Evan Selin & Terrance Hess.  Find temperature at points throughout a square plate subject to several types of boundary conditions  Boundary Conditions:

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Presentation transcript:

Evan Selin & Terrance Hess

 Find temperature at points throughout a square plate subject to several types of boundary conditions  Boundary Conditions: ◦ 4 Constant Temperature surfaces ◦ 3 Constant Temperatures and 1 heat flux surface ◦ 2 Constant Temperatures and 2 heat flux surfaces  Automate the construction of solver matrices

 Required Properties: ◦ Temperatures at each boundary ◦ Conductivity, k ◦ Heat flux, q” (W/m 2 )  Positive flux entering plate

 Equations used:

 Determine (x,y) position of each node  Create finite difference equations for desired set of boundary conditions  Build augmented matrix for solution  Solve matrices for temperatures at each node (matrix inversion)  Build algorithm to automatically generate solution matrix Coefficient Matrix for 1 heat flux

T1 = 35 ℃, T2 = 50 ℃, T3 = 100 ℃, T4 = 50 ℃ 4 divisions5 divisions 9 divisions

T1 = 0 ℃, T2 = 50 ℃, T3 = 100 ℃, q” 4 = 50 W/m 2, k = 15.1 W/m*K 4 divisions 5 divisions 9 divisions

T1 = 100 ℃, q” 2 = 75 W/m 2, T3 = 50 ℃, q” 4 = -25 W/m 2, k = 15.1 W/m*K 4 divisions 5 divisions9 divisions

 Numerical Solution Software is very complex  Setting up equations is the hard part  Matrix increases size on order of divisions squared  Calculations take a long time for large very fine mesh