Lumped Capacitance Model: Applications
M.M. Yovanovich
LCM2.MWS
Lumped capacitance model.
Applications.
> restart:
> ode:= diff(theta(t),t) = -m*theta(t)+n+p;
> ic:= theta(0) = thetai;
> sol:= dsolve({ode,ic},theta(t));
> pars:= (m=h*S/(rho*cp*V), n=q[i]*S/(rho*cp*V),p=P/(rho*cp));
Sphere with incident flux and volumetric heat sources.
> case1:= (V=Pi*D^3/6, S=Pi*D^2, h=100, rho = 8900, cp=385, q[i]=1e4, P = 1e3, D=10/1000, thetai= 50);
> theta1:= subs(pars, case1, rhs(sol));
> plot(theta1, t=0..300);
> theta_ss:= n/m+p/m;
> theta_ss1:= subs(pars,case1, theta_ss);
> case2:= (V=Pi*D^3/6, S=Pi*D^2, h=100, rho = 8900, cp=385, q[i]=0, P = 0, D=10/1000, thetai= 100.0167);
> theta2:= subs(pars,case2, rhs(sol));
> plot(theta2, t=0..300);
Time constant of the system.
> tc:= (rho*cp*V)/(h*S);
> tc1:= evalf(subs(pars,case1,tc),5);
>