Shown above is a computer animated design of a heat exhanger. Thanks to Joseph Fourier, the behavior of the heat exchanger can now be modelled if the temperatures, and composition of each fluid is known. Both Fourier's Law and Newton's Law of Cooling allow all sorts of systems such as cooling fins, reactors, distillation columns and condensers. For each tpye of system, the applicable laws can be applied, and understanding the formulation of the laws allows engineers to model a system, and may provide clues to problems of the system.
Fourier's law also provided a base for other laws. From Fourier's Law, Fick's law and Newton's Law of Viscocity was derived. Fick's Law models mass transport, and Newton's Law of Viscocity models momentum transfer. Once these laws were formed, the field of Transport Phenomena was formed and allowed the complete modelling of any chemical process. Each type of transport is often coupled, and the field has allowed general formulas for all couplings in different geometries. Fourier's law acted as a domino effect that led to the revolutionizing of the field of Chemical Engineering.
The Fourier Series and Transform also impacted chemical engineering, though not as exclusively. The series and transform are used in many different fields to sovle a variety of problems. In chemical engineering, the transform can take a periodic function, such as a temperature control device that turns on and off periodically to maintain a certain temperature, and model the process. The series is used in boundary problems to model unsteady-state processes where the conditions change over time which would change a differential equation in time space to an algebraic or trigonometric equation in s space for easier solving. All in all, Fourier's discoveries revolutionized chemical engineering and made such an impact that they are still in use today.