ADIABATIC LAMINAR FLOW WITH NO RADIAL MASS TRANSPORT AND NO AXIAL DIFFUSION

Result

Observing the graphs we see that the maximum temperature is found somewhere between the center and the wall and that the location of the maximum point gets closer to the center throughout the reactor. Try to explain this behavior.

Since the flow is laminar, the flow close to the wall is low whereas the flow in the middle is high. Because of this, the exothermic reaction producing the temperature rise doesn’t have time to occur to the same extent at the center as close to the wall. Therefore, an area of high temperature will initially be found close to the wall. The heat from this area is conducted towards the center of the reactor. However, all the reactants will eventually be consumed close to the wall, preventing further heat production there. In this way the temperature maximum will shift towards the center of the reactor as the reactants closer to the wall are being consumed. Since there is no radial mass transport of reactants to the wall due to the assumption D_i = 0, the effect of the shifting temperature top is seen clearly. The area close to the wall still experiences a slight temperature increase even after the reactants are consumed. This temperature increase is due to the conduction of heat from the nearby high temperature area.

Have a look at the conversion plot for this case, it might help you understand the discussion above.

From the conversion plots you see that the conversion reaches one close to the wall even at the half axial location. As mentioned in the discussion above, this means that the reaction ceases close to the wall preventing further heat production there.

The fact that the temperature continues to increase close to the wall even after all the reactants been consumed is due to the heat conductivity. Remember that we still have radial energy effects even though we are neglecting the radial mass transport effects.