RESULTS AND DISCUSSION
The MATLAB program outputs the concentration c, pressure P and velocity u for each node.
This was based on the finite volume method. The first point of discussion is grid independence.
As the number of nodes N increases, so does the

CFDN 410M Sample Exam
1) Natural gas flows in a circular pipe (diameter D) which loses heat to the surroundings via
convection. The convection coefficient is h, and the temperature of surroundings is T. Gas
enters the pipe at temperature T0 and uniform ve

2D Steady State Heat Conduction in a Rectangular Section
q = h(T-T)
h = 5 W/m C
T = 30 C
qgen = -4T (W/m)
k = 400 (W/m C)
kT + qgen = 0
1m
2T 2T T 2
+
=0
x 2 y 2 100
q = h(T-T)
2m
T = 100 C
The domain is discretized using a 50x50 grid with uniform spacin

% CFD example of air drying
% This program solves the class example for
% u*C'(x) = D*C"(x) + S
% S = k(Csat - C)
% BCs: C(0) = 0, C'(L) = 0
% CONSTANTS
N = 100; % number of grid points
u = 0.01;
k = 0.1;
Diff = 2.5e-5;
Csat = 1.5;
C0 = 0;
L = 0.1;
dx = L

4. Drying of a Porous Material
Moisture is to be removed from a 1m long porous material by passing dry air through the
material at a constant rate of 0.01 m/s. The density of the air remains constant at 1 kg/m, and the
saturation vapor concentration is 0.

1. Temperature of an Electrical Wire with Insulation Missing
A copper wire (9 m long, 1 mm diameter) is carrying an electrical current. One end of the wire is
held at 30 C while the other end is insulated. The curved surfaces (sides) of the wire are also

Flow in a Heated Tube with Constant Surface Temperature
Water flows with average velocity 0.01 m/s through a cylindrical tube of length 10 m and
diameter 0.1 m. The walls of the tube are maintained at 100 C due to condensing steam on the
outer surface, wh

5. Concentration Polarization in Reverse Osmosis Applications
Reverse osmosis is the process whereby pure water is extracted from salt water using a semipermeable filtering membrane. During this process as pure water flows through the membrane,
the salt c

Heat Flow in a Rectangular Fin
A fin is used to enhance heat removal from a material by increasing the effective surface area
over which convection heat losses can occur. A 0.1 m long fin, with rectangular cross section
5mm x 1mm, has a base temperature o