat transfer coefficient effected if a non-condensible fluid were to also be present in a heat exchanger/condenser with a condensing fluid?
Heat transfer coefficient reduces.
The non-compressible fluid acts as a barrier and reduces h.
How does velocity (of vapour) affect condensation?
At low velocities, condensate drains in (first in discrete drops, then condensate columns and then as a condensate sheet as inundation rate increases.)
At high vapour velocities, if:
- Vapour flows downwards: liquid velocity increases=>film thickness decreases=>heat transfer increased
- Vapour flows upwards: liquid velocity decreases=>film thickness increases=>heat transfer decreased
What is the effect of non-condensable gases in condensers?
If condensers operate at P<1atm, leaks of non- condensable gases may occur.
This gas sits on the vicinity of the solid surface =>barrier between vapour and surface => decrease in heat transfer
If the velocity of the vapour is high => stagnant phase is removed => heat transfer increased
What are the main types of heat exchanger?
Shell and tube
Plate
Spiral
Compact
What do shell and tube HX consist of?
Thin tubes (100reds) packed in a shell.
Baffles placed to force circulation/turbulence of fluid in the shell side => enhance heat transfer.
Heat transfer coefficients in the shell and tube side are of comparable importance: large to attain high overall heat transfer coefficient
Standard length of tubes for heat exchanger construction are 8, 12, 16 and 20 ft (=2.5-6m)
Tubes are arranged in a triangular or square layout, known as triangular pitch or square pitch (pitch = distance between centres of adjacent tubes).
What are the advantages and disadvantages of arranging shell and tube HX with triangular and squared pitch?
Triangular pitch:
+ densely packed thus high SA for heat transfer
- hard to clean so can foul badly
Squared pitch:
+ easy to clean
+ lower P drops
- accumulates space
How are shell and tube HX configured?
- Single pass
- One shell-two tube passes
- Two shell-4 tubes passes
The fluids in the tubes and shell will flow co- currently in some of the passes and counter- currently in the others.
Multipass (baffles or U-shape tube) allows the fluids to come in contact multiple times => improved performance
What do plate HX consist of?
Closely packed thin (0.5-3mm) plates with corrugations
A thin gasket seals the plates on the edges
Hot and cold fluids flow between plates alternatively
Surface area: 0.03-1.5m2
What are advantages and disadvantages of using plate heat exchangers?
Advantages:
- Low cost material
- Easy to maintain
- Operation at low temp
- Flexible to extend
- Good for viscous fluids
- Low fouling
Disadvantages:
- Not good for P>30bar
- Max temp=250C
- Selection of the gasket is critical
What do spiral HX consist of?
Sheets rolled up forming a spiral- single passage for each fluid
Gap between plates:4-20mm
Hot and cold fluids flow between plates counter-currently
Surface area: 250 m2
Good for subcooling, condensation, vapourizing
What are advantages and disadvantages of spiral HX?
Advantages :
-Self cleaning mechanism (turbulent flow)
- Compact (10m3)
- Low pressure drop
Disadvantages:
- Not good for P>20bar
- Max temp=40
How can compact HX be categorised?
1) Plate fins
2) Finned tubes
What are properties of compact HX?
Have a high surface density (area/volume>700m2/m3).
Thin plates or corrugated fins are attached onto plates separating two fluids.
Fluids can have a mixed or unmixed flow. (Unmixed when fluid flows between plates. Mixed when there are no plates)
Short paths =>laminar flow assumed
What are properties of plate fins and finned tube compact HX?
Plate fins:
-Are plates separated by corrugated sheets which
form fins
-Have high surface area density and streams can be mixed
Application: Vehicle radiators
Disadvantages:
- Temp limitations (cryogenic temp-100C for aluminium, <650C for stainless steel)
- P<60 bar
Finned tubes:
Used when heat transfer outside the tube is low, i.e. in air-cooled HE
Dimensions:
Pitch 2-4mm Height: 12-16mm
Adv and disadv of horizontal thermosyphon reboilers:
+ Moderately high heat transfer rates possible
+ Low residence time in heating zone
+ Moderate fouling
+ Good control
+ Easy to maintain and clean
+ Cheaper than kettle
+ Lower static head than vertical thermosyphon
- Extra piping and space needed compared to vertical thermosyphon
- No design data
Adv and disadv of kettle reboilers:
+ Easy maintenance and cleaning
+ Vapour disengaging zone built in
+ Less sensitive to hydrodynamics
+ Unlimited surface in a single shell
+ Can use low fin tubing
- Only moderate heat transfer surface
Extra piping and space needed
- High residence time in heating zone
- High fouling tendencies
- Expensive
What’s the purpose of baffles in a shell and tube HX?
To increase shell side heat transfer coefficient and encourage mixing
From the same inlet and exit temp’ of 2 fluids, how does log mean temp difference compare for counterflow in shell/tube HX?
It will a,wags be greater than LMTD for parallel flow.
What does correction factor F (applied to the log mean temperature ΔΤlm to account for the departure from ideal counter-current flow) depend on?
HX geometry (plate, crossflow, shell/tube, number of shells etc)
Inlet and outlet temperature
How are the two dimensionless ratios, P and R, found to determine correction factor, F?
P = (t2 - t1) / (T1 - t1)
R = (T1 - T2) / (t2 - t1)
= (mcp) tube side / (mcp) shell side
These are needed to find true LMTD which will find overall heat transfer
How is heat transfer effectiveness (of fins or HX) determined?
ę = Q / Q max
= actual heat transfer rate / maximum possible heat transfer rate
When does Q max occur?
It is determined between points where max temperature difference occurs.
(d T max = T h,in - T c,in)
Q max = C (min) * dT max
What does NTU stand for?
Number of transfer units
NTU = UAs/C min
= UAs / (mCp) min
How is NTU calculated?
NTU = UAs/C min
What is capacity ratio?
Cr = C min / C max
What are the main parts of a plate HX?
- Cover plates: - Front (fixed) - Back (removable)
- Corrugated plates
- Plate gaskets
- Plate port
- Side bars (tighten plates)
- Channels (space between plates)
What are features of gasketed plates (used in plate HX)?
• Corrugated stainless steal or Ti plates with rubber gaskets
- Operate at low T and P
- High turbulent flow
• Easy to add/remove plates
120C and 30 bar
What are features of brazed plates (used in plate HX)?
- Corrugated stainless steal plates with copper brazing
- Compact
- Low cost
- Operate at high T and P
- High thermal efficiency
- High turbulent flow
200 to 550C and 50 bar
What are features of welded plates (used in plate HX)?
- Corrugated plates, welded
- Used for corrosive fluids
- Compact
- Low cost
- Operate at high T and P
- High thermal efficiency
- High turbulent flow
600C and 70 bar
What are the meanings of: β W Lh Lp Dp t s N Nc de
when considering the corrugation dimensions of plates used in plate HX?
β: Chevron (corrugation) angle
W: plate width
Lh : plate length for heat transfer
Lp: plate height (length) ≈ Lh (for preliminary calc)
Dp: port diameter
t: plate thickness
s: plate spacing
N: number of plates
Nc: number of channels = N-1
de: hydraulic mean diameter
How is hydraulic mean diameter, de, calculated when considering HX dimensions?
de = 2*s
Where s is plate spacing
How is cross sectional flow surface area, Af, calculated when considering HX dimensions?
Af = W*s
Where W is plate width and s is plate spacing
What are causes of pressure drop?
- Friction of fluid with the plate (surface roughness; type of corrugations)
- Height of the plate
- Due to connections (inlet/outlet ports)
- High channel velocity
How is pressure drop calculated (considering HX)?
ΔP = 2j(Lp / de)𝜌𝑢𝑐^2
Where: ΔP - pressure drop j - friction factor Lp - plate length de - hydraulic diameter uc - (nominal) channel velocity
How is the number of transfer units (NTU) calculated considering plate HX?
NTU = (Tin-Tout)/ΔTlm
Where Tin-Tout is the maximum temperature difference for a single fluid
How are the Nusselt and Reynolds numbers found (considering plate HX design)?
Nu = hp*de/kf
Re = mc*de/mu Re = rho*uc*de/mu
Where:
ℎ𝑝: plate heat transfer coef.
𝑑𝑒: hydraulic diameter=2 x plate spacing
𝑢𝑐:c hannel velocity
𝑚𝑐: mass flow rate/cross sectional area for flow
How is it decided which fluid is used in HX shells and tubes?
Tubes:
- More corrosive fluids
- Fluids that cause fouling (easier to clean)
- Fluids at high temp (lower cost and heat loss)
- Fluids at higher P (cheaper)
- Lowest P drop fluid
Shells:
- More viscous (if turbulent flow)
- Lower flow rate fluids
What do the performance of HX plates and the whole HX depend on?
Plate performance:
- corrugation angle (beta)
- plate dimensions
Whole unit:
- flow arrangement (single, multiple passes)
- plate spacing
- flow velocities
- pressure drop
What are some (6) mechanisms of fouling?
- Crystallization (deposition of salts, i.e. from hard water)
- Accumulation of biological materials
(presence of micro-organisms in sea water - Particle deposition
(i.e. from clay, soot particles, minerals from river) - Chemical reaction between the stream components
(presence of organic compounds, pronounced at high temp, deposition of carbon) - Corrosion
(from reaction with the surface - oxidization) - Solidification of liquids/freezing (i.e., ice formation, wax)
What are the stages of fouling?
- O-A: Initiation period, surface slightly modified to accommodate fouling
- A-B: Steady growth of deposit on the surface
• B-C: Plateau, fouling resistance resistance remains constant
What variables must be considered in fouling?
Fluid velocity:
Increases diffusivity of impurities towards the walls BUT shear forces increase tending to remove the deposits
Temperature and Temperature difference: At T<< ⇒crystallization At T>>⇒ precipitation of salts Growth of microorganisms Depositions from chemical reactions.
Concentration of foulants:
The higher their presence, the highest probability exist for precipitation, reaction, etc..
Other: Residence time, surface chemistry, surface roughness
What is the balance for the rate of fouling?
dR/dT = Rd - Rr
Where Rd is the rate of deposition and Rr is the rate of removal
What are examples of techniques to overcome fouling?
Addition of anti-foulants (chemicals)
Mechanical removal of the deposits by circulating ‘’pigs’’
Modification of heat transfer area to avoid fouling
Stop the process and clean the HE and/or restore it
Be proactive and design the HE in such a way that fouling is eliminated
Model reactions causing fouling to predict the reaction and diffusion kinetics
What type of condenser configuration should be used to achieve film and drop-wise condensation?
Film - horizontal or vertical tube bundles
Dropwise - horizontal tube bundles only
How is the characteristic length for a hot 0ate found?
Lc = As / P (area / perimeter)
How is log mean temp difference ca,curated for flow in tubes?
LMTD = (Ti - To)/ln[(Ts - To) / (Ts - Ti) ]
Where:
Ts - pipe surface temperature
Ti - inlet temperature
To - outlet temperature
How is NTU calculated for plate HX?
(T in - T out) / Tlm
How is Nu number calculated for plate HX?
Nu = h*de/k
= h*2S / k
How is Re calculated for plate HX?
Re = m*de/mu
= rhoucde / mu
= rhouc2S/mu
Briefly, what are the 4 boiling regimes and what happens at each?
Natural convection:
- no bubbles
- liquid is at sat temp
Nucleate boiling:
- nuclei of bubbles form
- initially, the break before teaching the surface
- T excess and h both increase
- as more bubbles form, h decreases but T excess increases still
Transition:
- surface gets vapour locked
- h and Q” decrease to Leidenfrost point
Film:
- heater surface completely covered by vapour
- initially low Q by conduction
- for high T excess, Q by conduction and radiation
What’s sub-cooled boiling?
When T bulk < T sat, so bubbles form near the heated surface but disappear before reaching the top, releasing heat to the colder bulk.
