Heat Transfer

Big Ideas

• The law of conservation of energy gives rise to systems of differential equations which models heat transfer.

• Constitutive laws such as the Stefan–Boltzmann law are equations that describe individual components of a mathematical model. Constitutive laws are themselves mathematical models!

• Any model of a real-world phenomenon will involve many parameters and the nondimensionalization procedure simplifies the model and determines what role the system parameters play.

• Use SciPy to compute numerical solutions of differential equations. A computational approach to mathematical modelling allows us to easily simulate and visualize models.

Learning Goals

• Apply physical laws to construct mathematical models of heat transfer

• Apply nondimensionalization process and interpret dimensionless parameters

• Compute numerical solutions of systems of differential equations