Contents

Heat Transfer Home Work

% Programmer: Aaron Klapheck
% Chapter 8
% 22-April-2009
clear, clc, home
fprintf('The date and time: %s \n', datestr(now))

The date and time: 22-Apr-2009 09:08:49 

Part b

% Graph the heat trasfer per unit length vs. velocity for air (A),
% water (W), and engine oil (O).

% Equations to use:

% Reynolds number for cylinder (R_D) = v*D/(nu) = v*D/(Sv*mu) ... (eqn 1)
% where: Sv = specific volume.

% Nusselt number for cylinder (Nu_D) = 0.3+(0.62.*R_D.^(1/2).*Pr^(1/3))./(1+(0.4./Pr).^(2/3)).^(1/4).*(1+(R_D/282000)^(5/8))^(4/5) ... (eqn 2)

% Convection coefficiant (h) = Nu_D.*k./D ... (eqn 3)

% Heat trasfer per length q/L = h.*(Ts - T_infin).*pi.*D ... (eqn 4)

% Given:



Ts = 323; %K
T_infin = 293; %K
Tf = 310; %K. Film temperature

D = 0.01; %m

A_nu = 16.9e-6; %m^2/s
A_k = 27.04e-3; %W/(m*k)
A_Pr = .7056;

W_Sv = 22.93; %m^3/kg
W_mu = 9.49e-6; %N*s/m^2
W_k = 20.4; %W/(m*k)
W_Pr = .873;

O_nu = 288e-6; %m^2/s
O_k = 145e-3; %W/(m*k)
O_Pr = 3400;

Heat Trasfer Per Unit Length vs. Velocity of Air (A)

v = [0.5:0.0001:10];  %m/s

R_D = v.*D./(A_nu);
Nu_D = 0.3+ ...
  (0.62.*R_D.^(1/2).*A_Pr^(1/3))./ ...
  (1+(0.4./A_Pr).^(2/3)).^(1/4).* ...
  (1+(R_D./282000).^(5/8)).^(4/5);

h = Nu_D.*A_k./D;
q_per_L = h.*(Ts - T_infin).*pi.*D;


plot(v, q_per_L), xlabel('Velocity v, (m/s)'), ...
    ylabel('Heat Trasfer Per Unit Length q/L, (W/m)'), ...
    title('Heat Trasfer Per Length vs. Velocity of Air')

Heat Trasfer Per Unit Length vs. Velocity of Water (W)

v = [0.5:0.0001:10];  %m/s

R_D = v.*D./(W_mu.*W_Sv);
Nu_D = 0.3+ ...
  (0.62.*R_D.^(1/2).*W_Pr^(1/3))./ ...
  (1+(0.4./W_Pr).^(2/3)).^(1/4).* ...
  (1+(R_D./282000).^(5/8)).^(4/5);

h = Nu_D.*W_k./D;
q_per_L = h.*(Ts - T_infin).*pi.*D;


plot(v, q_per_L), xlabel('Velocity v, (m/s)'), ...
    ylabel('Heat Trasfer Per Unit Length q/L, (W/m)'), ...
    title('Heat Trasfer Per Length vs. Velocity of Water')

Heat Trasfer Per Unit Length vs. Velocity of Engine Oil (O)

v = [0.5:0.0001:10];  %m/s

R_D = v.*D./(O_nu);
Nu_D = 0.3+ ...
  (0.62.*R_D.^(1/2).*O_Pr^(1/3))./ ...
  (1+(0.4./O_Pr).^(2/3)).^(1/4).* ...
  (1+(R_D./282000).^(5/8)).^(4/5);

h = Nu_D.*O_k./D;
q_per_L = h.*(Ts - T_infin).*pi.*D;


plot(v, q_per_L), xlabel('Velocity v, (m/s)'), ...
    ylabel('Heat Trasfer Per Unit Length q/L, (W/m)'), ...
    title('Heat Trasfer Per Length vs. Velocity of Engine Oil')

Published with MATLAB® 7.5