Rotary dryers: within what range of number of heat transfer units (HTU or NTU) are these dryers most economically designed for typical services?

Introduction / Context:
Rotary dryers are widely used for bulk solids. Economic design weighs capital cost (length, diameter, internals) against operating cost (fuel, air handling) and performance (moisture removal). The number of transfer units (NTU/HTU) is a convenient performance metric expressing how effectively the driving force for heat/mass transfer is utilized.

Given Data / Assumptions:

• Direct-heated rotary drum with typical flights.
• Steady operation with reasonable inlet/outlet moisture targets.
• Ambient or preheated air; conventional burner duty.

Concept / Approach:
NTU relates the integrated driving force to the actual temperature/moisture approach accomplished. Very low NTU implies short residence and poor approach to equilibrium, inflating fuel use; very high NTU requires long drums, high capital, and diminishing returns. Industry practice and design heuristics place economic NTU for rotary dryers roughly around 1.5–2.5 for many non-critical solids.

Step-by-Step Solution:
Define NTU from heat/mass transfer balances for the drum.Evaluate cost vs. benefit: as NTU increases, outlet moisture decreases but length and pressure drop rise.Find the “knee” in the curve—commonly 1.5–2.5 NTU—for economic sizing.Confirm with vendor charts or past plant data for the specific solid/air conditions.

Verification / Alternative check:
Equipment vendor guidelines and empirical correlations align with this range for many granular products; special materials (heat-sensitive, highly cohesive) may require adjustments.

Why Other Options Are Wrong:
(a) under-sizes and wastes energy; (c)–(d) increase length and cost with limited added benefit; very large NTU values (e) are rarely economical.

Common Pitfalls:
Ignoring particle entrainment limits; neglecting dew point control; applying the same NTU to very different solids without pilot tests.

Final Answer:
1.5 to 2.5