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+//Exa 4.2

+clc;

+clear;

+close;

+//given data

+k=40;// in W/mK

+rho=7800;// in kg/m^3

+C=450;// in J/kgK

+d=20*10^-3;// in m

+r=d/2;

+t_i=400;// in degree C

+t=85;// in degree C

+t_infinite=25;// in degree C

+h=80;// in W/m^2K

+//l_s=V/A = (4/3*%pi*r^3)/(4*%pi*r^2) = r/3

+l_s=r/3;// in m

+Bi= h*l_s/k;

+// since Biot number is less than 0.1, hence lumped heat capacity system analysis can be applied

+

+// Part(a)

+// Formula (t-t_infinite)/(t_i-t_infinite)= %e^(-h*A*toh/(rho*V*C)) = %e^(-h*toh/(rho*l_s*C))

+toh= -log((t-t_infinite)/(t_i-t_infinite))*(rho*l_s*C)/h;// in sec

+disp(toh,"The time require to cool the sphere in sec");

+

+// Part(b)

+// dtBYdtoh = h*A*(t_i-t_infinite)/(rho*V*C) = h*(t_i-t_infinite)/(rho*l_s*C)

+dtBYdtoh = h*(t_i-t_infinite)/(rho*l_s*C);// in degree C/sec

+disp(dtBYdtoh,"Initial rate of cooling in degree C/sec");

+

+// Part(c)

+A=4*%pi*r^2;

+toh=60;

+q_in= h*A*(t_i-t_infinite)*%e^(-h*toh/(rho*l_s*C));// in watt

+disp(q_in,"Instantaneous heat transfer rate in watt");

+

+// Part(d) Total energy transferred during first one minute

+V=4/3*%pi*r^3;

+TotalEnergy = rho*C*V*(t_i-t_infinite)*(1-%e^(-h*toh/(rho*C*l_s)));

+disp(TotalEnergy,"Total energy transferred during first one minute in watt")

+

+// Note: Answer of first and last part in the book is wrong