Single variables are equations with single variables. ODE45 gives t and y as the arguments passed on to the function fname. Note, the arrangement of t and y is essential. The t must come first, followed by y. After this, we need to define our function firstODEfun. It should be on a separate script. The code below defines our function. Then, when we run our program, we get an error, as displayed in the command window. The error indicates that the t1 is undefined since the input variable was t.
Keep in mind that our t and y are dummy variables. The only thing that you should note is to use a similar name for the input, and in the definition, your function dy. Also, as you use a different name, the order of the variable must remain, independent variable followed by the independent. Plug flow reactor, also known as tabular reactor, consists of a cylindrical pipe with an opening on each end for the reactor and products to flow through.
Consumption of reactors is continuous as they flow down the length of the reactors. It means that as the reaction continues, the products increases. You can figure the plug flow reactor as one long tube or several short tubes. They have different diameters. Determining the diameter to use is based on construction cost, pumping cost, and the heat transfer needed. Their application is used widely in gas or liquid systems. When modelling the PFR, you take an increment of the reactor when balancing the chemical equation occurring in the reactor and integrate the holdings.
This is because it is a distributed parameter system. Holdings are the values used to balance the equation. Now, after balancing the equation and integrating the holding, you end up with the below equation.
Note that in equation2 above, k takes the initial form ko. Now, when we plug the equation2 into equation1, we end up with:. This is how to calculate the concentration profile in the reactor. Add a comment. Sonnhard Graubner Dr. Sonnhard Graubner 1.
Jameson Jameson 4 4 silver badges 16 16 bronze badges. Eric Towers Eric Towers Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Example Question 4 : Initial Value Problems.
Explanation : So this is a separable differential equation with a given initial value. To start off, gather all of the like variables on separate sides. Plug in the initial condition to get: So raising e to the power of both sides: Solving for C: giving us a final answer of:. Solve the separable differential equation with the initial condition. Notice that when you divide sec y to the other side, it will just be cos y , and the csc x on the bottom is equal to sin x on the top.
Solve the differential equation Subject to:. Possible Answers: none of these answers. Then just take the square root, and you arrive at: Then, to get the correct answer, simplify by factoring out an and pulling it outside of the square root to get:.
Solve for y. Explanation : So this is a separable differential equation. We can think of as and as. Taking the anti-derivative once, we get: Then using the initial condition We get that So Then taking the antiderivative one more time, we get: and using the initial condition we get the final answer of:. Example Question 8 : Initial Value Problems. Solve the differential equation for y subject to the initial condition:. Then integrate, and make sure to add a constant at the end Plug in the initial condition Solving for C: Which gives us: Then taking the square root to solve for y, we get:.
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