Firebox design feature: “The crown (top) of certain furnace or firebox chambers is made hemispherical to better resist severe heat and pressure in the firebox region.” Evaluate this statement.

Introduction / Context:
High-temperature, high-pressure furnace enclosures require shapes that minimize thermal stresses and resist pressure. Hemispherical and other curved surfaces are common in pressure-vessel design due to favorable stress distributions.

Given Data / Assumptions:

• Hemispherical (or domed) crowns are used in some boiler furnaces (e.g., Scotch marine, certain shell boilers).
• Intense radiant heat exists in the firebox; pressure acts on the furnace surface from the water/steam side.
• Materials are adequately stayed or self-supporting depending on geometry.

Concept / Approach:
Curved shells like hemispheres distribute membrane stresses more uniformly than flat plates. Under pressure and severe thermal exposure, a hemispherical crown minimizes bending stress, reduces the need for extensive staying, and withstands cyclic thermal gradients more effectively than flat crowns. Thus, the statement that hemispherical crowns are used to resist intense service conditions is correct in principle for applicable boiler types.

Step-by-Step Solution:
Recognize pressure-vessel principle: spherical shapes offer highest strength for given thickness.Apply to firebox crown: curved crown reduces bending and local hot spots.Contrast with flat crown: requires dense stays (e.g., locomotive firebox) to handle pressure and distortion.Conclude: hemispherical crowns are chosen to resist heat and pressure more effectively.

Verification / Alternative check:
Design codes and historical practice show domed crowns in marine shell boilers where geometry allows, confirming the advantage.

Why Other Options Are Wrong:
Flat plates do not “always” perform better; they typically need extensive staying.

Limiting to a specific boiler type or low pressure ignores the general structural advantage of curved shells.

Common Pitfalls:
Assuming all fireboxes are hemispherical (e.g., locomotive fireboxes are often flat but heavily stayed); conflating specific boiler types with the general design principle.

Final Answer:
True