This module deals with mathematical modelling of the flow of heat and mass within a building and its components. They are modelled in the main by sets of non-linear algebraic and differential equations. A variety of mathematical approaches are covered. Solutions are implemented using industry-standard software tools such as Excel and ANSYS/CFX.
Ordinary differential equations: classification (linear/non-linear, stiff/non-stiff); reduction to first order autonomous form; stiffness and stability; explicit and implicit numerical methods; stability criteria; computational efficiency.
Algebraic equations: direct and iterative solution methods for linear systems; fixed-point iteration and Newton iteration for non-linear systems; convergence criteria; stopping criteria.
Heat transfer: modelling of steady state conduction; simulation of transient conduction; various boundary conditions; internal heat generation.
Definition of Computational Fluid Dynamics: How it was developed and where it is used i.e. Heating ventilation and air conditioning applications and Fire engineering.
Continuity, momentum and energy equations conservation and non-conservation formulations
Discretisation of flow equations. Explicit and implicit solution schemes.
Turbulence modelling.
Finite difference and finite volume methods
Derivation of a simple flow solution techniques e.g. Couette flow, Diffusion problems, simple convection problems.
Geometry modelling, transformation and grid generation.
Use of Computational Fluid Dynamics in the design process.
Analysis of error minimisation and convergence.
Laboratories include ventilation and air conditioning modelling, combined convection and radiation heat transfer, cooling/heating system modelling, fluid mixing modelling and optimisiation of building design. These will be implemented using the ANSYS/CFX computational fluid dynamics software package and IES software package.
