Non-Newtonian Flow: Forced Convection of a Nanofluid, Paper Validation

Forced Convection of a Non-Newtonian Nanofluid in a Tube, Paper Numerical Validation, ANSYS Fluent Training

Description

This project simulates the forced-convection heat transfer of a non-Newtonian nanofluid flowing through a horizontal tube under constant wall heat flux, using ANSYS Fluent. It reproduces and validates against the reference paper "Modeling of forced convective heat transfer of a non-Newtonian nanofluid in the horizontal tube under constant heat flux with computational fluid dynamics."

The defining feature of this case is the non-Newtonian flow model. A Newtonian fluid has a single, constant viscosity, but many real fluids do not — their apparent viscosity changes with the local shear rate. Here the working fluid is water carrying Al₂O₃ nanoparticles together with xanthan: the aluminium-oxide particles make it a nanofluid, while the xanthan makes it non-Newtonian, so its viscosity is no longer constant and cannot be described by Newton's law. Capturing this shear-dependent viscosity is exactly what the non-Newtonian flow model does, and this tube flow is a clean setting to demonstrate it.

Rather than treating the nanofluid as a multiphase mixture, it is defined as a single new material with effective thermophysical properties taken from the paper: density 1126.384 kg/m³, specific heat 3700.264 J/kg·K, and thermal conductivity 0.615 W/m·K. Its non-Newtonian viscosity is described with the Herschel-Bulkley model — a yield-stress fluid that only begins to flow once a threshold stress is exceeded, after which it follows a power law. The model parameters are a power-law index of 0.149, a yield stress of 2.92 Pa, and a critical shear rate of 58.4 s⁻¹, all from Table 1 of the paper, at a 4% nanofluid concentration.

The 2-D geometry was built in Design Modeler as a horizontal tube 1.2 m long and 0.00475 m in diameter. Because it is symmetric about its centerline, it is modeled as axisymmetric. The domain was meshed in ANSYS Meshing using a structured grid of 40,000 elements.

Simulation Methodology

The simulation uses a pressure-based, steady solver with gravity neglected, a laminar viscous model, and the energy equation enabled. The flow is studied at two Reynolds numbers, 900 and 1600. Because the fluid is non-Newtonian, the inlet velocity for each case is computed from the generalized Reynolds-number definition given in the paper, giving 1.2698 m/s for Re = 900 and 1.7327 m/s for Re = 1600. The nanofluid enters at 295 K, and the tube wall carries a constant heat flux of 8846.4 W/m². Pressure-velocity coupling uses SIMPLE, with second-order discretization for pressure, momentum, and energy.

Paper Validation & Results

Validation follows Figure 3-a of the paper, which plots the convective heat transfer coefficient (h) against Reynolds number at a dimensionless station of x/D = 147 (with D = 0.00475 m). The heat transfer coefficient is evaluated from Equation 9 of the paper using the applied heat flux (8846.4 W/m²) together with the wall temperature (Tw) and the fluid bulk temperature (Tf), extracted at that station from the wall and from a line through the tube.

The simulation matches the paper closely at both Reynolds numbers:

The agreement is strong on both counts that matter: the error magnitude stays within about 5.5%, and the behavior is reproduced correctly — the heat transfer coefficient rises with Reynolds number, exactly as in the reference. Two-dimensional temperature and velocity contours are also obtained at both Reynolds numbers along the mid-section of the tube.