captaincook
New member
- Joined
- Dec 25, 2012
- Messages
- 1
Hi guys,
I am trying to solve this equation, but I have problem with the second boundary condition. I am trying to use combination of variables but it wont work. Could you please give me some hints about how to tackle this problem, using any solving method.
(∂^2 T)/(∂x^2 )=1/∝ ∂T/∂t
IC: T(x,0) = Ti
BC1: T(x→∞, t) = Ti
BC2: -k ∂T/∂x|x=0 = h[T∞-T(0,t)]
I tried combining the variables by W= x/(4∝t)^0.5
and the equation became : (d^2 T)/(dW^2 )=-2W dT/dW
and
IC: T(W→∞) = Ti
BC1: T(W→∞) = Ti
BC2: -k dT/dW * 1/(4∝t)^0.5 |W=0 = h[T∞-T(W=0)]
As you see term "t" can not be canceled out the second boundary condition. Please give me a hint to what to do.
Thank you
I am trying to solve this equation, but I have problem with the second boundary condition. I am trying to use combination of variables but it wont work. Could you please give me some hints about how to tackle this problem, using any solving method.
(∂^2 T)/(∂x^2 )=1/∝ ∂T/∂t
IC: T(x,0) = Ti
BC1: T(x→∞, t) = Ti
BC2: -k ∂T/∂x|x=0 = h[T∞-T(0,t)]
I tried combining the variables by W= x/(4∝t)^0.5
and the equation became : (d^2 T)/(dW^2 )=-2W dT/dW
and
IC: T(W→∞) = Ti
BC1: T(W→∞) = Ti
BC2: -k dT/dW * 1/(4∝t)^0.5 |W=0 = h[T∞-T(W=0)]
As you see term "t" can not be canceled out the second boundary condition. Please give me a hint to what to do.
Thank you