exemplo_21.m

% NASBHT - Numerical and Analytical Solutions of BioHeat Transfer problems
% 
% Copyright (C) 2018. Hugo Fernando Maia Milan
%
% File:   exemplo_21.m
% Author: Hugo Fernando Maia Milan
% Email:  hugofernando@gmail.com
%
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% Algoritmo que resolve o exemplo 21.

wb=0.0005;%perfusão sanguínea
pb=1085;%peso específico do sangue
cb=3680;%calor específico do sangue
Tb=37;%temperatura do sangue
k=0.3;%condutividade térmica do tecido
qmet = 700;%produção de calor metabólico
L=0.03;%comprimento do tecido

TC=37;%temperatura na fronteira interna
Tar = 20;% temperatura do ar
rc = 0.02;% resistência
Tr = 22; % temperatura radiante média
rr = 17e6; % resistência ao fluxo de calor por radiação

l = sqrt(wb*pb*cb/k);

n = Tb + qmet/(wb*pb*cb);


g = k*l;

s = sinh(l*L);
c = cosh(l*L);
t = tanh(l*L);


x = 0:L/100:L;
TL1 = 37;

rre = rr/((TL1 + Tr + 273.15*2)*...
    ((TL1+273.15)^2 + (Tr+273.15)^2));

re = rre*rc/(rre + rc);

Te = (rc*Tr + rre*Tar)/(rre + rc);

TL2 = (Te/re + TC*g/s + n*g*(1/t - 1/s))/(g/t + 1/re);

dif = (TL2 - TL1)/TL2*100;

%TL3
rre = rr/((TL2 + Tr + 273.15*2)*...
    ((TL2+273.15)^2 + (Tr+273.15)^2));

re = rre*rc/(rre + rc);

Te = (rc*Tr + rre*Tar)/(rre + rc);

TL3 = (Te/re + TC*g/s + n*g*(1/t - 1/s))/(g/t + 1/re);

dif = (TL2 - TL3)/TL3*100;

xa = x;

Ta = TL3*sinh(l*xa)/s ...
    + TC*sinh(l*(L - xa))/s ...
    + n*(1 - (sinh(l*xa) + sinh(l*(L - xa)))/s);

qC = -TL3*g/s + TC*g/t + n*g*(1/s - 1/t);

qconv = (TL - Tar)/rc;
% plot(xa,Ta)

%% efeito do fluxo de calor
qLq = -2500:2500;
TLq = -qLq*t/g + TC/c + n*(1 - 1/c);
% plot(qLq,TLq)