(587b) The Role of Mathematics and Transport Phenomena In Undergraduate Courses of Chemical Engineering

Based on the results of an investigation using the programs of chemical engineering reported in the internet, for universities of several countries, this material will discuss the role and the contents of mathematics and transport phenomena that should be taught in the undergraduate courses of chemical engineering, what material should be covered, what the complexity is and where the boundary begins with these subjects taught in graduate programs. According to the survey, mathematics in undergraduate courses are not enough to solve problems with middle complexity raised by transport phenomena. For example, the cooling of water circulating in a cylindrical tube in steady state leads to a partial differential equation with two coordinates which are the independent variables. The transient conduction of heat in just one direction in a cylindrical bar leads also to a partial differential equation. The average level of the maximum topics in undergraduate courses of mathematics are, besides ordinary differential equations linear or not, the separation of variables for partial differential equations. This demonstrates the complexity of the reality, hardly described by mathematical models. Transport phenomena provides the understanding of all the physical processes involved to construct the mathematical model.

We are aware that currently a lot of software exists for solving complicated mathematical problems, and also its application is discussed without a fundamental knowledge in mathematics.  Software should give training to the student to handle a computational tool but with the basic mathematical knowledge.

In summary, transport phenomena allows to construct a mathematical model, and mathematics lets to solve this model and to be able to simulate the physical process. Simulation in chemical engineering is essential to design the pieces of industrial equipment.