360 m2 content

under unsteady state, temp may be a function of…

position and time

Rate of heat transfer of solid depends on…

Internal thermal resistance of solid, external thermal resistance (usually fluid opposition to heat coming from solid it is stuck to)

Limiting cases of unsteady state

Negligible internal resistance, negligible external resistance, or when neither is negligible

When to use lumped parameter

temperature change in all 3 directions can be ignored, ie temperature only varies with time

Total resistance under lumped parameter

Rtot = Rext

When to ignore Rint

L/kA —> large surface area (A), high heat transfer coefficient (k), small characteristic length (L)

Biot # formula

conductive resistance/convective resistance = internal resistance/external resistance

Lumped parameter good for…

high surface area (A), high thermal conductivity (k), low volume (V), low convective heat transfer coefficient (h)

Characteristic length for infinite slab, long cylinder, sphere, thin cylinder

½ thickness, radius, radius, ½ thickness

Heisler charts need to satisfy conditions of:

initial and final temps uniform, far from edges, fourier # > 0.2, Q = 0, perfect geometry, thermal properties constant

m for Heisler charts

inverse of biot #, convective/conductive resistance or external/internal resistance

n for Heisler charts

x/L - how far are you from boundary, non-dimensional

Fo Heisler charts

alpha*t/L²

What necessitates semi-infinite case?

short time or thick material

semi infinite solution needs use of…

error function

Fourier number represents…

heat conduction rate/heat storage rate

Fluid velocity regions

inside (for large velocity gradients), outside (for small gradients)

If fluid has uniform initial velocity as it flows over a flat plate, u = () at surface

0

Velocity boundary layer

where most of change in fluid’s velocity happens

Fluid thermal regions

inside boundary layer (for large thermal gradients), outside thermal boundary layer (for small thermal gradients where temp is uniform)

Thermal boundary layer forms if…

temp of plate different from initial uniform fluid temp

velocity boundary layer () exists, thermal boundary layer () exists

always, not always

Reynold’s number conceptual

inertia/viscous force

Prandtl number conceptual

momentum diffusivity/thermal diffusivity

thermal boundary layer for laminar flow over flat plate related to…

velocity boundary layer, Prandtl #