Air-side film coefficient change: a single-pass air heater is replaced by a two-pass unit at the same air flow rate and conditions. If flow area per pass halves (velocity doubles), what is the approximate ratio of the new air-side film coefficient to the original (use h ∝ v^0.8)?

Introduction / Context:
In convective heat transfer for gases inside passages, the film coefficient increases with velocity. Reconfiguring a heater from single-pass to two-pass reduces the flow area per pass, increasing velocity and changing h.

Given Data / Assumptions:

• Same total volumetric/mass flow rate of air.
• Two-pass arrangement halves area per pass → velocity doubles.
• Correlation scaling: h ∝ v^0.8 (typical turbulent gas heating estimate).

Concept / Approach:
With v_new / v_old = 2, the ratio of film coefficients is (2)^0.8. This reflects the sub-linear sensitivity of turbulent heat transfer to velocity, common in Dittus–Boelter-type behavior where Nu ∝ Re^m with m ≈ 0.8.

Step-by-Step Solution:
Step 1: Compute velocity ratio: v_ratio = 2.Step 2: Apply exponent: h_ratio = (v_ratio)^0.8.Step 3: Evaluate: 2^0.8 ≈ exp(0.8 * ln 2) ≈ exp(0.8 * 0.693) ≈ exp(0.554) ≈ 1.74.Step 4: Select 1.74 as the closest option.

Verification / Alternative check:
Direct calculation with a calculator confirms 2^0.8 ≈ 1.741. Design charts show similar scaling in relevant Reynolds regimes for air.

Why Other Options Are Wrong:
1.26: Would imply v_ratio ≈ 1.3, not 2.2.00: Overstates increase; exponent less than 1.0.80: Would require a velocity decrease or exponent < 0.≈1.00: Ignores velocity impact of pass arrangement.

Common Pitfalls:
Assuming h scales linearly with velocity; turbulent convection typically follows a power < 1. Also ensure pressure-drop implications are acceptable when increasing passes.

Final Answer:
1.74