Abstract:
A viscous fluid flowing through a cylinder is studied. The
flow is reacting and heat is generated through reaction and
viscosity.
To ensure that the problem represents a physical problem we
discuss the existence and uniqueness of the problem. It is shown
that.the solution is unique when the parameters a and d are
greater than zero and h-mesh size is such that
h <: 2 .0/ (11/ a-3a (~a)% I) and h < 2.0/ (11/ d, - 3d, (~dl);'-01 )
for Equations (2.27) and (2.33).
The problem has no analytical solution, hence, we investigate
the problem using numerical techniques based on Shooting method and
Finlte difference Scheme. The methods are compared and the best
recommended based on a test solution.
Finally, the effects of the parameters a,b, d., d2, d3 and
viscosity on the temperature was discovered. The results show that
the temperature of khe reacting system increases as the parameters
a, d2 and d3 increase. On the other hand the parameters band di
have opposite effects on the temperature, that is, the temperature
decreases as the two parameters increase. Moreover, our numerical
scheme confirmed what is physically expected the temperature
increases as we increase the viscosity of the reactants. Graphs
depicting the relationships between, the temperature and the
parameter, and that of the temperature and the space variable
feature prominently in the thesis.
