Thermodynamics- Convection and External Flow

Question 1

What is velocity boundary layer thickness (δ) defined by?

Answer 1

Distance from surface that the flow velocity is 99% of the free stream velocity.

Question 2

Where is thermal boundary layer thickness defined to be?

Answer 2

The distance from the surface where

Ts-T)=0.99(Ts-Tinf

Question 3

Are the velocity and thermal boundary layer thicknesses the same?

Answer 3

No

Question 4

Formula for critical Reynolds number

Answer 4

ρ uinf xc/μ

Where xc is distance along surface to where transition to turbulence begins (start of transition region)

Question 5

How does δ vary as you go further along the surface?

Answer 5

Starts at 0. Up like root x curve. At start of transition region root x style curve is steeper upwards.

Question 6

How does heat transfer coefficient vary as you go further along the surface?

Answer 6

Starts high near x=0. Curves down quite steep like exponential decay to start of transition region. Steep straight line up to highest point at end of transition region. Curves down exponentially very slowly in turbulent region due to the thermal resistance of the fluid.

Question 7

Formula for heat transfer coefficient, h

Answer 7

h=(-kdT/dy)/(Ts-Tinf)

ds are curly and derivative is at y=0

Question 8

Formula for h bar over a uniform surface temperature

Answer 8

h bar=(1/A)ShdA

Where integral is between 0 and whole area

Question 9

Formula for h bar for flat plate in parallel flow

Answer 9

h bar=(1/L)ShdL

Integral is between 0 and L

Question 10

Approximations for velocity boundary layer

Answer 10

Sending partial derivative of u with respect to x is much less than that with respect to y.
dp/dx is about dpinf/dx
Think p is pressure

Question 11

Approximation for thermal boundary layer

Answer 11

Second partial derivative of T with respect to x is much less than that with respect to y

Question 12

Governing equations for conservation of mass, momentum, energy for boundary layers

Answer 12

See slide 10 of intro to convection

Question 13

Formula for Prandtl number

Answer 13

Pr=Cpμ/k=ν/α

Question 14

Formula for Nusselt number

Answer 14

Nu=hL/kf

Question 15

External flow

Answer 15

Fluid not surrounded by surface, eg over flat plate

Question 16

When does similarity solution for laminar constant property flow over an isothermal plate apply?

Answer 16

Only when the fluid is incompressible

Question 17

Just have a look at slides 5 and 6 for external flow

Answer 17

It’s just a joke

Question 18

Formula for Nusselt number in terms of Re and Pr for laminar flow

Answer 18

Nu=0.332Re^1/2 Pr^1/3

Question 19

What is Pr^1\3 equal to?

Answer 19

δ/δt

Question 20

Another formula for h bar in laminar flow

Answer 20

h bar=(1/x)Shdx

From 0 to x

Question 21

Formula for film temperature for turbulent flow

Answer 21

Tf=(Ts+Tinf)/2

Question 22

Formula for h bar in turbulent flow

Answer 22

h bar=(1/x)(S hlamdx+S hturbdx)
First integral from 0 to xc
Second from xc to L

Question 23

Formula for average Nusselt number in laminar flow

Answer 23

Nux bar=0.664Re^1/2 Pr1/3

Question 24

Formula for local Nusselt number in turbulent flow

Answer 24

Nux=0.0296Re^4/5 Pr1/3

Question 25

Formula for average Nusselt number in turbulent flow

Answer 25

Nux bar=(0.037ReL^4/5 - 871)Pr^1/3

Re subscript L is one term

Question 26

What does formula for average Nusselt number in turbulent flow reduce to when Rex,c=0 or L»xc?

Answer 26

Nux bar = 0.037ReL^4/5 Pr^1/3