Rotary dryers: the solids retention (residence) time is governed by which set of design and operating variables?

Introduction / Context:
Rotary dryers are widely used in minerals, fertilizers, and chemical industries. The residence time of solids inside the rotating drum controls moisture removal and product quality. Correctly identifying the factors that influence residence time is essential for capacity sizing and product consistency.

Given Data / Assumptions:

• Cylindrical rotary dryer operating at steady state.
• Solids advance by a combination of cascading, showering from flights, and axial transport due to slope and rotation.
• No unusual internals beyond conventional flights.

Concept / Approach:
Residence time increases as rotational speed decreases (less forward motion per unit time) and as slope decreases (flatter drums hold solids longer). Longer drums naturally give longer paths. Flight design (number, angle, pattern) dictates how solids are lifted and dropped, which affects axial velocity and holdup. Therefore, rpm, slope & length, and flight arrangement together determine retention time.

Step-by-Step Solution:

Verification / Alternative check:
Semi-empirical residence-time correlations include terms for rotational speed, drum slope, length, fill, and flighting factors, confirming multi-parameter dependence.

Why Other Options Are Wrong:

• Any single-variable answer is incomplete.
• “None” contradicts practice and design correlations.

Common Pitfalls:
Neglecting particle size distribution and stickiness (which alter holdup); assuming scale-up without re-optimizing flights and rpm.

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