Where does the heat go in a fired furnace? The split between heat absorbed by the charge/stock and the heat lost to furnace structure and flue gases depends primarily on which factors?

Introduction / Context:
Furnace efficiency is the fraction of fuel energy delivered to the stock. Understanding what controls the split between useful absorption and losses helps engineers tune firing patterns, choose materials, and set operating modes for best performance.

Given Data / Assumptions:

• A refractory-lined furnace heats a metallic or ceramic load.
• We consider steady, representative operation with proper combustion.
• Variables include firing rate, radiative properties, materials conductivities, and process scheduling.

Concept / Approach:
Higher firing rates and high-emissivity flames increase radiative transfer to the stock but can also raise flue losses if residence is short. The thermal conductivity of the stock and linings governs temperature gradients, warm-up time, and wall losses. Batch versus continuous operation changes transient losses, soak uniformity, and average wall temperatures—all of which affect efficiency.

Step-by-Step Solution:
Relate firing rate/emissivity to radiative heat flux to the charge.Account for material properties: conductive stock heats faster and more uniformly; refractory conductivity affects shell losses.Consider operating mode: batch cycles incur more start-stop and warm-up losses than well-loaded continuous systems.Therefore, all listed factors jointly determine the heat split.

Verification / Alternative check:
Heat-balance audits consistently vary with burner settings, charge properties, and production scheduling; efficiency improves when these are optimized together.

Why Other Options Are Wrong:
Any single factor alone is incomplete; real furnaces respond to combined thermal and operational parameters.Excess-air setting matters, but it is only one among several drivers.

Common Pitfalls:
Over-focusing on combustion tuning while ignoring stock properties or process cadence; capacity utilization and lining selection can shift losses dramatically.

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