QUESTION A uniform bar of length 10 centimetres is held at 0C at x = Ocm...

Transcribed Image Text:

QUESTION A uniform bar of length 10 centimetres is held at 0°C at x = Ocm and 100°C at X = 10cm. The bar is first heated with an initial temperature distribution given by, f(x) = 100-x; 0<x<10 at the point r the temperature u on the bar satisfies the heat at any timer conduction equation, 0 <x 10, t > 0 (a) State the boundary condition and initial conditions for this physical problem. (b) Using finite difference approximation, approximate the heat distribution along the bar after 10 minutes. (c) Construct the analytical solution of the heat equation. (d) Discuss about the accuracy of the approximation solution in (b). QUESTION A uniform bar of length 10 centimetres is held at 0°C at x = Ocm and 100°C at X = 10cm. The bar is first heated with an initial temperature distribution given by, f(x) = 100-x; 0<x<10 at the point r the temperature u on the bar satisfies the heat at any timer conduction equation, 0 <x 10, t > 0 (a) State the boundary condition and initial conditions for this physical problem. (b) Using finite difference approximation, approximate the heat distribution along the bar after 10 minutes. (c) Construct the analytical solution of the heat equation. (d) Discuss about the accuracy of the approximation solution in (b).