du Consider the heat equation in 2D ou (x, y, t) = AA * u(x, y,...

 

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du Consider the heat equation in 2D ou (x, y, t) = AA * u(x, y, t) = A(dxxu + Əyyu) A is the diffusitivity coefficient with dimensions square metres per second. (L²T-¹) Where T is time Non-dimensionalize the equation above and show that it turns into this form: du = ÂAû dt HINT: When considering the heat equation, there are three different systems: F, C, and K. Let u(x, y, t) denotes the temperature at time t and location at (x, y, z). Consider x = xL. L is the characteristic Length. du Consider the heat equation in 2D ou (x, y, t) = AA * u(x, y, t) = A(dxxu + Əyyu) A is the diffusitivity coefficient with dimensions square metres per second. (L²T-¹) Where T is time Non-dimensionalize the equation above and show that it turns into this form: du = ÂAû dt HINT: When considering the heat equation, there are three different systems: F, C, and K. Let u(x, y, t) denotes the temperature at time t and location at (x, y, z). Consider x = xL. L is the characteristic Length.

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To nondimensionalize the given heat equation in 2D we introduce nondimensional variables and paramet... View the full answer