Chemical Engineering Hand Written_Notes_Part_9

Chemical Engineering Hand Written_Notes_Part_9 - 20 1....

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20 1. MATHEMATICAL MODELING AND SIMULATION (4.1) ∂u/∂t +( d 2 u/dz 2 ) n = u 3 Here the Oredr =2 and Degree = n. Solutions of PDEs are sought such that it is satis f ed in the domain and on the boundary conditions are satis f ed. A problem is said to be well posed when the solution uniquely determined and it is su cient smooth and di f erentiable function of the independent variables. The boundary conditions have to be consistent with one another in order for a problem to be well posed. This implies that at the points common to boundaries, the conditions should not violet each other. A linear PDE can be classi f ed as: Homogeneous equations:Di f erential equation that does not contain any terms other than dependent variables and their derivatives. (4.2) ∂u/∂t = ∂u 2 /∂x 2 2 u/∂x 2 + 2 u/∂y 2 =0 Non homogeneous equations: Contain terms other than dependent vari- ables (4.3) ∂u/∂t = 2 u/∂x 2 +sin x (4.4) 2 u/∂x 2 + 2 u/∂y 2 =sin
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This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

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Chemical Engineering Hand Written_Notes_Part_9 - 20 1....

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