Solving Square Box Reactor Question: Flux General Equation

In summary, the flux general equation for a square box with side length a is flux = Acos(pi*x/a)cos(pi*y/a)cos(pi*z/a), where -a/2 < x < a/2 and zero flux boundary conditions are assumed. This equation is described by three independent functions X, Y, Z and can be solved using the neutron diffusion equation. In steady state with no source, the general equation becomes flux = Aexp(-x/a) + Bexp(x/a).
  • #1
matt222
132
0
Iam trying to work out question related to sequare box, my question is what the flux general equation for the sequare box?

I work it out and found it is

flux=Acos(pi*x/a)cos(pi*y/a)cos(pi*z/a)

where a is side lenght, am i right
 
Engineering news on Phys.org
  • #2
matt222 said:
Iam trying to work out question related to sequare box, my question is what the flux general equation for the sequare box?

I work it out and found it is

flux=Acos(pi*x/a)cos(pi*y/a)cos(pi*z/a)

where a is side length, am i right
Yes - with -a/2 < x < a/2, and similarly for y and z.

This assumes zero flux boundary condition at the edges (flux(-a/2) = flux(a/2) = 0), and max flux at flux(x,y,z) = flux(0,0,0) = A and even symmetry.

Flux is then described by 3 independent functions X, Y, Z which are described by X'' + (pi/a)2X = 0 and X(0) = Y(0) = Z(0) = A1/3
 
  • #3
do you agree with me when we use neutron diffusion equation, that the general solution will be

flux(x,y,z)=S/(D[3pi^2/a^2+1/L^2])


and what about if we have no source and steady state? How the general equation going to be, should we take it as

flux(x,y,z)=Aexp(-x/a)+Bexp(x/a)
 

1. What is a square box reactor?

A square box reactor is a type of reactor used in chemical engineering to model certain chemical reactions. It is a simplified version of a larger reactor system and is often used for theoretical calculations and experiments.

2. What is the Flux General Equation?

The Flux General Equation is a mathematical formula that describes the rate at which reactants are converted into products in a chemical reaction. It takes into account factors such as the concentration of reactants, the temperature, and the reaction rate constant.

3. How is the Flux General Equation used to solve square box reactor questions?

The Flux General Equation is used in square box reactor questions to calculate the flux, or the rate of reaction, within the reactor. This allows scientists to understand how the reaction is progressing and make predictions about the final product yield.

4. Why is it important to solve square box reactor questions?

Solving square box reactor questions is important for understanding and optimizing chemical reactions in various industries. It allows scientists to predict the outcome of a reaction, determine the most efficient conditions for the reaction, and troubleshoot any issues that may arise.

5. Are there any limitations to using the Flux General Equation to solve square box reactor questions?

While the Flux General Equation is a useful tool for solving square box reactor questions, it does have some limitations. It assumes that the reaction is taking place in a well-mixed and uniform environment, which may not always be the case in real-world systems. Additionally, it may not account for certain factors that could affect the reaction, such as catalysts or impurities.

Similar threads

  • Nuclear Engineering
Replies
0
Views
399
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
8
Views
962
Replies
1
Views
81
  • Precalculus Mathematics Homework Help
Replies
25
Views
380
  • Calculus
Replies
29
Views
514
  • Nuclear Engineering
Replies
4
Views
3K
  • Differential Equations
2
Replies
52
Views
523
  • Calculus and Beyond Homework Help
Replies
3
Views
488
  • Advanced Physics Homework Help
2
Replies
36
Views
2K
Back
Top