Question

- pes The one dimensional transient conduction can be expressed as: 22T 1 OT Oxzat a. Rewrite this equation with finite differences using forward differencing in time and central differencing in space. b. Since you are using forward time differencing, the resulting algebraic equation will be explicit. What is the condition for stability in explicit finite differences? c. To solve the resulting algebraic equation, you need two boundary conditions. What else do you need?

Answer 1

Solution : 221 1 2T 22 x 22 a. Forward difference in time central difference in Space (FTCS) Tily - 27 tt Tinti n - Tit - Dua a AX → internal space From taylor series At & interval time > ttp*. Tht to ot Г . - 2ттетя At AX2 b. Stability Condition in FTCS - At saka Dag 3 c. Along with two Boch with need one initial I condition T(0,0) =( T (13, t)=K - T(x,0) =k - this is the one we need