By Richard G. Rice
Bridges the space among classical research and sleek functions. Following the bankruptcy at the version development level, it introduces conventional options for fixing traditional differential equations, including new fabric on approximate answer tools akin to perturbation concepts and straight forward numerical ideas. additionally contains analytical the right way to care for very important sessions of finite-difference equations. The final part discusses numerical resolution concepts and partial differential equations.
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Extra info for Applied Mathematics and Modeling for Chemical Engineers
We saw an example of this equation in Chapter 1, Eq. 13) where we have denoted locally varying wall temperature Tw (z), rather than the special case Tw = constant. If the wall temperature was fixed and constant, we showed earlier that a common sense change of variables allowed direct integration after separation of variables. However, such is not the case if the wall temperature varies with position z. For the general case, given in functional form as Eq. 12, we shall allow the coefficient a and the forcing function / to vary with respect to the independent variable x.
83c) It is clear that these independent variables (£ and O are defined relative to the maximum possible lengths for the r and x variables, R and L 2 , respectively. However, the way u (nondimensional temperature) is defined is certainly not unique. 84) 1 O I and so on. There are good reasons for the selection made here, as we discuss in Chapters 10 and 11. The solution of Eq. 83) is given in Chapter 11 and its expression is given here only to help illustrate model hierarchy. 86a") where J0 (/3) and Jx (/3) are tabulated relations called Bessel functions, which are discussed at length in Chapter 3.
Lumped Thermal Model for Thermocouple We wish to estimate the dynamics of a cold thermocouple probe suddenly placed in a hot flowing fluid stream for the purpose of temperature measurement. The probe consists of two dissimilar metal wires joined by soldering at the tip, and the wires are then encased in a metal sheath and the tip is finally coated with a bead of plastic to protect it from corrosion. Take the mass of the soldered tip plus plastic bead to be m, with specific heat Cp. Denote the transfer coefficient as h.
Applied Mathematics and Modeling for Chemical Engineers by Richard G. Rice