Find. The maximum size of a rubber-waste batch the incinerator can process without exceeding its design heat-release capacity.
Approach. The incinerator is designed around a fixed heat-RELEASE rate (Btu/hr), not a fixed mass-feed rate — a higher-heating-value waste must be fed at a proportionally LOWER mass rate to stay within that same design capacity. Find the maximum allowable mass feed rate first, then convert to a batch mass using the stated residence time.
Maximum allowable feed rate. Divide the incinerator's design heat-release capacity by the rubber waste's (much higher) heating value:
$$\dot{m}_{max}=\frac{Q_{design}}{HV_{rubber}}=\frac{2\times10^{7}\ \text{Btu/hr}}{12{,}000\ \text{Btu/lb}}=\boxed{1{,}666.7\ \text{lb/hr}}$$
This is well below the roughly 20,000–28,600 lb/hr the same $2\times10^7$ Btu/hr capacity would allow at the incinerator's NORMAL 700–1,000 Btu/lb waste — confirming that a high-heating-value waste like rubber must be fed much more slowly, or co-fired/blended with lower-heating-value waste, to avoid over-firing the unit.
Maximum batch size. Convert the residence time to hours and multiply by the maximum feed rate found above — the batch size is the mass of waste present in the incinerator at any one time as it moves through at that feed rate over one residence time:
$$t_{res}=6\ \text{min}=0.100\ \text{hr}$$
$$m_{batch}=\dot{m}_{max}\times t_{res}=1{,}666.7\ \text{lb/hr}\times0.100\ \text{hr}=\boxed{166.7\ \text{lb}}$$
Final results
Quantity
Value
Maximum allowable feed rate
1,666.7 lb/hr
Maximum batch size
166.7 lb
Check: the incinerator's heat-release capacity is treated as the binding constraint (standard assumption for this class of problem) — a real installation would also need to check that the resulting lower mass throughput still meets minimum turbulence/mixing and secondary-combustion-chamber residence-time requirements for complete destruction, which are not addressed by this heat-balance calculation alone.
