How do I find B using the boundary condition ux(0,t) = -Q in Laplace transforms?

squenshl
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I'm deriving the heat equation using Laplace transforms.
I'm up to u(bar) = Aesqrt(s)x + Be-sqrt(s)x.
My boundary conditions are lim(x tends to 0) = 0 & this makes A = 0, so u(bar) = Be-sqrt(s)x
My other BC is ux(0,t) = -Q
My question is how do I get B using this BC?
I tried using the def of Laplace transforms and get -dQ(bar)/dx
 
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I got B = Q/sqrt(s) and this implies that U(bar) = Qe-sqrt(s)x/sqrt(s), I hope that's right
 
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