- #1
math2011
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The original question is:
Try and apply the Similarity solution method to the following boundary value problems for u(x,t).
u_t = k u_{xx} for all x > 0 with boundary conditions
u_x(0,t) = 1
u(x,t) \to 0 as x \to \infty
u(x,0) = 0 for x > 0.
I know from my tutorial that I should first find u = \sqrt{kt} f(\eta) where f is an unknown function of similarity variable \displaystyle \eta = \frac{x}{\sqrt{kt}}. What I don't know is how to find the similarity variable \eta and the formula u = \sqrt{kt} f(\eta).
Please tell me the procedure for finding similarity solution. Thank you in advance.
The original question is:
Try and apply the Similarity solution method to the following boundary value problems for u(x,t).
u_t = k u_{xx} for all x > 0 with boundary conditions
u_x(0,t) = 1
u(x,t) \to 0 as x \to \infty
u(x,0) = 0 for x > 0.
I know from my tutorial that I should first find u = \sqrt{kt} f(\eta) where f is an unknown function of similarity variable \displaystyle \eta = \frac{x}{\sqrt{kt}}. What I don't know is how to find the similarity variable \eta and the formula u = \sqrt{kt} f(\eta).
Please tell me the procedure for finding similarity solution. Thank you in advance.