Boiler Surfaces — Water-Tube vs Fire-Tube (Same Tube Size) For the same outside diameter and thickness of a tube, compare the available heating surface area in a water-tube boiler with that in a fire-tube boiler. Choose the most appropriate relation.

Introduction / Context:
Heating surface is the area through which heat is transferred from hot combustion gases to water/steam. Understanding which side of the tube is exposed to the hot gases determines the effective heating surface and helps explain why water-tube boilers achieve high steaming rates in compact envelopes.

Given Data / Assumptions:

• Same tube outside diameter and wall thickness are considered for both boiler types.
• In a fire-tube boiler, hot gas flows inside the tubes and water surrounds the outside.
• In a water-tube boiler, water flows inside the tubes and hot gas surrounds the outside.
• Heating surface is taken as the surface on the hot-gas side that drives convection/radiation heat transfer.

Concept / Approach:
For a cylindrical tube, the outside area A_o = π * D_o * L and the inside area A_i = π * D_i * L, where D_o > D_i. With identical tube geometry, the hot-gas-side area in a fire-tube is A_i (smaller), whereas in a water-tube it is A_o (larger). Therefore, per tube, a water-tube boiler provides a larger heating surface for the same length.

Step-by-Step Solution:
Let tube outside diameter = D_o, thickness = t ⇒ D_i = D_o − 2t.Fire-tube hot-gas area = A_F = π * D_i * L.Water-tube hot-gas area = A_W = π * D_o * L.Since D_o > D_i, A_W > A_F for the same L.Hence, water-tube boilers offer more heating surface per tube.

Verification / Alternative check:
Beyond single-tube geometry, practical boilers also differ in tube counts and gas-side arrangements. However, the per-tube comparison still holds: the hot gases bathe the larger outer circumference in water-tube designs, increasing area and enhancing convective coefficients.

Why Other Options Are Wrong:

• Less / Equal: Contradict the geometric inequality A_o > A_i.
• Cannot be compared without gas temperature: Temperature affects heat flux, not the fundamental area comparison for identical tubes.

Common Pitfalls:
Confusing “heating surface” with water-side area, or assuming that tube count or gas temperature overrides the basic diameter-based area difference. The question fixes diameter and thickness, so area comparison is straightforward.

Final Answer:
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