Heat Transfer Exam 2

Explain the physical mechanisms that contribute to the convective heat transfer coefficient (h). Why does increasing fluid velocity generally increase h?

• type of flow affects h: turbulent flow mixes fluid strongly which increases heat transfer and creates a thinner boundary layer.

• increasing fluid velocity means the boundary layer is thin (smaller) which creates a larger h.

Describe the difference between the thermal boundary layer and the velocity boundary layer. Under what conditions is one typically thicker than the other?

• Thermal boundary layer controls how heat diffuses away from the wall where Velocity Boundary layer controls how momentum diffuses away from the wall.

• It depends on the Pradtl #:

  • if ν > α → momentum spreads faster than heat → velocity boundary layer is thicker

  • if α > ν → heat spreads faster than momentum →thermal boundary layer is thicker

In internal flow, why does the Nusselt number become constant in the fully developed region for both laminar and turbulent flow?

@ fully developed flow the boundary layers stop growing because they converge, so the nusselt # stops changing

Define effectiveness and explain why it depends on C_min.

• ε = (actual heat transfer) / (maximum possible heat transfer)

  • a measure of how well a heat exchanger performs compared to the max possible heat transfer it could achieve

• The max possible heat transfer is limited by the fluid that can only absorb or release a small amount of heat relative to a temperature change.

Explain why the Dittus–Boelter correlation should not be used for laminar flow.

It was a curve fit only in the turbulant regine

Why does the entrance region in internal flow produce a higher heat transfer coefficient than the fully developed region?

Entrance region = thin boundary layer = high h
Fully developed region = thick boundary layer = lower h

Explain the role of the Prandtl number (Pr) in convection.

Pr tells you whether heat or momentum spreads faster, which directly affects the convective heat transfer coefficient

What does it mean when we say the thermal boundary layer is fully developed?

It means the thermal boundary layer stop changing → so h stops changing

Explain differences between parallel-flow and counter-flow. Why does counter-flow produce larger LMTD?

• parallel-flow: fluids enter @ same end & flow in same direction

• counter-flow: fluids enter from opposite ends & flow against each other

• Parallel-flow → smaller ΔT → smaller LMTD
  Counter-flow → higher ΔT → larger LMTD

Describe what a fouling factor is and how it affects U.

fouling factor: a measure of thermal resistance added by deposits that build up

more fouling → worse heat transfer → lower U

The Nusselt number represents:

dimensionless wall temp gradient

Transition on a flat plate is mainly determined by:

Re #

For fully developed laminar flow in a tube (constant Ts):

3.66

Even though Koch uses it more often than he should, the Dittus–Boelter correlation is technically valid only when flow is:

Internal, Turbulent, fully developed

Pr is a ratio of:

ν/α

Increasing Re generally:

lowers h

Laminar entry length scales with:

0.05ReD

Turbulence enhances convection mainly via:

enhanced mixing

the maximum theoretical cold-fluid outlet T in a counter-flow heat exchanger is:

Hot inlet T

The log-mean temperature difference (LMTD) is used instead of a simple average temperature difference because:

temp difference varies along the heat exchanger length

Effectiveness defined as:

q_actual/q_max

Increasing the overall heat transfer coefficient 𝑈 will generally:

increase overall heat transfer rate

Given similar initial conditions for laminar boundary layers forming during flow over a flat plate (one thermal, one velocity), the velocity boundary layer is likely to be much thicker than the thermal boundary layer at a given downstream location if the Prandtl number of the fluid is

large (>>1)

What’s Nu?

• a function of Re & Pr for a given geometry

• a nondimensional form of the convection coefficent

• hD/k (for flow over a cylinder)

The heat transfer during an adiabatic process is 

zero

If the fouling resistance for the heat exchanger described above was non-negligible, which of the following would occur?

• the exit temp of the hydrocarbon fluid would be lower than the hydrocarbon exit temp without fouling

• the effectiveness of the heat exchanger would decrease

Planck’s Law describes the

spectral intensity from a blackbody

What’s a blackbody

the perfect absorber and emitter of radiation

What’s absorptivity

property that describes the fraction of incident radiation that is converted to internal energy by an object

emissive power is

the radiative flux emitted by a surface

a spectral property refers to 

a single wavelength or per-unit-wavelength component of that property

What’s transmissivity

Property that describes the fraction of incident radiation passing through an object

thermal radiation occurs as a

result of matter having a finite temperature, generally between 0.1 and 100 microns in wavelength.

What’s wavelength?

A quantitative property that describes the spectral character of light, (µm or nm)

Wien’s Law describes

the peak wavelength of emission by a blackbody

What’s frequency

a quantitative property that describes the spectral character of light (Hz or rad/sec).

What’s reflectivity

Property of a surface that describes the fraction of irradiation that is redirected away from the surface.

What’s radiosity

the total radiative flux leaving a surface (not including the radiation coming into the surface)

What’s irradiation

total radiative flux incident upon a surface

What’s a solid angle

a spatial region subtended by the partial surface area of a sphere divided by the radius squared of the sphere.  Its units are steradians

what’s gray surface

A surface whose properties are independent of wavelength, but the absorptivity and emissivity are less than one.

If you were asked to find the time required for the ball bearing mentioned above to cool to 200 °C, what is the next thing you would calculate? (Provide a verbal or symbolic answer without providing a number.)

Biot Number

Water enters a circular tube whose walls are maintained at constant temperature at a specified flow rate and temperature. For fully developed turbulent flow, the Nusselt number can be determined from Nu = 0.023 Re0.8 Pr0.4. The correct temperature difference to use in the algebraic (integrated) form of Newton’s law of cooing (q = hA∆T) in this case is

The log mean temp difference

For the same initial conditions, one can expect the laminar thermal and momentum boundary layers on a flat plate to have the same thickness when the Prandtl number of the flowing fluid is

approximately one