Consider the one-dimensional heat conduction equation. Apply forward difference method to approximate time rate and central difference method to approximate x-derivative. The resulting equation is in _____________(a) Implicit linear form(b) Explicit linear form(c) Explicit non-linear form(d) Implicit non-linear formThe question was asked in a job interview.I need to ask this question from Explicit and Implicit Finite Difference Methods topic in section Finite Difference Methods of Computational Fluid Dynamics

Consider the one-dimensional heat conduction equation. Apply forward d

1.	Consider the one-dimensional heat conduction equation. Apply forward difference method to approximate time rate and central difference method to approximate x-derivative. The resulting equation is in _____________(a) Implicit linear form(b) Explicit linear form(c) Explicit non-linear form(d) Implicit non-linear formThe question was asked in a job interview.I need to ask this question from Explicit and Implicit Finite Difference Methods topic in section Finite Difference Methods of Computational Fluid Dynamics
Answer» Correct ANSWER is (b) Explicit linear form Best explanation: The one-dimensional heat CONDUCTION equation is \(\frac{\partial T}{\partial t}=α \frac{\partial^2 T}{\partial t^2} \) Applying the difference APPROXIMATIONS, \(\frac{T_i^{n+1}-T_i^n}{\DELTA t}=\ALPHA \frac{T_{i+1}^n-2T_i^n+T_{i-1}^n}{(\Delta x^2)} \) \(T_i^{n+1}=T_i^n+\alpha\frac{\Delta t(T_{i+1}^n-2T_i^n+T_{i-1}^n)}{(\Delta x^2)} \) The equation is in explicit linear form.

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