The heat and wave equations in 2D and 3D 18.303 Linear Partial Differential Equations
نویسنده
چکیده
We desire the heat flux through the boundary S of the subregion V , which is the normal component of the heat flux vector φ, φ n̂, where n̂ is the outward unit · normal at the boundary S. Hats on vectors denote a unit vector, n̂ = 1 (length 1). | | If the heat flux vector φ is directed inward, then φ n̂ < 0 and the outward flow of · heat is negative. To compute the total heat energy flowing across the boundaries, we sum φ n̂ over the entire closed surface S, denoted by a double integral � � dS. · S Therefore, the conservation of energy principle becomes
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