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+//Exa 4.10

+clc;

+clear;

+close;

+//given data

+L=40*10^-2;// in m

+k=1.5;// in W/mK

+A=4;// in square meter

+alpha=1.65*10^-3;// in m^2/h

+//T = 50-40*x+10*x^2+20*x^3-15*x^4 , so

+// dtBYdx= -40+20*x+60*x^2-60*x^3

+// d2tBYdx2 = 20+120*x-180*x^2

+

+// Part (a) Heat entering the slab

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

+x=0;

+qi= -k*A*(-40+20*x+60*x^2-60*x^3);// in w

+disp(qi,"Heat entering the slab in watt")

+// Heat leaving the slab

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

+x=L;

+ql= -k*A*(-40+20*x+60*x^2-60*x^3);// in w

+disp(ql,"Heat leaving the slab in watt")

+

+// Part (b) Rate of heat storage

+RateOfHeatStorage = qi-ql;// in watt

+disp(RateOfHeatStorage,"Rate of heat storage in watt");

+

+// Part (c) Rate of temperature change

+// d2tBYdx2 = 1/alpha*dtBYdtoh

+// dtBYdtoh= alpha*d2tBYdx2, at

+x=0;

+dtBYdtoh = alpha*(20+120*x-180*x^2);// in degree C/h

+disp(dtBYdtoh,"The rate of temperature change at entering the slab in degree C/h")

+// dtBYdtoh= alpha*d2tBYdx2, at

+x=L

+dtBYdtoh = alpha*(20+120*x-180*x^2);// in degree C/h

+disp(dtBYdtoh,"The rate of temperature change at leaving the slab in degree C/h")

+

+// Part (d) for the rate of heating or cooling to be maximum

+// dBYdx of dtBYdtoh = 0

+// dBYdx of (alpha*d2tBYdx2) =0

+// d3tBYdx3 = 0

+x=120/360;// in meter

+disp(x,"The point where rate of heating or cooling is maximum in meter")