1.9.1 Introduction

Sections 1.6 through 1.8 present analytical solutions to extended surface problems. Only simple problems with constant properties can be considered analytically. There will be situations where these simplifications are not justified and it will be necessary to use a numerical model. Numerical modeling of extended surface problems is a straightforward extension of the numerical modeling techniques that are described in Sections 1.4 and 1.5.

If the extended surface approximation discussed in Section 1.6.2 is valid, then it is possible to obtain a numerical solution by dividing the computational domain into many small (but finite) one-dimensional control volumes. Energy balances are written for each control volume; the energy balances can include convective and/or radiative terms in addition to the conductive and generation terms that are considered in Sections 1.4 and 1.5. Each term in the energy balance is represented by a rate equation that reflects the governing heat transfer mechanism; the result is a system of algebraic equations that can be solved using EES or MATLAB. The solution should be checked for convergence, checked against your physical intuition, and compared with an analytical solution in the limit where one is valid.