Solve the following problem, plane wall with convection, by separation of variables.Include a...

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Solve the following problem, plane wall with convection, by separation of variables.Include a diagram of the problem with your solution.Non-Dimensional Governing Equation:Boundary Conditions:Initial Condition:
	
Document Preview: Plane Wall with ConvectionSolve the following problem, plane wall with convection, by separation of variables.Include a diagram of the problem with your solution.Non-Dimensional Governing Equation:		uxx= u?Boundary Conditions:		u0,?= 0		ux1,?= -Bi*u(1,?)Initial Condition: 		ux,0= 1.0

Robert · Accepted Answer

Plane Wall with Convection 
Solve the following problem, plane wall with convection, by separation of variables. 
Include a diagram of the problem with your solution. 
Non-Dimensional Governing Equation: 
  ?????? =  ????  
Boundary Conditions: 
  ????(0,??) =  0 
  ????(1,??) =  −???? ∗ ??(1,??) 
Initial Condition:  
  ??(??, 0) =  1.0 
Solution
Here we can express the above non dimensional temprature in the form of  
u (x,θ) = X(x) * θ(t) 
on substututing it in the given governing equation we get 
1
??
??2??
????2  = 
1
θ
 ??θ????  
Now the equation has seprate variables on seprate side,

Solve the following problem, plane wall with convection, by separation of variables. Include a diagram of the problem with your solution. Non-Dimensional Governing Equation: Boundary Conditions:...

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