Colburn j-factor for heat transfer (j_H): as temperature increases for a typical fluid in turbulent flow, how does the j_H factor usually vary, considering the concurrent change in fluid properties (notably Prandtl number)?

Introduction:
The Colburn j-factor provides a convenient way to correlate convective heat transfer data: j_H = St * Pr^(2/3). It ties heat transfer to momentum transfer and is widely used in exchanger rating and air-side correlations. Because j_H contains Pr^(2/3), variations in temperature that alter viscosity and thermal diffusivity will influence its value.

Given Data / Assumptions:

• Turbulent forced convection with property variations evaluated at film temperature.
• Increasing temperature usually reduces viscosity and Prandtl number for many liquids and gases.
• Flow rate (velocity) held fixed for comparison; Re may rise if μ drops, but property corrections are applied consistently.

Concept / Approach:
Since j_H = St * Pr^(2/3) and, for a given geometry, St correlates primarily with Re, a drop in Pr with temperature tends to reduce j_H. Even though Re may increase as μ decreases, the explicit Pr^(2/3) dependence usually dominates the j_H trend in standard charts, leading to a net decrease with temperature for common fluids over practical ranges.

Step-by-Step Solution:
Note typical property trend: as T rises, μ ↓ and Pr = ν/α often ↓.Recognize j_H’s explicit Pr^(2/3) multiplier.Infer the overall tendency: j_H decreases with rising temperature.

Verification / Alternative check:
Air- and water-side j-factor charts display lower j-values at higher film temperatures for otherwise similar conditions, consistent with Prandtl decreases.

Why Other Options Are Wrong:

• Increases/remains unchanged: Contradict typical property-driven behavior.
• May increase or decrease: While special cases exist, the question asks the usual trend; decrease is the standard expectation.
• Oscillation with Re: j_H varies smoothly with Re; no periodic oscillation.

Common Pitfalls:
Confusing j_H with Nusselt number alone; property grouping in j_H makes temperature trends more apparent.

Final Answer:
decreases.