Graphical Analysis—The Schmidt Plot

A graphical technique of historical note may be employed to establish transient temperature distributions when the problem is one-dimensional. The method is based on the choice of the parameter 

An example of the method is shown in Fig. 4-23, where an initial temperature distribution is given and the construction is carried out for four time increments. The boundary temperatures are maintained at constant values throughout the cooling process indicated in this example. Notice that the construction approaches the steady-state straight-line temperature distribution with increasing time. 

When a convection boundary condition is involved, the construction at the boundary must be modified. Rewriting Eq. (4-39), we have 

Refinements in the Schmidt graphical method are discussed by Jakob [5], particularly the techniques for improving accuracy at the boundary for either convection or other boundary conditions. The accuracy of the method is improved when smaller Ax increments are taken, but this requires a larger number of time increments to obtain a temperature distribution after a given time. 

Graphical techniques are seldom ed anymore because of the ready avail- 

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