- #1

HalfManHalfAmazing

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A slender homogeneous conducting bar of uniform cross section lies along the x-axis with ends at x = 0 and x = 1. The lateral surface of the bar radiates heat into the surroundings at temperature zero. The left end is insulated and heat is added through the right end. The initial temperature distributions is u(x,0) = f(x).

Okay so the PDE we have here is:

[tex]u_t = \alpha^2u_{xx} - u[/tex]

[tex]u_x(0,t) = 0[/tex]

[tex]u_x(1,t) = q[/tex]

[tex]u(x,0) = f(x)[/tex]

And to find the steady solution I do the usual tricks. I know how to get it I just want someone to explain a bit. Thanks.