Eric L. Pheterson - Homework 5 - Problem 10.26

function p10_26
fprintf('\n\nEric L. Pheterson - Homework 5 - Problem 10.26\n\n');
syms h

%Liquid (Table A6)
hfg=2257E3; %J/kg
pl =1/1.044E-3; %kg/m^3

%Vapor (Table A4)
pv =.3829; %kg/m^3
kv =.0401; %W/m-K
cpv=2.012E3; %J/kg-K
vv=51.82E-6; %m^2/s

%Al-2024
ks=185; %W/m-k
ps=2700; %kg/m^3
cps=875; %J/kg-K

%Given
Ts=500+273; %K
Tsat=100+273; %K
dT=500-100; %K, ºC
g=9.81; %m/s^2
dt=30; %s

%Sphere
D=20E-3; %m
E=0.25;
As= pi*D^2 %m^2
Vs=4/3*pi*(D/2)^3 %m^3

%Constants
C=0.67;
s=5.67E-8; %W/m^2-K^4

hfgp=hfg+0.8*cpv*dT
NuD=C*((g*(pl-pv)*hfgp*D^3)/(vv*kv*dT))^(1/4)
hconv=NuD*kv/D

hrad=E*s*(Ts^4-Tsat^4)/(Ts-Tsat)

h=solve(-h^(4/3)+hconv^(4/3)+hrad*h^(1/3),h);
h=180

f=hrad/h*100

Lc=(D/2)/3;
Bi=h*Lc/ks

DT=h*(Ts-Tsat)*As*dt/(ps*cps*Vs)
Tf = (Ts-DT)-273