Problem Set 2 (Numerical Simulation of Energy System)
EM503
Problems 1-4, use matlab
1. Using the Newton-Raphson method, solve the following equation for the value of x, which is
known to be real and positive:
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2. The generation of two quantities, F and G, in a chemical reactor is governed by the equations
Solve this system of equations using the Newton-Raphson method and starting with F = G = 1.0
as the initial guess.What is the nature of these equations and do you expect the scheme to
converge? Set the system up also as a root-solving problem. Suggest a method to solve it and
obtain the solution.
3. In a metal forming process, the force F and the displacement x are governed by
Solve for F and x, applying the Newton-Raphson method to this system of equations. Also,
determine the sensitivity of the force F to a variation in the total input S, ∂F/∂S, where S is the
given value of 250, by slightly varying this input.
4. The dimensionless temperature x and heat flux y in a thermal system are governed by the
nonlinear equations.
Solve this system of equations by the Newton-Raphson.
5. In a chemical reaction, the effect of the concentration C of a catalyst on the
reaction rate is investigated and the experimental results are tabulated as
Using the method of least squares and considering polynomials up to
the fifth order, obtain a best fit to these data. Which curve provides the
best approximation to the given data?
