BVP_Example

# BVP_Example - NONLINEAR BOUNDARY VALUE PROBLEM EXAMPLE The...

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1 NONLINEAR BOUNDARY VALUE PROBLEM EXAMPLE The temperature distribution of the rectangular fin shown in Figure 1(a) below, considering conduction and radiation heat transfer, is given by ) ( 4 4 2 2 = T T kA P dx T d σε (1) where T = temperature, x = location along the fin, k = thermal conductivity, bd A = = cross sectional area, ) ( 2 d b P + = = perimeter, T = surrounding temperature, σ = Stefan-Boltzman constant, and ε = emissivity. The values for the constants are given in the table below, where are values are reported in a consistent set of units: Constant Value Units k 42 W/m – º b 0.5 m d 0.2 m T 500 º K l 2 m 0.1 dimensionless 8 10 7 . 5 × W/m 2 – º K 4 The boundary conditions are given as 1000 ) 0 ( = = x T º K 350 ) ( = = l x T º K The temperature at three equally spaced interior node points 1, 2, and 3, as shown in Figure 1(b), is to be determined using three different methods. This distance h between each pair of nodes is 0.5 m.

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2 a) Using Eq. (1), derive a nonlinear set of finite difference equations for the temperature at
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BVP_Example - NONLINEAR BOUNDARY VALUE PROBLEM EXAMPLE The...

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