Which equation is solved with ThermalModel?

With the PDE toolbox, equations of the general form m∂2u∂t2+d∂u∂t−∇·(c∇u)+au=f can be solved. On the other side, I can use the Thermal model object which seems to be very comfortable for solving the heat equation. However, it's not clearly defined what the parameters stand for. For example, what is 'HeatFlux'? Is it the variable g in the generalized Neumann boundary condition n · (c∇u)+qu=g? Isn't there a complete documentation? How can I be sure that the correct problem is solved, when I cannot see the underlying equations?

Answer 1

[Yash Sharma]

For thermal analysis, the thermalModel object in MATLAB simplifies the process of setting up and solving heat transfer problems. When you're working with functions like thermalBC to specify boundary conditions, terms like HeatFlux correspond to parameters in the generalized boundary conditions of PDEs.

In the context of the generalized Neumann boundary condition:

[ n \cdot (c \nabla u) + qu = g ]

• ( n ) is the outward normal to the boundary.
• ( c ) is the thermal conductivity.
• ( \nabla u ) is the temperature gradient.
• ( q ) is a coefficient that multiplies the solution ( u ) or its gradient on the boundary.
• ( g ) represents the heat flux across the boundary (in terms of power per unit area, W/m²) when you're setting a Neumann boundary condition.

So, when you use HeatFlux in MATLAB's PDE Toolbox for a thermal model, you are essentially specifying ( g ), the heat flux across the boundary.Documentation and Verification