BIOE 360 Exam 2

Lumped parameter

• negligible internal resistance (Bi < 0.1)

• temperature only varies with time (temp variation in all 3 spatial directions can be ignored)

When can we ignore internal resistance

small L (thin slab)

high k

large A

Biot number

conductive resistance (R_int) / convective resistance (R_ext)

thermal diffusivity

alpha = k / rho*cp

What happens to the series solution when t is large?

The exponential terms drop off more quickly, so you don’t need as many terms for a good approximation

What are long times?

Fo > 0.2

Conditions to use Heisler

• uniform initial temp (T_i)

• constant boundary fluid temp (T_inf)

• perfect geometry

• far from edges

• no heat gen

• constant thermal properties

• long times

Semi-infinite region

• extends to infinity in two directions

• has a single identifiable surface in another direction (depth)

• idealization of heat transfer for short times and/or tick material

In reality do semi-infinite regions exist

No, it’s simply an idealization

When can we use the series approach?

Fo > 0.2 (long times)

When should we use semi-infinite approach?

Thickness >= 4sqrt(alpha*t)

What are the two forms of convective heat transfer

1. free/natural - driven by material density

2. forced - due to external force

What is the velocity boundary layer

a small layer of fluid where most of the change in the fluid’s velocity happens (0—> u_inf)

When does the thermal boundary layer exist?

If there is a temperature difference between the surface and bulk fluid

Reynolds number (Re)

ratio of inertia to viscous force

Prandtl number (Pr)

ratio of momentum diffusivity and thermal diffusivity

Does flux change along the flow?

Yes, ask you move down the plate the boundary layer changes thickness and the temperature gradient changes.

When is flux along the plat the highest?

Start of the plate b/c it has the biggest gradient here

Laminar flow

Re < 2e5

orderly

Turbulent flow

Re > 3 e 5

chaotic

Nusselt number (Nu)

ratio of the fluid’s conductive resistance to the fluid’s convective resistance

• depends on type of convection

  • forces (Re, Pr)

  • natural (Ra, Pr)

What happens when the fluid velocity is increased?

• more heat transfer

• thinner boundary layer (smaller diff over which temp change observed)

What is the characteristic length for convection?

entire length of plate or diameter of long cylinder/sphere

Grashof number (Gr)

ratio of the bouyancy to viscous force on fluid

Rayleigh number (Ra)

buoyancy-driven flow in natural convection

latent heat of fusion

enthalpy difference due to change of phase from solid —> liquid (occurs at melting temp Tm)

latent heat of vaporization

enthalpy difference due to change of phase from liquid —> vapor (occurs at boiling temp)

Freezing stages of pure water

1. supercooling

2. nucleation

3. crystal growth

4. maturation

What happens to water at it freezes?

volume and density change, high degree of expansion, k increases (takes longer to thaw)

Freezing stages in tissues

1. intracellular and extracellular fluid reach melting temp

2. ice nucleation begins in extracellular space first

3. plasma membrane prevents ice crystals into cytoplasm

4. osmotic pressure develops

5. water flows out of cell and freezes there (causes cellular dehydration)

mass concentration vs molar concentration

mass concentration = mass / unit vol

molar concentration = moles / unit vol

related by molecular weight

What is solubility

The extent to which a solute is dissolved in a solvent

Henry’s law

describes the pressure dependence of the solubility of a gas in solution

Hygroscopic vs. non-hygroscopic

hygroscopic - vapor pressure surrounding solid is a function of solid temperature AND moisture content

non-hygroscopic - vapor pressure surrounding a solid is only a function of termperature

Arrhenius law

rxn rate general increate with temperature

What is k”

partition coefficient; explains solid liquid equilibrium

What variable determines if the convection is forced or natural?

free fluid velocity (u_inf). If this value is zero, then natural.