For turbulent liquid flow inside tubes, the tube-side heat-transfer coefficient varies approximately with mass velocity G as:

Introduction / Context:Correlations like Dittus–Boelter and Sieder–Tate are used to estimate convective heat-transfer coefficients for turbulent flow in tubes. These relate Nusselt number to Reynolds and Prandtl numbers, revealing how h changes with mass velocity G (or Reynolds number) at otherwise similar conditions.

Given Data / Assumptions:

• Turbulent regime in smooth tubes (Re > ~10^4).
• Moderate Prandtl number liquids, heating or cooling without strong property variation.
• Comparable diameters and fluid properties for scaling arguments.

Concept / Approach:Dittus–Boelter: Nu = 0.023 * Re^0.8 * Pr^n (n ≈ 0.3 for heating, ≈ 0.4 for cooling). Since h = Nu * k / D and Re ∝ G * D / μ, holding D and properties fixed implies h ∝ Re^0.8 ∝ G^0.8. Hence, the strongest dependence among common exponents listed is roughly the 0.8 power for turbulent single-phase flow in clean tubes.

Step-by-Step Solution:

Verification / Alternative check:Other correlations (e.g., Sieder–Tate) give similar exponents near 0.8 for Re dependence in smooth tubes, validating the trend.

Why Other Options Are Wrong:

• 0.2 and 0.5 underpredict the dependence for turbulent regimes.
• 1.5 is unrealistically strong and inconsistent with established correlations.

Common Pitfalls:Extending the 0.8 exponent to laminar or transitional regimes, or to fouled tubes where h is dominated by deposits and not strongly by G.

Final Answer:h ∝ G^0.8