VVT17 - Convecting zone on an edge

Description

This validation case examines the thermal convecting zone boundary condition applied to the edge of a two-dimensional aluminum plate. The steady-state temperatures predicted by the solver are compared with the analytical solution.

Geometry

The model geometry consists of a two-dimensional plate with dimensions of 100 mm by 200 mm in the y and x directions.

Simulation model

This model uses the Simcenter Multiphysics solver.

A 2D mesh is generated using plane stress parabolic quadrilateral elements with the size of 10 mm.

The meshed elements have the following material and physical properties:

• Material: Aluminum
• Mass density: ρ = 2660 kg/m³
• Thermal conductivity: k = 117 W/m °C
• Specific heat at constant pressure: C_p = 900 J/kg °C

The fluid is modeled using air with the following properties:

• Mass density: ρ = 1.2041 kg/m³
• Specific heat at constant pressure: C_p = 1007 J/kg °C
• Dynamic viscosity: µ= 1.85 × 10⁻⁵ kg/m·s

The following boundary conditions are applied:

• Temperature constraint on one edge of the metal plate with a value of T = 20 °C.
• Thermal Convecting Zone on another edge of the metal plate with an environment temperature T_f = 100 °C, and a heat transfer coefficient h = 0.01 W/mm²·°C.

The following figure shows the applied boundary conditions.

The default solver parameters are selected.

Theory

The thermal convecting zone allows for convection between the solid and a fluid at a prescribed temperature.

The two-dimensional steady-state heat equation is defined as:

The solution for T=T₀ at y=y₀ is given by:

Results

The following table compares the solid metal temperature computed by the thermal solver with the analytical solution: