An automotive catalytic convertor is a packed bed in which a platinum catalyst is coated on the surface of small alumina spheres. A metal container holds the catalyst pellets and allows engine exhaust gases to flow through the bed of pellets. The catalyst must be heated by the exhaust gases to 300°C before the catalyst helps combust unburned hydrocarbons in the gases. The time required to achieve this temperature is critical because unburned hydrocarbons emitted by the vehicle during a cold start comprise a large fraction of the total emissions from the vehicle during an emission test. A fixed volume of catalyst is required but the shape of the bed can be modified to increase the heat-up rate. Compare the heat-up time for a bed 5-cm-diameter and 20-cm-long with one 10 cm diameter and

Question

5-cm-long. The catalyst pellets are spherical, 5-mm-diameter, have a density of 2 g/cm3, thermal conductivity of 12 W/(m K) and specific heat of 1100 J/(kg K). The packed-bed void fraction is 0.5. Exhaust gas from the engine is at a temperature of 400°C, a flow rate of 6.4 gm/s, and has the properties of air.



GIVEN



FIND

The heat-up time (t) for the pellet surface temperature (Tp) to reach 300°C

ASSUMPTIONS

The initial temperature of the bed (To) = 20°C

SKETCH

Answer 1

The Reynolds number is



Applying



The Bio number for case (a) is



Therefore, the internal resistance of the spheres is negligible in both cases and the lumped parameter

analysis can be used. The upstream portion of the bed will reach 300°C first. Since

they will be continuously exposed to 400°C air at a constant heat transfer coefficient,

may be applied. Solving Equation 3.3 for time



For case (a)



COMMENTS

The short configuration takes more than twice as long to heat up because of the lower heat transfer

coefficient due to the lower gas velocity through the bed.

Once the front row of the bed reaches 300°C, catalytic combustion will occur and quickly heat the rest

of the packed bed.