Heat Transfer Equations

mo TAUQ

1

Uo

1

houtsidex

kw

1

hinside

FoulingLayers of dirt, particles, biological growth, etc. effect resistance to heat transfer

We cannot predict fouling factors well

Allow for fouling factors when sizing heat transfer equipment

Historical information from similar applications

Little fouling in water side, more on product

ioodirtyo

RRUU

11

,

Log Mean Temperature Difference

Parallel Flow Counter Flow

Length

Temperature

T1 T T2

Length

Temperature T1

TT2

Log Mean Temperature Difference

For Round Tubes

2

1

21

lnT

TTT

Tm

1

2

12

ln2

r

rrr

LAm

Heat LossesTotal Heat Loss = Convection + Radiation

Preventing heat loss, insulation

Air – low thermal conductivity

Air, good

Water – relatively high thermal conductivity

Water, bad

Vessels/pipes above ambient temperature – open pore structure to allow water vapor out

Vessels/pipes below ambient temperature - closed pore structure to avoid condensation

RadiationVibrating atoms within substance give off photons

Emissivity of common substancesPolished aluminum: 0.04Stainless steel: 0.60Brick: 0.93Water: 0.95Snow: 1.00

Radiation between surface and surroundings:

4T RadiatedEnergy

4surr

4surf TT Q surfsurf A

RadiationSometimes, we’ll make an analogy to convection

A 3 cm diameter, 15 m long pipe carries hot wort at 85C. The pipe has 1.0 cm thick insulation, which has thermal conductivity of 0.08 W/m.K. The insulation exterior surface temperature is 35C and its emissivity is 0.85. The temperature of the surroundings is 20C. Determine the rate of heat loss by radiation.

surrsurfrad TT Q surfradAh

Heat Transfer – Continued

Hot wort at 95C is transferred from one tank to another through a 2.5 cm diameter stainless steel pipe (k = 120 W/m.K, wall thickness 0.2 mm). The pipework is 150 m long and the wort has specific heat capacity of 4.0 kJ/kg.K and density of 1020 kg/m3. The heat transfer coefficients on the inside and outside of the pipe are 4000 W/m2K and 125 W/m2K and the temperature of the surroundings is 10C. Assume that the pipe’s wall is “thin.” Approximate the rate of heat loss from the pipe and the exit temperature at the end of the pipe. The velocity in the pipe is 1.0 m/s.

Heat Transfer – ContinuedPrevious Problem continued…

Our pipe has an external emissivity of 0.7. Calculate the heat loss by radiation and compare it to the heat loss by convection.

Steam…