An analytical solution for the multidimensional degradation of a packed bed thermocline

A multidimensional, time-dependent model of the thermocline degradation in a packed bed thermal storage tank is presented. The formulation includes the effects of finite tank length, multidimensional thermal conduction, heat transfer between the fluid and solid portions of the bed, and heat losses across all tank surfaces. The technique used to solve the coupled pair of parabolic partial differential equations describing the degradation of the thermocline is based on a vectorized separation of variables approach. Assuming cylindrical geometry, the analysis leads to separate eigenvalue problems for the radial, angular, and axial spatial dependencies of the fluid and solid temperatures in the bed. The eigenvalues are readily calculated and the corresponding eigenfunctions are shown to form a complete set of spatial basis functions for the solution space. The method and results are illustrated by several examples.     

Controlling for Background Beliefs When Developing Multiple-Choice Critical Thinking Tests

This paper describes briefly a methodology for developing multiple-choice critical thinking tests which attempts to overcome certain problems of validity and fairness facing such tests. The paper proposes that direct evidence on test validity be gathered using verbal reports of students' thinking on trial items.