Heat Conduction Simulation

Interactive demonstration of heat diffusion through materials

Cold Hot
Time: 0.00 s
Max Temp: 0 K
Min Temp: 0 K

Parameters

Initial Condition

Physical Equations

Heat Equation (1D): ∂T/∂t = α·∂²T/∂x²
Heat Equation (2D): ∂T/∂t = α·∇²T
Thermal Diffusivity: α = k/(ρc)

Temperature Scale

Cold Room Temp Hot

What is Heat Conduction?

Heat conduction is the transfer of thermal energy through a material due to temperature differences. When one part of an object is heated, the energy spreads through collisions between neighboring atoms or molecules, causing the heat to propagate from hot to cold regions. This process is described by the heat equation, a partial differential equation that relates the rate of temperature change to the spatial curvature of temperature.

The Heat Equation

The heat equation ∂T/∂t = α·∇²T states that the rate of temperature change at any point is proportional to the thermal diffusivity α and the Laplacian of temperature (∇²T), which measures how much the temperature at a point differs from the average temperature of its surroundings. Higher diffusivity materials conduct heat faster, and regions with greater temperature curvature experience more rapid temperature changes.

Boundary Conditions

Dirichlet boundary conditions fix the temperature at the boundaries (e.g., holding one end at a constant temperature), while Neumann boundary conditions fix the heat flux (insulated boundaries allow no heat flow). The choice of boundary conditions significantly affects how heat propagates through the material and the steady-state temperature distribution.

Applications

Heat conduction principles are essential in engineering and science: designing building insulation and heating/cooling systems, optimizing heat exchangers and radiators, understanding thermal management in electronics, analyzing temperature distributions in manufacturing processes, studying geothermal heat transfer, and predicting thermal response in materials. From cooking to spacecraft thermal protection, heat conduction plays a fundamental role in energy transport.