Single Fin in Forced Flow

Overview

This validation case reproduces the straight steel-fin study in Section 3.1 of Renze and Akermann (2019). A $10 m / s$ turbulent air stream at $300 K$ cools a rectangular steel fin whose base is held at $363 K$ . The fully three-dimensional fluid and solid energy equations are coupled through a general CHT interface.

Problem Setup

The four paper cases vary only the fin length: $0.02$ , $0.04$ , $0.06$ , and $0.08 m$ . The three-dimensional domain is $0.3 m$ by $0.1 m$ by $0.1 m$ ; fin height and thickness are $0.05 m$ and $0.002 m$ . All four points share the same material properties, boundary conditions, turbulence model, and numerical recipe.

Quantities of Interest

The header image is a case-b mid-span cut ( $y = 0.05 m$ ) through the three-dimensional CHT solution: velocity magnitude is shown in the air region and temperature in the steel region.

The validation plot samples the centreline of the steel fin from $(0.15, 0.05, 0)$ to $(0.15, 0.05, L)$ for every sweep point. It plots $θ = (T - T_{a}) / (T_{b a s e} - T_{a})$ against $z / L$ . The solid reference curves use the one-dimensional straight-fin relation, $θ = \cosh [m (L - z)] / \cosh (m L)$ .

Results

Normalized temperature along the fin

Solid-centreline temperature from the fin base to its tip. Solid lines are the paper's one-dimensional straight-fin model; dashed lines are Luminary CFD.

Reference: P. Renze and K. Akermann, "Simulation of Conjugate Heat Transfer in Thermal Processes with Open Source CFD," ChemEngineering 3(2), 59, 2019. (Eq. (11) and Fig. 3), https://doi.org/10.3390/chemengineering3020059

Theory curves use the paper's one-dimensional straight-fin model.