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MEC203 > Chapter 8 Internal Forced Convection > Flashcards

Chapter 8 Internal Forced Convection Flashcards

1
Q

What is the advantage of circular pipes over non circular pipes

A

they can withstand large pressure differences between the inside and the outside without undergoing any significant distortion
for fixed surface area gives the most heat transfer for the least pressure drop

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2
Q

What it the fluid velocity maximum in a pipe and why

A

at the centre as the no slip condition makes it zero at the wall increases inwards

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3
Q

As dP/dx is constant what does this mean for curvature

A

v*d^2U/dy^2 = dP/dx = const therefore curvature is constant, making it a parabola

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4
Q

What is the average velocity and why is it used

A

average velocity remains constant in incompressible flow when the cross section area is constant
used for convenience

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5
Q

For fully developed laminar flow in a pipe Vavg is defined as the

A

the average speed through a cross section, equal to half the maximum velocity

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6
Q

Equation for finding V avg =

A

2/R^2 * integral 0 to R of the velocity profile *r *dr

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7
Q

derive the equation for V avg

A

use equations for mass flow rate rho V avg * Ac = integral of the cross sectional area rhovelocity profiledAc see book

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8
Q

How is the average temperature calculated

A

found by averaging the energy within a flow profile

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9
Q

Derive the equation for Tm (or Tavg)

A

Start with energy flow in pipe E.fluid = m.cpTm = integral from m. of cpT(r) * delta m.

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10
Q

Equation for Tm =

A

2/Vavg*R^2 * integral from 0 to R of T(r) * u(r) * r * dr

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11
Q

Transition does no occur…

A

suddenly occurs over some range of velocity where the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent

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12
Q

What does the transition region depend on

A

reynolds number as well as the degree of disturbance of the flow by surface roughness, pipe vibrations and the fluctuations in the flow

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13
Q

What does the hydraulic diameter =

A

Dh = 4*Ac/p

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14
Q

What does the hydraulic diameter = in cricular pipes

A

D

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15
Q

In a channel what does the the hydraulic diameter =

A

Dh = 4*ab/2a + b, perimeter is only bit touching the fluid

only the wetted perimeter is included

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16
Q

When is a flow fully turbulent

A

Re > 10,000

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17
Q

When is the Dh used

A

when calculating Re, Nu and Pr

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18
Q

What is the entrance region

A

area where the velocity profile develops

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19
Q

Draw the velocity entrance region

A

see book

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20
Q

What is the boundary layer region,

A

the viscous effects and the velocity changes are significant

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21
Q

What is the irrotional core flow region

A

the region where the frictional effects are negligible and the velocity remains essentially constant in the radial direction
fully inviscid and irrotional

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22
Q

what is the hydrodynamic entrance region

A

the region from the pipe inlet to the point at which the velocity profile is fully developed

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23
Q

What is the hydodynamic entrance length Lh

A

the length of the hydrodynamic entrance region

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24
Q

What is the hydrodynamic fully developed region

A

the region beyond the entrance region in which the velocity profile is fully developed and remains unchanged

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25
Q

What is the velocity gradient strongest

A

just after the fluid enters the pipe

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26
Q

what region does the velocity profile no longer depend on x

A

fully developed region

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27
Q

where can bernouillis be used

A

in the irrotational core region and not experiencing viscous effects

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28
Q

At what temperature are fluid properties evaluated at

A

the bulk mean fluid temperature, which is the arithmetic average of the mean temperatures at the inlet and exit Tb= Tmi + Tme /2

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29
Q

What is the thermal entrance region

A

the region of flow over which the thermal boundary layer develops and reaches the tube centre

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30
Q

What is the thermal entry length

A

the length of the thermal entrance region

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31
Q

Thermally developing flow

A

flow in the thermal entrance region, where the temperature profile develops

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32
Q

Fully developed flow

A

the region in which the flow is both hydrodynamically and thermally developed

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33
Q

thermally fully developed region

A

the region beyond which the thermal entrance region in which the dimensionless temperature profile remains unchanged

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34
Q

In the core region of the thermal entrance region what = 0

A

dT/dy ie there is no heat transfer as no temperature difference

35
Q

What happens in the thermally fully developed region of a tube

A

the local convection coefficient is constant (does not vary with x)

36
Q

what is higher in the entrance regions of a tube

A

the pressure drop and heat flux

37
Q

what does an entrance region always increase

A

the average friction factor and heat transfer coefficient for the entire tube

38
Q

What partial derivative is used to describe hydrodynamically fully developed flow

A

d u(r,x)/ dx = 0 -> u = u(r)

39
Q

What partial derivative is used to describe thermally fully developed flow

A

d/dx *((Ts(x) - T(r,x))/(Ts(x)-Tm(x)) = 0

40
Q

Derive an equation for finding h using the surface energy balance

A

q.s = hx(Ts -Tm) = k * pardT/pardr at r=R

gives hx = (k*pardT/pardr @ r=R) / Ts - Tm

41
Q

Prandtl number =

A

kinematic viscousity / thermal conductivity

42
Q

What does a high Pr number mean for the entrance region

A

high kinematic viscosity therefore momentum diffuses fast therefore velocity entrance length is small

43
Q

What does a low Pr number mean for the entrance region

A

high thermal conductivity therefore thermal entrance length is small

44
Q

Pr ratios =

A

v/alpha = partial v^2/ partial T^2 = L temp/ L Vel

45
Q

what does the thermal profile look like once fully developed

A

parabola, the shape will remain constant, this is why for the equation
d/dx *((Ts(x) - T(r,x))/(Ts(x)-Tm(x)) = 0
we take away heat to keep it constant

46
Q

What dimensionless number is much higher in the entrance region

A

Nu and thus h values are much higher in the entrance region

47
Q

When does the Nu number reach a constant

A

at a distance of less than 10 diameters meaning we can assume flow fully developed after x>10D

48
Q

Lv or Lh laminar approx =

A

0.05 Re D

49
Q

Lt laminar approx =

A

0.05 Re Pr D = Pr Lh laminar

50
Q

Lv turbulent approx =

A

Lt turbulent approx = 10D

51
Q

How does the local nusselt number vary between constant surface temperature and constant heat flux

A

it takes longer for constant heat flux to return to the local Nu number to a constant level

52
Q

How can thermal conditions at the surface by approximate

A

constant surface temperature Ts = const

Constant surface heat flux qs =const

53
Q

Rate of heat transfer =

A

Q. = m. cp (Te - Ti)

54
Q

Surface heat flux =

A

q.s = hx (Ts - Tm) where hx is the local heat transfer coefficient

55
Q

Heat transfer to a fluid flowing in a tube is

A

= to the increase in energy of the fluid

56
Q

when does constant surface temperature occur

A

when a phase change process such a boiling or condensation occurs at the outer surface of a tube

57
Q

when does constant surface heat flux condition occur

A

when the tube is subjected to radiation or electric resistance heating uniformly from all directions

58
Q

Can we have Ts = const and qs = const

A

No

59
Q

By considering constant surface heat flux derive mean fluid temperature at tube exit

A 
Q. = q.s As = m.cp (Te - Ti)
Te = Ti + q.s As/m. cp
60
Q

By considering constant surface heat flux derive mean surface temperature

A

q.s = h (Ts - Tm) -> Ts = Tm + q.s/h

61
Q

What does Ts = Tm + q.s/h mean for Ts

A

Ts grows linearly as q is constant

62
Q

Draw a temperature vs x graph for Ts and Tm

A

See book

63
Q

Prove that the shape of the temperature profile remains unchanged in the fully developed region of a tube subject to constant surface heat flux

A

see book

64
Q

With constant surface temperature what can not constantly increase

A

the temperature of the fluid, it will max out at Ts

65
Q

Equation for rate of heat transfer to or from a fluid flowing in a tube with constant Ts

A

Q. = hAs deltaTavg = h As (Ts - Tm)avg

66
Q

What does delta Tavg approx =

for constant Ts

A

Ts - Tb

from approx = change in Ti + Change in Te /2 = (Ts - Ti) + (Ts - Te) /2 = Ts - (Ti + Te)/2 = Ts - Tb

67
Q

Whats the issue with using arithmetic mean temperature difference
Ts

A

we assume that the mean fluid temperature varies linearly along the tube which is hardly ever the case when Ts = const

68
Q

Te for constant Ts =

A

Ts - (Ts - Ti)exp(-hAs/m.cp)

69
Q

Derive the equation for Te

A

see book

70
Q

What does NTU stand for

A

number of transfer units, a measure of the effectiveness of the heat transfer system
says how fast we get temp of fluid reaching temp of surface

71
Q

for NTU = 5

A

Te = Ts, limit of heat transfer is reached

72
Q

What does a small value of NTU

A

more opportunities for heat transfer

73
Q

what is delta Tln

A

An exact representation of the average tempearture difference between the fluid and the surface

74
Q

What is the error in using the arithmetic mean temperature when difference in change in Te and change in Ti is 40 percent

A

less than 1%

75
Q

what does an NTU of greater than 5 represent

A

that fluid flowing in a tube will reach the surface temperature at the exit regardless of the inlet temperature

76
Q

Heat transfer for Ts Q. =

A

Q. = hAs * delta Tln

77
Q

What does delta Tlin =

A

(Change in Te - Change in Ti)/ ln(Change in Te)/(Change in Ti)

78
Q

what does NTU =

A

hAs/m.cp

79
Q

what does NTU =

A

hAs/m.cp

80
Q

Constant surface temp what does Nu =

A

3.66 = hD/k

81
Q

For turbulent flow in tubes what is the colburn equation Nu =

A

0.023 Re^0.8 Pr ^1/3 0.7 <= Pr <= 160 and Re>10000

82
Q

For turbulent flow in tubes what is the chilton colburn analogy Nu =

A

0.125 f * Re*Pr^1/3

where f = 0.184 Re^-0.2

83
Q

For turbulent flow in tubes what is the dittus boelter equation Nu =

A

0.023 Re ^0.8 Pr ^n where n = 0.4 for heating and 0.3 for cooling

84
Q

When variation in properties is large due to a large tempearture difference Nu

A

0.027 Re ^0.8 Pr ^1/3 (mu/mu(s))^0.14 0.7 <= Pr <= 17600 and Re>10000
all properties evaluated at Tb expect mu(s) which is evaluated at Ts

MEC203 (12 decks)

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