A Second Degree Approximation for the Calculation of the Transfer Function Coefficients for Heat Flux Through Walls

Calculation of the conduction Transfer Function Coefficients using a state space representation requires the transient governing differential equation to be discretized in space by the use of finite difference or finite element methods in order to obtain a set of first order differential equations. In this paper the one-dimensional heat flow problem is tackled using a new quadratic element for use with the finite element method. The variational formulation for the governing differential equation is developed, the Ritz Approximation to construct the finite element formulation is used and the approximation functions are presented using a normalized local coordinate system for elements with three equally spaced nodes. Results with 1, 2 and 5 three-node elements are compared with those obtained by the use of finite differences with 2, 5 and 20 nodes and shown to be in good agreement.