Heat Transfer Final content

q for constant surface temps

q = hAΔT (LMTD)

Assumptions to use LMTD

Ts = constant, constant properties, steady state, no generation, no radiation, no axial conduction.

ΔT in LMTD

Ts-Tm,o or T inf - Tm,o

fully developed laminar

Lhydro = 0.05 Re*D. Lthermal = 0.05Re*D*Pr

fully developed turbulent

L/D >= 10

3 things needed for free convection

1) temperature difference within the fluid

2) fluid must change density with respect to change in temperature

3) there must be a field that gives rise to a force based on mass (ex gravity)

β

thermal volume expansion coefficient. if =0, no free convection.

Grashoff number

ratio of buoyancy to viscous forces

pool boiling

pot of water on stove (analogous to free convection)

flow boiling

pushing liquid through a pipe (analogous to forced convection)

subcooled

Tavg < Tsat

saturated

Tavg=Tboil

Gray body

black body scaled down by a number between 0 and 1. No dependence on wavelength λ.

specular

emission depends on direction

diffuse

emission does not depend on direction

E

emission. photons born at a surface (due to its temp)

G

irradiation. everything incident on a surface.

J

radiosity. everything leaving a surface.

α

percent absorbed

ρ

percent reflected

τ

percent transmitted (goes through the surface)

opaque

nothing is transmitted

qrad

= E-αG = J-G

α, ρ, τ for black bodies

ρ=0, α=1, τ=0 for all wavelengths.

ε for diffuse gray bodies

ε=α

view factor

the fraction of the radiation leaving surface i that strikes surface j directly.

qrad resistance

q = (Ji-Jj)/Rij