4. A 1-D heat diffusion problem is given defined by: T T at with T(0,t)=100C T(10,...

 

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4. A 1-D heat diffusion problem is given defined by: ²T ƏT at with T(0,t)=100°C T(10, t) = 50°C and T(x,0)=0 °C Əx²2 0≤x≤10cm t≥0 t≥0 0≤x≤10 dT a) Graphically derive forward and backward difference approximations for dx (4 Marks) b) Use these forward and backward difference approximations to derive a central d²T difference for (4 Marks) ƏT c) By making the appropriate choice of difference formula for OT explicit finite difference formula for the PDE at - t> 0 a²T Əx :0 at - and 0²T Ox derive an (4 Marks) d) Taking c = 0.82, a step size in x of h = 2.5 and a time step k = 2 seconds estimate what the value of T will be at the grid points at time t = 2 seconds. (8 Marks) 4. A 1-D heat diffusion problem is given defined by: ²T ƏT at with T(0,t)=100°C T(10, t) = 50°C and T(x,0)=0 °C Əx²2 0≤x≤10cm t≥0 t≥0 0≤x≤10 dT a) Graphically derive forward and backward difference approximations for dx (4 Marks) b) Use these forward and backward difference approximations to derive a central d²T difference for (4 Marks) ƏT c) By making the appropriate choice of difference formula for OT explicit finite difference formula for the PDE at - t> 0 a²T Əx :0 at - and 0²T Ox derive an (4 Marks) d) Taking c = 0.82, a step size in x of h = 2.5 and a time step k = 2 seconds estimate what the value of T will be at the grid points at time t = 2 seconds. (8 Marks)

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a Graphical derivation of forward and backward difference approximations for T Tx t 1... View the full answer