Determinants of furnace capacity: Which variables most directly influence the achievable throughput (capacity) of a heating furnace?

Introduction / Context:
“Capacity” is not just burner nameplate. The real limit is how fast heat can be transferred and absorbed to bring product to target temperature uniformly. This question highlights key thermal variables that set the pace of heating and, therefore, the achievable throughput.

Given Data / Assumptions:

• A direct-fired or radiant-tube furnace heating metal or ceramic stock.
• We consider steady, tuned combustion.
• Heat transfer to and within the stock controls ramp-up and soak times.

Concept / Approach:
High flue-gas temperatures imply higher gas-to-surface temperature difference and radiative/convective driving force. Stock thermal conductivity governs how quickly surface heat penetrates to the core. Stock thickness sets the conduction path length; thicker sections need longer times to equalize temperature. All three therefore determine how many tons per hour can be processed to specification.

Step-by-Step Solution:
Connect flue-gas temperature with heat-transfer coefficients and driving force.Relate stock conductivity to internal temperature gradients during heating.Relate thickness to characteristic heating time ~ L^2/alpha (qualitative), where alpha is thermal diffusivity.Thus, capacity depends on all listed variables.

Verification / Alternative check:
Heating curves and soak calculations in design handbooks explicitly depend on material properties (k, rho, cp), section size, and furnace temperature profiles, corroborating the selection.

Why Other Options Are Wrong:
Only burner rating: insufficient; you cannot force heat into thick, low-conductivity parts arbitrarily fast without quality loss.Any single factor alone ignores the coupled nature of external and internal heat transfer.

Common Pitfalls:
Equating bigger burners with higher capacity; product heating limitations often dominate, especially for thick or low-k materials.

Final Answer:
All (a), (b) and (c).