be modified if the problem were not axisymmetric?

Question

GIVEN

Non-axisymmetric, steady, cylindrical geometry with heat generation and convective boundary

condition.

FIND

(a) Difference equations for the centerline and surface control volumes

SKETCH

Answer 1

For the control volume at the centerline we have



and the energy balance gives



For the control volume at the surface, we have for the volume per unit length



and for the surface area (per unit length) of the circumferential face inside Ro

For the surface area of the circumferential face at Ro we have



The surface area per unit length of the radial faces of the control volume are



The energy balance is



The solution of the above set of equations would be carried out in parallel with the method explained

for two-dimensional steady problems. The difference equation for the interior nodes

(steady state terms only) would be added to the above difference equations

and an iterative solution procedure would be employed to find the solution.