From TecQuipment TE93 User Guide (2009) | Source: TecQuipment Ltd User Guide, Experiment 3 + Dimensionless Calculations
Tags: velocity profile, downstream velocity, pitot traverse, Nusselt number, Reynolds number, Prandtl number, dimensionless groups, Nu-Re correlation, wake region, negative velocity, TE93
Experiment 3 maps the velocity distribution downstream of the rods by traversing a pitot probe across the working section in 2 mm steps. The profile shows peaks between rods and negative-velocity wake regions behind each rod. The dimensionless calculations section then ties all three experiments together: the heat transfer coefficient α from Experiment 2 and the mean velocity V from Experiment 1 are converted into Nusselt and Reynolds numbers, producing correlations that can be compared against published theoretical curves.
Velocity profile
A plot of local flow velocity against position across the working section height. Reveals how the rods redistribute the airflow.
Wake region
The low-pressure zone directly behind each rod where flow separates. Characterised by recirculation and negative velocities (flow moving against the main direction).
Negative velocity
When the pitot probe measures a negative pressure difference (p_t − p_d < 0), this indicates reversed flow in the wake of a rod. The absolute value of the pressure is used to calculate velocity magnitude, then a negative sign is applied.
Nusselt number (Nu)
A dimensionless measure of convective heat transfer: Nu = α × d / λ. Compares convective to conductive heat transfer across the fluid. Higher Nu means more effective convection.
Reynolds number (Re)
A dimensionless measure of the flow regime: Re = ρ × V × d / μ. Compares inertial to viscous forces. Higher Re means more turbulent flow and generally higher heat transfer.
Prandtl number (Pr)
A dimensionless ratio of momentum diffusivity to thermal diffusivity: Pr = c_p × μ / λ. For air at the conditions in this apparatus, Pr ≈ 0.71 and is effectively constant, so it provides no useful variation for comparison.
Aim: determine the velocity distribution (profile) downstream of the rods.
Setup differences from Experiment 1:
Pitot Assembly moved to the downstream position
Pitot probe connected to ΔP1 (+); downstream static tapping to ΔP1 (−)
This measures (p_t − p_d) directly
Datum and probe positioning:
The probe is slid down until it touches the bottom of the working section
The digital display is zeroed at this point
The pitot probe has a 2 mm diameter, so at an indicated 0 mm, it measures pressure 1 mm from the wall
Measurements start at an indicated 4 mm (actual position 5 mm from the wall) to avoid the turbulent boundary layer at the floor
Measurements end at 118 mm (actual 119 mm) to avoid the ceiling boundary layer
Steps are 2 mm apart, giving 58 measurement positions
Velocity calculation:
V₂ = √(2 × |p_t − p_d| × 287 × T₁ / p_A)
For negative pressure differences, the absolute value is used in the square root, then a negative sign is placed in front of the resulting velocity.
The sample profile from the guide reveals a clear periodic pattern:
Peak velocities (~18–20 m/s at 100 % valve) occur at the midpoints between rods, where the flow accelerates through the narrowest gap
Negative velocities (down to approximately −15 m/s) occur directly behind each rod, in the wake recirculation zone
Sharp transitions between positive and negative regions correspond to the edges of each rod
The pattern repeats five times across the working section, matching the five rod positions
The overall shape is roughly sinusoidal, reflecting the alternating acceleration (between rods) and separation (behind rods).
Purpose: convert experimental results into dimensionless form so they can be compared with published correlations and across different experimental conditions.
The three dimensionless groups:
Nusselt number: Nu = α × d / λ
Prandtl number: Pr = c_p × μ / λ ≈ 0.71 (constant for this apparatus)
Reynolds number: Re = ρ × V × d / μ
Since Pr is constant, the useful comparison is Nu vs Re.
Thermal conductivity of air (λ) = 0.0259 J/ms°C
Dynamic viscosity of air (μ) = 18.2 × 10⁻⁶ kg/ms
Specific heat of air (c_p) = 1004.5 J/kg°C
Gas constant for air (R) = 287 J/kgK
Specific heat of copper (c) = 380 J/kg°C
The textbook "Heat Transmission" by McAdams provides theoretical Nu-Re correlations for this geometry:
One rod only: Nu = 0.24 × Re⁰·⁶
Rod in column 1 (all rods fitted): Nu = 0.18 × Re⁰·⁶
Rod in column 2: Nu = 0.246 × Re⁰·⁶
Rod in column 3: Nu = 0.30 × Re⁰·⁶
Rod in column 4: Nu = 0.315 × Re⁰·⁶
All correlations share the same exponent (0.6) but differ in the leading coefficient. The coefficient increases from column 1 to column 4, reflecting the turbulence enhancement from upstream rods.
A single rod alone has a higher coefficient (0.24) than column 1 of a full bank (0.18). This is because in a full bank, the upstream rods partially shelter column 1 from the full oncoming flow, slightly reducing its heat transfer.
For each air valve setting, take V (mean velocity, from Experiment 1) and α (heat transfer coefficient, from Experiment 2)
Calculate ρ = p_A / (R × T₁)
Calculate Re = ρ × V × d / μ
Calculate Nu = α × d / λ
Plot Nu on the vertical axis against Re on the horizontal axis
Overlay the theoretical curve (dotted line) for comparison
The sample results from the guide show experimental data tracking the theoretical curves reasonably well, with some scatter.
Downstream velocity from pitot traverse:
V₂ = √(2 × |p_t − p_d| × 287 × T₁ / p_A)
Apply a negative sign if the pressure difference was negative.
Nusselt number:
Nu = α × d / λ
Reynolds number:
Re = ρ × V × d / μ
Prandtl number:
Pr = c_p × μ / λ ≈ 0.71
Theoretical Nu-Re correlations:
Nu = C × Re⁰·⁶
Where C = 0.24 (one rod), 0.18 (col 1), 0.246 (col 2), 0.30 (col 3), 0.315 (col 4).
⚠️ Negative pressure differences from the pitot traverse indicate reversed flow, not instrument error. Use the absolute value for the velocity magnitude, then assign a negative sign.
⚠️ The Prandtl number is constant (~0.71) for air in this experiment, so it carries no information. The examinable comparison is Nu vs Re.
⚠️ The leading coefficient in Nu = C × Re⁰·⁶ increases from column 1 to column 4. This directly reflects increasing turbulence intensity deeper into the rod bank.
⚠️ A single isolated rod has a higher coefficient (0.24) than a rod in column 1 of a full bank (0.18). The full bank partially shields column 1, reducing its effective heat transfer.
⚠️ All five correlations share the exponent 0.6, meaning the relationship between Nu and Re has the same fundamental character regardless of position. Only the magnitude shifts.
⚠️ When computing Re, use the mean velocity V (not V₁ or V₂). V accounts for the blockage effect.
Q: Why does the velocity profile show negative values behind each rod?
A: Each rod creates a wake region where the flow separates from the rod surface. In this low-pressure zone, air recirculates and flows backwards (against the main flow direction), producing a negative velocity reading on the pitot probe.
Q: A student calculates α = 150 W/m²K at a mean velocity of 20 m/s, with rod diameter 0.0124 m, air density 1.2 kg/m³, λ = 0.0259 J/ms°C, and μ = 18.2 × 10⁻⁶ kg/ms. What are the Nusselt and Reynolds numbers?
A: Nu = 150 × 0.0124 / 0.0259 = 71.8. Re = 1.2 × 20 × 0.0124 / (18.2 × 10⁻⁶) = 16,352.
Q: Why does the heat transfer coefficient increase for rods deeper in the bank (column 1 to column 4)?
A: Upstream rods shed turbulent wakes. Each successive column encounters progressively more turbulent flow, which disrupts the thermal boundary layer more effectively and enhances convective heat transfer.
Q: The Prandtl number for air in this experiment is approximately 0.71. Why is it not useful for comparing results?
A: It is effectively constant across all test conditions (it depends on fluid properties at roughly the same temperature and pressure). A dimensionless group that does not vary cannot reveal trends or differentiate between test cases.
Q: What does the exponent 0.6 in the Nu-Re correlation physically represent?
A: It describes how sensitive the heat transfer is to changes in flow velocity. An exponent of 0.6 means that if Reynolds number doubles, the Nusselt number increases by a factor of 2⁰·⁶ ≈ 1.52. This is characteristic of turbulent forced convection over cylinders.
velocity profile, pitot traverse, wake region, flow separation, recirculation zone, negative velocity, Nusselt number, Reynolds number, Prandtl number, dimensionless analysis, Nu-Re correlation, heat transfer coefficient, turbulence enhancement, rod bank, cylinder in crossflow, forced convection correlation, McAdams, TE93 Experiment 3, thermal boundary layer