Conduction Crank-Nicolson method

The system of Eqs. 13.3-17 and 13.3-18 can be solved for the adiabatic, isothermal, or constant wall flux cases using the Crank-Nicolson method. The thermomechanical and reaction data for such systems were evaluated by Lifsitz, Macosko, and Mussatti (99) at 45°C for a polyester triol and a chain extended 1,6-hexamethylene diisocyanate (HDI) with dibutyltin as a catalyst. Figure 13.46 gives the temperature profiles for the isothermal-wall case. Because of the high heat of polyurethane formation and the low conductivity of... 

Generally, the Crank-Nicolson method is used for numerical solution of heat conduction problems that are parabolic in nature. This method solves a mesh with mesh size h in x-direction and mesh size k in y-direction (time direction). It calculates the values of u at six points as shown in Figure 1.17. 

J. Crank and P. Nicolson, A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat-conducting Type, Proc. Cambridge. Philos. Soc., 43,50-67 (1947). 

Crank, J. Nicolson, P. A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proc. Camb. Phil. Soc. 43 (1947) 50-67... 

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See also in sourсe #XX -- [ ]

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