Contents

Heat Transfer Home Work

% Programmer: Aaron Klapheck
% Chapter 7
% 7-April-2009
clear, clc, home
fprintf('The date and time: %s \n', datestr(now))

The date and time: 07-Apr-2009 14:14:11 

Part b

% Graph the velocity and thermal boundry layer vs. position for air (A),
% water (W), engine oil (O), and mercury (M).

% Equations to use:

% Reynolds number (R) = v*x/(nu) = (rho)*v*x/(mu) ... (eqn 1)

% velocity boundry layer (vBL) = 5*L/R^(1/2) ... (eqn 2)

% thermal boundry layer (tBL) = (vBL)/Pr^(1/3) ... (eqn 3)

% Given:

v = 1; %m/s
T = 300; %K
L = 0.04; %m

A_nu = 15.89e-6; %m^2/s
A_Pr = 0.707;

W_rho = 1e3; %kg/m^3
W_mu = 855e-6; %N*s/m^2
W_Pr = 5.83;

O_nu = 550e-6; %m^2/s
O_Pr = 6400;

M_nu = 0.1125e-6; %m^2/s
M_Pr = 0.0248;

velocity and thermal boundry layer vs. position for air (A)

x = [0:0.00001:L];

R = v.*x./(A_nu);
vBL = 5.*x./R.^(1/2);
tBL = (vBL)./A_Pr.^(1/3);

plot(x, vBL, x, tBL), xlabel('Position x, (m)'), ...
    ylabel('Position y, (m)'), ...
    legend('Velocity Boundy Layer', 'Thermal Boundry Layer', 'Location', 'NorthWest'), ...
    title('Air Boundry Layers for Position Along Plate')

velocity and thermal boundry layer vs. position for water (W)

x = [0:0.00001:L];

R = (W_rho).*v.*x./(W_mu);
vBL = 5.*x./R.^(1/2);
tBL = (vBL)./W_Pr.^(1/3);

plot(x, vBL, x, tBL), xlabel('Position x, (m)'), ...
    ylabel('Position y, (m)'), ...
    legend('Velocity Boundy Layer', 'Thermal Boundry Layer', 'Location', 'NorthWest'), ...
    title('Water Boundry Layers for Position Along Plate')

velocity and thermal boundry layer vs. position for engine oil (O)

x = [0:0.00001:L];

R = v.*x./(O_nu);
vBL = 5.*x./R.^(1/2);
tBL = (vBL)./O_Pr.^(1/3);

plot(x, vBL, x, tBL), xlabel('Position x, (m)'), ...
    ylabel('Position y, (m)'), ...
    legend('Velocity Boundy Layer', 'Thermal Boundry Layer', 'Location', 'NorthWest'), ...
    title('Engine Oil Boundry Layers for Position Along Plate')

velocity and thermal boundry layer vs. position for mercury (M)

x = [0:0.00001:L];

R = v.*x./(M_nu);
vBL = 5.*x./R.^(1/2);
tBL = (vBL)./M_Pr.^(1/3);

plot(x, vBL, x, tBL), xlabel('Position x, (m)'), ...
    ylabel('Position y, (m)'), ...
    legend('Velocity Boundy Layer', 'Thermal Boundry Layer', 'Location', 'NorthWest'), ...
    title('Mercury Boundry Layers for Position Along Plate')

Published with MATLAB® 7.5