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);

>