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+//Exa 4.1

+clc;

+clear;

+close;

+//given data

+format('v',9)

+L=1;// in m

+rho=1600;// in kg/m^3

+k=40;// in w/mK

+Cp=4*10^3;// in J/kgK

+a=900;// in  degree C

+b=-300;// in  degree C/m

+c=-50;// in  degree C/m^2

+Qg=1*10^3;// in kW/m^2

+A=10;// area in m^2

+//t=a+b*x+c*x^2 at any instant, so

+// dtBYdx= b+2*c*x

+// d2tBYdx2 = 2*c, then

+

+// Part(a)

+//q1= -k*A*dtBYdx , at

+x=0;

+q1= -k*A*(b+2*c*x);// in w

+//q2= -k*A*dtBYdx , at

+x=L;

+q2= -k*A*(b+2*c*x);// in w

+E_stored= (q1-q2)+Qg*A*L;// in watt

+disp(E_stored,"The rate of change of energy storage in watt")

+

+// Part(b)

+alpha= k/(rho*Cp);// in m^2s

+d2tBYdx2 = 2*c;

+dtBYdtoh= alpha*(d2tBYdx2+Qg/k );// in degree C/sec

+disp(dtBYdtoh,"Rate of change of temperature in degree C/sec");

+disp("Since dt by dx is independent of x. Hence time rate of charge of temperature throughout wall will remain same.")

+

+

+

+