The most direct path runs through an air-cooled (fin‑fan) heat exchanger pilot plant. By systematically varying the air mass flow rate (G_A) while holding the process‑side conditions constant, you collect inlet/outlet temperatures and flow rates for both fluids. From these stead‑state data, you compute the experimental overall heat transfer coefficient (U) using the log‑mean temperature difference (LMTD). Because the process‑side thermal resistance is kept nearly fixed, the change in (U) directly tracks the change in the air‑side heat transfer coefficient (h_A). Plotting (U) (or the derived (h_A)) against (G_A) then lets you extract the power‑law relationship (h_A \propto G_A^n) that underpins industrial thermal design correlations.
Core takeaway: The experiment leverages the fact that the air‑side resistance typically dominates the overall coefficient. By measuring (U) at several air flow rates while keeping everything else steady, students can quantitatively confirm that the air‑side film coefficient follows a predictable function of mass velocity—transforming an abstract correlation into a tangible, measured trend.
The Experimental Foundation: The Fin‑Fan Pilot Plant
Why a Fin‑Fan Exchanger is Ideal for This Study
A unit‑operations pilot plant with a fin‑fan heat exchanger gives you direct control over the air‑side variable of interest. The extended surface (fins) amplifies the air‑side resistance, making the overall (U) highly sensitive to air‑side changes. This sensitivity is what turns a simple flow‑rate adjustment into a clear, measurable response.
Key Measurements You Must Record
You will collect steady‑state data at every air flow setting:
- Process fluid: inlet temperature, outlet temperature, mass flow rate.
- Cooling air: inlet temperature, outlet temperature, and the air‑side face mass flow rate (G_A) (calculated from air velocity and face area).
- Geometric constants: tube outside diameter, fin parameters, and the base heat transfer area.
These values feed directly into a standard heat balance and the log‑mean temperature difference (LMTD) to yield the experimental overall coefficient.
Step‑by‑Step Verification Process
1. Run Steady‑State Experiments at Multiple Air Flow Rates
Adjust the fan speed or damper position to give at least five distinct (G_A) values. Keep the process‑side flow rate and inlet temperature constant throughout all runs. This locks the process‑side resistance so that any observed change in (U) originates almost entirely from the air side.
2. Calculate the Experimental Overall Heat Transfer Coefficient ((U))
For each run, compute the heat duty twice—once from the process fluid and once from the air—to verify closure. Use the energy balance ((Q = \dot{m} c_p \Delta T)) and the rate equation:
[ Q = U \cdot A \cdot \Delta T_{lm} ]
where (A) is the reference area (often the bare tube outside area) and (\Delta T_{lm}) is the LMTD. The resulting (U) is your primary experimental fingerprint of the air‑side influence.
3. Isolate the Air‑Side Resistance from the Total Resistance
The overall coefficient on the outside‑tube basis is:
[ \frac{1}{U_o} = \frac{1}{h_o} + \frac{1}{h_{od}} + R_{wall} + \frac{d_o}{d_i}\frac{1}{h_{id}} + \frac{d_o}{d_i}\frac{1}{h_i} ]
If the process‑side conditions are unchanged, the sum of the process‑side film resistance, fouling, and wall resistance remains approximately constant. Subtracting this constant baseline from each (1/U_o) yields a value proportional to (1/h_A). A quick calibration run at the highest practical air flow (where the air‑side resistance is smallest) can help estimate that constant. In many laboratories, students simply plot (U) versus (G_A) and interpret the trend directly, as the process‑side resistance acts as a fixed offset.
4. Plot the Air‑Side Coefficient vs. Air Mass Velocity
With (h_A) values in hand, plot them against the corresponding face mass flow rate (G_A). Most air‑side correlations take the form (h_A = C \cdot G_A^n), with (n) typically between 0.6 and 0.8. Use a log‑log plot to confirm linearity and extract the exponent (n).
Connecting Experiment to Theory
The Theoretical Air‑Side Correlation and Its Variables
Industrial standards express the extended‑tube film coefficient (h_A) as a function of the face‑area mass velocity, fluid properties (thermal conductivity, viscosity, Prandtl number), and geometry. By fixing the air inlet temperature and the exchanger geometry, you reduce the correlation to a simple power law in (G_A). This is the function students validate.
How to Assess the Fit and Validate the Exponent
Overlay the experimental data with the theoretical curve. Compute the coefficient of determination ((R^2)) for the log‑log linear fit. A strong linear fit confirms that the fundamental relationship matches theory, while any deviation prompts discussion about measurement accuracy, flow maldistribution, or unexpected thermal resistances.
Understanding the Trade‑offs and Pitfalls
Pitfall: Variations in the Process‑Side Resistance
Even with a constant process‑side flow rate, temperature‑dependent fluid properties can cause the process‑side film coefficient to drift. If the process fluid’s viscosity changes significantly across the temperature range, the “constant” resistance assumption breaks down. In that case, you should either correct for the Reynolds‑number dependence or use a more rigorous isolation method.
Pitfall: Failing to Account for Fouling
New pilot plants may have negligible fouling, but repeat runs without cleaning can build a fouling layer that adds a variable thermal resistance. Always record the pressure drops and visually inspect tube surfaces before and after the experiment.
Trade‑off: The Wilson Plot Method for Greater Precision
The supplementary references highlight the Wilson plot technique for extracting individual film coefficients. By running experiments where the air‑side flow is varied while the process‑side flow is held at several different constant levels, you can plot (1/U) versus (G_A^{-n}) (or a known Reynolds‑number function). The intercept isolates the sum of all non‑air‑side resistances, giving a pure air‑side coefficient. This is statistically more robust but demands careful experimental design and more runs.
When Temperature Variations Demand a Segmented Approach
If the overall coefficient (U) changes appreciably with temperature (due to strong property variations), the simple LMTD method with a constant (U) is no longer accurate. The experiment may then require treating the exchanger as a series of segments with local coefficients, or using numerical integration. For most educational fin‑fan studies with moderate temperature changes, this complication is unnecessary—but it is a valuable discussion point for advanced classes.
Making the Right Choice for Your Learning Goal
- If your primary focus is a quick, intuitive verification: Plot the experimental overall (U) directly against air mass velocity while keeping the process side fixed. The trend alone convincingly shows the air‑side dominance and its functional form.
- If your primary focus is isolating the pure air‑side film coefficient: Use the Wilson plot method or a baseline‑subtraction technique with rigorous heat balances. This approach yields a quantitative comparison with the theoretical correlation and teaches the art of separating series resistances.
- If your primary focus is bridging design standards and reality: Calculate fan power and pressure drop alongside the heat transfer data. This links the measured (h_A) to the whole picture of air‑cooled exchanger performance, exactly as an API 661 check would require.
This method turns the pilot plant into a living textbook, proving that a core engineering correlation is not just an equation—it is a measurable, repeatable physical law.
Summary Table:
| Experimental Step | Key Parameters Measured | Calculation / Output |
|---|---|---|
| 1. Vary Air Flow | Air face velocity ($G_A$), inlet/outlet temperatures | Base data for varying resistance |
| 2. Calculate Duty | Process/air temperatures & flow rates | Heat duty ($Q$) & LMTD ($\Delta T_{lm}$) |
| 3. Isolate Resistance | Overall heat transfer coefficient ($U_o$) | Plotting $1/U_o$ to isolate $1/h_A$ |
| 4. Validate Correlation | Exponent ($n$) from log-log plot | Verify power-law fit: $h_A \propto G_A^n$ ($n \approx 0.6$-0.8) |
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