Chemical Engineering Hand Written_Notes_Part_7

Chemical Engineering Hand Written_Notes_Part_7 - 16 1....

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16 1. MATHEMATICAL MODELING AND SIMULATION Figure 9. Shell and tube heat exchanger Since u ( t ) is a known function of time, we re-state the above problem as (2.54) d x dt = F u ( x ,t ); x (0) = x 0 F u ( x ,t )(= F ( x , u ( t ))) denotes F () with the given u ( t ) . 2.5. PDEs and ODE-Boundary value Problems. Most of the systems encountered in chemical engineering are distributed parameter systems. Even though behavior of some of these systems can be adequately represented by lumped parameter models, such simplifying assumptions may fail to provide accurate picture of system behavior in many situations and variations of vari- ables along time and space have to be considered while modeling. This typically result in a set of partial di f erential equations. Example 6 . Consider the double pipe heat exchanger in which a liquid f ow- ing in the inner tube is heated by steam f owing countercurrently around the tube (Figure 10). The temperature in the pipe changes not only with time but also
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Chemical Engineering Hand Written_Notes_Part_7 - 16 1....

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