These two equations (psatv =exp (A-B/(Tp+C))*133.322 and Cvs = (psatv*Nl)/(1000*R*Tp) have parameter Tp that solves by ode3 equation. My questions is how to write the coding for these two equations that depends on the solution of the ode3.
My full coding so far:
clc;
clear;
close all;
%parameters
R = 8.314; %gas constant J/mol K - the temperature must be absolute!
Tp = 298.15; %Initial temperature of the droplet/particle K
Nl = 18.015; %Molecular weight of the water, g/mol
A = 18.3036; %Antoine constant
B = 3816.44; %Antoine constant
C = -46.13; %Antoine constantTps = 304.4; %Temperature of particle at surface, Tps=Twb Are you sure?
Dp = 0.00152; %Diameter of droplet/particle, m
rp = Dp/2; %Radius of the droplet/particle, m
vp = 0.75; %Velocity of droplet/particle, m/s
rhog = 1.028; %Density of drying gas, kg/m3
ug = 2.052*10^-5; %Viscosity of drying gas, kg/m s
Dv = 2.78*10^-5; %Vapour air diffusion coefficient, m2/s
Cvi = 0.01024; %Vapour concentration in the drying gas, kg/m3
kg = 0.03; %Thermal conductivity of drying gas, W/m K
cpp = 4009; %Specific heat capacity of the droplet/particle, J/kg K
Tg = 343.15; %Temperature of drying gas, K
hfg = 2.33*10^6; %Latent heat of vapourisation, J/kg
rhod = 1052; %Density of the droplet, kg/m3
rhol = 997; %Density of the water, kg/m3
Dls = 1.5*10^-10; %Diffusivity of water into solid,m2/s
%Eqns
psatv =exp (A-B/(Tp+C))*133.322;
Cvs = (psatv*Nl)/(1000*R*Tp);
Re = (Dp*vp*rhog)/ug;
Sc = ug/(rhog*Dv);
Pr = cpp*ug/kg;
kc = (2+(0.6*Re^0.5*Sc^1/3))*Dv/Dp;
alpha = (2+(0.6*Re^0.5*Pr^1/3))*kg/Dp;
mp = rhod*(4*pi*(rp)^3)/3;
%Define the equations
%ode1 = @(t,y) -4*pi*rp^2*kc*(Cvs-Cvi);
%ode2 = @(t,y) ode1/(4*pi*rhol*rp^2);
%ode3 = @(t,y)(-4*pi*rp^2*alpha*t*(Tp-Tg)-hfg*(ode1))/(mp*cpp);
%f=[ode1;ode2;ode3]
format long
%f= @(t,y) [-4*pi*rp^2*kc*(Cvs-Cvi);
% (-4*pi*rp^2*kc*(Cvs-Cvi))/(4*pi*rhol*rp^2);
% (-4*pi*rp^2*alpha*(t)*(Tp-Tg)-hfg*(-4*pi*rp^2*kc*(Cvs-Cvi)))/(mp*cpp)]
% The functions
%y(1)=ml
%y(2)=rp
%y(3)=Tp
f= @(t,y) [-4*pi*(rp)^2*kc*(Cvs-Cvi);
(-4*pi*(rp)^2*kc*(Cvs-Cvi))./(4*pi*rhol*(y(2))^2);
(-4*pi*(rp)^2*alpha*(t)*(y(3)-Tg)-hfg*(-4*pi*(rp)^2*kc*(Cvs-Cvi)))/(mp*cpp)]
% time discretization
dt = 0.1;
t0 = 0;
tf = 100;
h=dt;
t = t0:dt:tf;
tspan=[t0 tf];
%Define Initial conditions
cond1 = 1.93e-6;
cond2 = 0.00076;
cond3 = 298.15;
y0=[cond1;cond2;cond3];% the initial value of the vector y
%Call the Euler function
[ T, Y ] = EULER( f, t0, tf, y0, h);
disp([' ' 'time' ' ' 'Ml (Y(1))' ' ' 'rp (Y(2))' ' ' 'Tp (Y(3))'])
disp([T(:) Y(:,1) Y(:,2) Y(:,3)])
figure(1)
plot(t,Y(:,1), 'r', 'linewidth', 2)
title('Droplet Mass versus Time')
xlabel('Time,t')
ylabel('Mass,kg')
grid on
figure(2)
plot(t,Y(:,2), 'g', 'linewidth', 2)
title('Droplet Radius versus time')
xlabel('Time,t')
ylabel('Droplet size,m')
grid on
figure (3)
plot(t,Y(:,3), 'b', 'linewidth', 2)
title('Temperature versus time')
xlabel('time,t')
ylabel('Temperature')
grid on
EULER
function [ T, Y ] = EULER( f, t0, tf, y0, h)
% [ T, Y ] = EULER( f, t0, tf, y0, h)
% uses Euler's method to solve a system of differential equations
% It's evaluated by f Starting at time instant t0 with initial condition,
% x0, a solution is approximated at time tf moving in time step h.
% T contains the evaluation times and
% Rows of Y contain the corresponding estimates for y(t).
T = t0 : h : tf;
Y = zeros(length(T),length(y0));
Y(1,:) = y0';
for i = 2 : length(T)
Y(i,:) = Y(i-1,:)+f(T(i-1),Y(i-1,:))'*h;
end
end
