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Why Do We Use Heat Equation?

January 24, 2024 by Emily Lee

Why Do We Use Heat Equation? The heat equation (also known as the diffusion equation) describes a time-varying evolution of a function u(x, t) given its initial distribution u(x, 0). Physically, this PDE is used to determine the spatial distribution of temperature on a conductive surface after it diffuses for time t: (10) Why is

How Do You Solve A One Dimensional Heat Equation?

January 24, 2024 by Emily Lee

How Do You Solve A One Dimensional Heat Equation? u(x,t) = temperature in rod at position x, time t. ∂u ∂t = c2 ∂2u ∂x2 . (the one-dimensional heat equation ) The constant c2 is called the thermal difiusivity of the rod. We now assume the rod has finite length L and lies along the