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DEPARTMENT OF CHEMICAL ENGINEERING University of California, Santa Barbara Computational Methods in Chemical Engineering HOME PROBLEM ChE 132B Fall 2005 1. It is desired to determine the uncertainty in the Nusselt number for developed transport in a tube due to uncertainties in the fluid velocity, the tube diameter, and they physical properties of the fluid. Suppose that the formula for the Nusselt number is given by Nu = C Re a Pr b where C, a, and b are known constants, Re = Du r / m is the Reynolds number and Pr = m C p / m is the Prandtl number. Estimate the relative error in the Nusselt number corresponding to the following possible percentage uncertainties. u ˛ 5% m ˛ 10% k ˛ 3% , Cp r ˛ ˛ 1% D ˛ 0.1% 2. The following differential equation arises in the modeling of a batch reactor with a heterogeneous catalytic reaction
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