The purpose of this project was to analyze heat transfer of various insulation materials. The small off-grid house is designed to maintain a stable and comfortable internal temperature while experiencing varying external conditions. We aim to analyze how heat is transferred between the inner and outer surfaces, as well as within its interior, to find the optimal insulation material for energy efficiency and thermal performance.

The structure consists of two main regions: the inner region representing the interior space and the outer region representing the walls.

The initial temperatures within the simulator parameterization are set to the following ranges:

• Temperature on the outside shell: -20°C to 50°C

• Temperature of walls + interior: 15°C to 25°C

To simulate the heat transfer, we use the diffusion equation, which is governed by the partial differential equation for thermal diffusion. Two main diffusion equations are defined for the inner and outer regions of the simulation domain:

• Diffusion Equation for Outer Region (walls):

  • Thermal Conductivity (D): parameterized for multiple values of W/mK (for analyzing multiple types of insulation materials)

  • Temperature Variable (T): theta_1

• Diffusion Equation for Inner Region (air):

  • Thermal Conductivity (D): 0.023 W/mK

  • Temperature Variable (T): theta_2

Below is an example of an equation settings for Diffusion PDE within node-based editor in Siml.ai, where you can make the variable parameterized, making it possible to set ranges of input, which allows for training the simulator once across multiple potential initial conditions.

Boundary and Interior Constraints

Various constraints are applied to the thermal domain to represent different conditions and interfaces within the simulation domain:

• Heat Source Constraint: Temperature (theta_1) is set as a constant value on the outer surface to represent a uniform external temperature.

• Fluid-Solid Interface Constraint: The diffusion interface between the walls (theta_1) and the interior (theta_2) is controlled by setting Dirichlet and Neumann conditions.

• Solid Interior Constraint: The solid interior (walls) of the structure has no diffusion (heat source) inside.

• Air Interior Constraint: The interior air of the structure has no diffusion (heat source) and a constant temperature (theta_2) representing the desired interior temperature.

Simulation and Results

The heat transfer process and temperature distribution within the structure are computed over different initial conditions. The results are obtained in less than 5 seconds, significantly lowring the time to analyze the effectiveness of the thermal properties of different insulation materials by changing Thermal Conductivity (theta_1) based on the specific material.

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