Finite Element Method with Applications in Engineering

6.6 ONE-DIMENSIONAL STEADY STATE HEAT CONDUCTION

A 2-node heat flow element as shown in Figure 6.18 can be utilized to analyse one-dimensional steady state heat conduction problems. Note that convection is neglected in the formulation. The solution is obtained in the following steps.

Step 1: Select element type

Sign convention: Heat flow entering a control volume is positive. Outgoing heat flow is negative.

Let q be the heat flow (per unit area) and t be the temperature. Then, q_i, i = 1, 2 are the nodal heat flow rates and t_i, i = 1, 2 are the nodal temperatures.

 

 

Figure 6.18 One-dimensional heat flow Element

 

Step 2: Select approximation ...