Two Dimensional Heat Equation
The two-dimensional heat equation is a partial differential equation that describes the distribution of heat in a 2D medium over time. The equation is typically written as:
∂u/∂t = α(∂²u/∂x² + ∂²u/∂y²)
where u(x,y,t) is the temperature at position (x,y) and time t, α is the thermal diffusivity of the medium, and ∂/∂x and ∂/∂y are partial derivatives with respect to x and y, respectively. The equation describes how the temperature of a medium changes over time as heat is transferred through the medium by diffusion. The equation is used to model a wide range of physical phenomena, including heat transfer in solids, liquids, and gases.
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