NUSSELT NUMBER CALCULATION, LAMINAR FLOW ANALYSIS

The study of laminar flow through a circular duct is fundamental in fluid mechanics and heat transfer, as it forms the basis for analyzing internal flows in engineering applications such as pipelines, heat exchangers, and cooling channels. In this analysis, ANSYS Fluent is used as a computational tool to model and simulate the flow characteristics within a circular duct under steady-state conditions.

The geometry of the duct is modeled as a straight cylindrical pipe with a specified diameter and length, ensuring that the length-to-diameter ratio is sufficient to allow the development of a fully developed velocity profile. The fluid domain is discretized Boundary conditions are defined by specifying a uniform velocity or pressure inlet, a pressure outlet, and no-slip conditions at the duct wall.

For laminar regime analysis, the Reynolds number is maintained below the critical value (Re < 2300). The solver applies the Navier–Stokes equations for incompressible, viscous, and steady laminar flow. Post-processing of results provides velocity profiles, pressure drop along the duct length, and wall shear stress distribution. The parabolic velocity profile characteristic of laminar flow is expected at the outlet, validating theoretical predictions.

This analysis not only demonstrates the development of the hydrodynamic boundary layer inside the duct but also provides insights into fundamental transport phenomena, which can later be extended to turbulent flow, heat transfer, and multiphase flow studies.

Learn how to:

1. Geometry Creation

• Open ANSYS Workbench → Drag and drop Fluent into the project.
• Open Geometry (Space Claim/ Design Modeler):
  • Create a cylinder (duct).
  • Typical size: Length = 1 m, Diameter = 0.05 m (choose any reasonable values).
  • Save and close geometry.

2. Meshing

• Open ANSYS Meshing:
  • Use structured (hexahedral) mesh if possible → better accuracy for pipe flows.
  • Apply inflation layers near the wall to capture boundary layer.
  • Keep mesh fine enough (quality > 0.8).
  • Update mesh and close.

3. Setup in Fluent

1. General

• Solver type: Pressure-based, steady, 3D.
• Turn ON laminar flow model (no turbulence model).

1. Materials

• Select fluid = air (or water) depending on case.
• Density: constant (if incompressible).

1. Boundary Conditions

• Inlet: Set velocity inlet with a low velocity (e.g., 0.1 m/s) → ensures Re < 2300 for laminar flow.
• Outlet: Set to pressure outlet (0 Pa gauge).
• Walls: Apply no-slip condition.

1. Operating Conditions

• Keep default (operating pressure = 101325 Pa).

4. Solution Methods

• Pressure–velocity coupling: SIMPLE scheme.
• Spatial discretization:
  • Momentum: Second-order upwind.
• Initialization: Standard initialization from inlet.

5. Run Calculation

• Set number of iterations (e.g., 500).
• Monitor residuals until they drop below 1e-5 (or velocity profile stabilizes).

6. Post-Processing

• Plot velocity contours and vectors → should see a parabolic profile.
• Create a line plot of velocity along pipe diameter at outlet → compare with theoretical laminar solution:

u(r)=Umax(1−r2R2)u(r) = U_{max}\left(1 – \frac{r^2}{R^2}\right)

• Measure pressure drop along the duct → compare with Hagen–Poiseuille equation:

ΔP=32μULD2\Delta P = \frac{32 \mu U L}{D^2}

Who is this course for :

This course is designed for:

 Undergraduate and postgraduate engineering students
Especially those studying Mechanical, Aerospace, Chemical, or Civil Engineering, who want to understand fundamentals of internal flows and gain hands-on CFD skills.

Beginners in Computational Fluid Dynamics (CFD)
Learners who are new to ANSYS Fluent and want to start with a simple but fundamental case (pipe flow) before moving on to advanced simulations.

Researchers and project students
those working on fluid flow, heat transfer, or pressure drop analysis in ducts, pipelines, and heat exchangers.

Industry professionals and engineers
People in HVAC, thermal systems, energy, and process industries who need CFD-based insights into laminar and turbulent duct flows.

Self-learners and enthusiasts
anyone curious about fluid mechanics and interested in using simulation tools to visualize real-world fluid flow behavior.