diff options
Diffstat (limited to '965/CH4')
32 files changed, 743 insertions, 0 deletions
diff --git a/965/CH4/EX4.1/1.sci b/965/CH4/EX4.1/1.sci new file mode 100644 index 000000000..962b43411 --- /dev/null +++ b/965/CH4/EX4.1/1.sci @@ -0,0 +1,22 @@ +clc;
+clear all;
+disp("required time calculation")
+As=2*0.5*0.5;// m^2 surface area of plate
+V=0.5*0.5*0.00625;// m^3 volume of plate
+Lc=V/As;// m characteristic length of plate
+h=90; //W/m^2/C
+k=370;//W/m.C
+rho=9000;// kg/m^3
+C=380;//J/kg.C
+t=108;// degree C
+ta= 36;// degree C
+ti=300;// degree C
+Bi=h*Lc/k;// biot number
+if (Bi< 0.1)
+disp("Bi is less than 0.1 hence lumped heat capacity method can be applied")
+disp("Temperature distribution is given by : (t-ta)/(ti-ta) = exp((-h*As*tau)/rho*V*C)")
+m=(t-ta)/(ti-ta);
+x=-h*As/(V*rho*C);
+disp("sunstituting the values we get,")
+tau = (log(m))/x;
+disp("sec",tau,"time required to attend the temperature is ")
diff --git a/965/CH4/EX4.10/10.sci b/965/CH4/EX4.10/10.sci new file mode 100644 index 000000000..ee6e65c77 --- /dev/null +++ b/965/CH4/EX4.10/10.sci @@ -0,0 +1,21 @@ +clc;
+clear all;
+disp("temperature and time")
+R=40/2000;//m
+ti=20;// degree C
+tau=4*60;//s
+ta=100;// degree C
+k=10;// W/m.C
+rho=1200;// kg/m^3
+c=2000;// J/kg.C
+h=100;//W/m^2.C
+Lc=R/3;// for sphere
+Bi=h*Lc/k
+
+t=ta+(ti-ta)*exp(-h*3*tau/(R*rho*c))
+disp("degree C")
+ti=5;// degree C
+X=(t-ta)/(ti-ta);
+Y=-h*3/(R*rho*c)
+tau=(log (X))/Y;// sec
+disp("min",tau/60,"time taken tau =")
diff --git a/965/CH4/EX4.11/11.sci b/965/CH4/EX4.11/11.sci new file mode 100644 index 000000000..decc11189 --- /dev/null +++ b/965/CH4/EX4.11/11.sci @@ -0,0 +1,33 @@ +clc;
+clear all;
+disp("ingot time required")
+R=50/2000;//m
+L=200/1000;//m
+k=60;// W/m.C
+c=200;// J/kg.C
+rho=800;// kg/m^3
+hw=200;//W/m^2.C
+ha=20;//W/m^2.C
+ta=30;// degree C
+ti=800;// degree C
+
+Lc=R/2;
+Bi=hw*Lc/k;
+disp(Bi,"Bi =")
+t=500;// degree C
+As=2*3.1416*R*L;//m^2
+V=3.1416*R*R*L;//m^3
+X=hw*As/(rho*V*c)
+tau1=(-1/X)*log((t-ta)/(ti-ta));
+disp(tau1,"tau1 =")
+
+t=100;// degree C
+ti=500// degree C
+X=ha*As/(rho*V*c);
+tau2=(-1/X)*log((t-ta)/(ti-ta));
+disp(tau2,"tau2 =")
+
+tau=tau1+tau2;
+disp("min",tau/60,"total time, tau =")
+
+
diff --git a/965/CH4/EX4.12/12.sci b/965/CH4/EX4.12/12.sci new file mode 100644 index 000000000..e946c3a3e --- /dev/null +++ b/965/CH4/EX4.12/12.sci @@ -0,0 +1,27 @@ +clc;
+clear all;
+disp("spherical thermocouple junction")
+h=400;//W/m^2.C
+k=20;// W/m.C
+c=400;// J/kg.C
+rho=8500;// kg/m^3
+tau=1;//second
+
+
+R=tau*h*3/(rho*c)
+disp("mm",2*R*1000,"Diameter =")
+
+Lc=R/3;
+Bi=h*Lc/k;
+disp(Bi,"Bi =")
+
+ti=25;//degree C
+t=198;//degree C
+ta=200;// degree C
+
+As=4*3.1416*R*R;//m^2
+V=4*3.1416*(R^3)/3;//m^3
+
+X=h*As/(rho*V*c);
+tau=(-1/X)*log((t-ta)/(ti-ta));
+disp("s",tau,"tau =")
diff --git a/965/CH4/EX4.13/13.sci b/965/CH4/EX4.13/13.sci new file mode 100644 index 000000000..71609efaa --- /dev/null +++ b/965/CH4/EX4.13/13.sci @@ -0,0 +1,32 @@ +clc;
+clear all;
+disp("spherical thermocouple junction")
+R=8/2000;//m
+hg=40;//W/m^2.C
+ha=10;//W/m^2.C
+k=40;// W/m.C
+c=420;// J/kg.C
+rho=8000;// kg/m^3
+
+As=4*3.1416*R*R;//m^2
+V=4*3.1416*(R^3)/3;//m^3
+
+
+tau1=rho*V*c/(hg*As);
+disp("s",tau1,"tau* =")
+
+ta=300;// degree C
+ti=40;//degree C
+tau2=10;//s
+X=-1*tau2/tau1;
+t=ta+(ti-ta)*exp(X);
+disp("degree C",t,"temperature during heating t =")
+
+tau3=20;//s
+tau4=rho*R*c/(3*ha);//s
+disp("s",tau4,"tau* =")
+ti=t;// degree C
+X=-1*tau3/tau4;
+ta=30;//degree C
+t=ta+(ti-ta)*exp(X);//degree C
+disp("degree C",t,"temperature during cooling t =")
diff --git a/965/CH4/EX4.14/14.sci b/965/CH4/EX4.14/14.sci new file mode 100644 index 000000000..92b2ea5ee --- /dev/null +++ b/965/CH4/EX4.14/14.sci @@ -0,0 +1,20 @@ +clc;
+clear all;
+disp("cylindrical thermometer ")
+R=3/2000;//m
+h=55;//W/m^2.C
+k=8.8;// W/m.C
+a=0.0166;// m^2/h
+c=420;// J/kg.C
+L=1;//m
+
+As=2*3.1416*R*L;//m^2
+V=3.1416*(R^2);//m^3
+
+
+tau1=k*V*3600/(h*a*As);
+disp("s",tau1,"tau* =")
+disp("for temperature to reach half its final")
+//theta/thetai=0.5=exp(-tau/tau1)
+tau= -tau1*log(0.5);
+disp("s",tau,"time required to temperature to half its final value t =")
diff --git a/965/CH4/EX4.15/15.sci b/965/CH4/EX4.15/15.sci new file mode 100644 index 000000000..82ac133fc --- /dev/null +++ b/965/CH4/EX4.15/15.sci @@ -0,0 +1,34 @@ +clc;
+clear all;
+disp("copper-constantan thermometer")
+R=2.5/2000;//m
+ti=25;//degree C
+ta=215;// degree C
+t=165;// degree C
+rho=8750;// kg/m^3
+c=380;// J/kg.C
+h=145;//W/m^2.C
+kth=28;// W/m.C
+
+As=4*3.1416*R*R;//m^2
+V=4*3.1416*(R^3)/3;//m^3
+Lc=V/As;
+a=k/(rho*c);
+//Fo=a*tau/Lc^2;
+Bi=h*Lc/k;
+th=t-ta;
+tha=ti-ta;
+thm=th/tha;
+
+Fo=(-1/Bi)*log(thm);
+tau=(Fo*Lc^2)/a;
+disp("s",tau,"tau =")
+
+Fo=1/Bi;
+tau=(Fo*Lc^2)/a;
+disp("s",tau,"tau* =")
+thm=exp(-1);
+th=thm*tha;
+t=th+ta;
+
+disp("degree C",t,"temperature t =")
diff --git a/965/CH4/EX4.16/16.sci b/965/CH4/EX4.16/16.sci new file mode 100644 index 000000000..0440c8aac --- /dev/null +++ b/965/CH4/EX4.16/16.sci @@ -0,0 +1,28 @@ +clc;
+clear all;
+disp("temperation variation")
+L=60/2000;//m
+k=42.6;// W/(m.C)
+a=0.043;// m^2/h
+ti=440;// degree C
+h=235;// W/(m^ 2.C)
+ta=50;// degree C
+tau=4.3*60;//seconds
+Lc=L;// characteristic length
+Fo=a*tau/Lc^2;
+Bi=h*Lc/k;
+if Bi>1
+disp("Internal temperature gradients are not small and can not be neglected")
+end
+Bii=1/Bi;
+x=0;// midplane
+//(to-ta)/(ti-ta)=0.6
+to=0.6*(ti-ta)+ta;
+disp("Degree C",to,"Temperature at midplane Tm =")
+ x=0.015/L;
+ Bii=6.06;
+ ti=to;
+ //(to-ta)/(ti-ta)=0.97
+ to=0.97*(ti-ta)+ta;
+ disp("Degree C",to,"Temperature inside the plate 15mm from the midplane To =")
+
diff --git a/965/CH4/EX4.17/17.sci b/965/CH4/EX4.17/17.sci new file mode 100644 index 000000000..918f54b29 --- /dev/null +++ b/965/CH4/EX4.17/17.sci @@ -0,0 +1,31 @@ +clc;
+clear all;
+disp("time and temperature ")
+L=6/2000;//m
+rho=7800;// kg/m^3
+c=460;// J/(kg.C)
+k=55;// W/(kgm.C)
+ti=30;// degree C
+ta=2150;// degree C
+t=1100;// degree C
+
+Lc=L;// characteristic length
+Bi=h*Lc/k;
+if Bi>1
+disp("Internal temperature gradients are not small and can not be neglected")
+end
+Fo=a*tau/Lc^2;
+T1=(t-ta)/(ti-ta);
+//T2=(to-ta)/(ti-ta);
+//T3=(t-ta)/(to-ta);
+T3=0.93;
+T2=T1/T3;
+Bii=1/Bi;
+Fo=4.4;
+//a*tau/Lc^2
+a=k/(rho*c);
+tau=Fo*Lc*Lc/a;
+disp("sec",tau,"Tau =")
+ to=0.495*(ti-ta)+ta;
+ disp("Degree C",to,"Temperature inside To =")
+
diff --git a/965/CH4/EX4.18/18.sci b/965/CH4/EX4.18/18.sci new file mode 100644 index 000000000..2b1dbd809 --- /dev/null +++ b/965/CH4/EX4.18/18.sci @@ -0,0 +1,29 @@ +clc;
+clear all;
+disp("time and temperature")
+R=80/1000;//m
+k=17.4;// W/(m.C)
+ti=830;// degree C
+ta=40;// degree C
+t=120;// degree C
+a=0.019;// m^2/h
+h=180;// W/(m^2.C)
+
+Lc=3.1416*R*R*L/(2*3.1416*R*L);// characteristic length
+Bi=h*Lc/k;
+if Bi>1
+disp("Internal temperature gradients are not small and can not be neglected")
+end
+Bii=1/Bi;
+Fo=3.2;
+tau=3600*Fo*Lc^2/a;
+disp("sec",tau,"Tau =")
+r=R;
+Bii=1/Bi;
+T1=0.83;
+t1=T1*(t-ta)+ta;
+ts=t1;
+disp("degree C",ts,"Temperature at the surface Ts =")
+gradt=h*(ts-ta)/k;
+disp("C/m",gradt,"Temperature gradient =")
+
diff --git a/965/CH4/EX4.19/19.sci b/965/CH4/EX4.19/19.sci new file mode 100644 index 000000000..b778dcd8e --- /dev/null +++ b/965/CH4/EX4.19/19.sci @@ -0,0 +1,26 @@ +clc;
+clear all;
+disp("temperature at centre")
+R=60/1000;//m
+rho=990;// kg/m^3
+c=4170;//J/(kg.C)
+k=0.58;// W/(m.C)
+ti=25;// degree C
+ta=6;// degree C
+tau=2*3600;// seconds
+h=5.8;// W/(m^2.C)
+
+Lc=(4/3)*3.1416*R*R*R/(4*3.1416*R*R);// characteristic length
+Bi=h*Lc/k;
+if Bi>1
+disp("Internal temperature gradients are not small and can not be neglected")
+end
+Bii=1/Bi;
+Fo=k*tau/(rho*c*R^2);
+r=0;// midplane of the apple
+Bii=1/Bi;
+
+T1=0.75;
+t1=T1*(ti-ta)+ta;
+disp("degree C",t1,"Temperature Tm =")
+
diff --git a/965/CH4/EX4.2/2.sci b/965/CH4/EX4.2/2.sci new file mode 100644 index 000000000..b55742fda --- /dev/null +++ b/965/CH4/EX4.2/2.sci @@ -0,0 +1,22 @@ +clc;
+clear all;
+disp("required time calculation")
+As=2*0.4*0.4;// m^2 surface area of plate
+V=0.4*0.4*4/1000;// m^3 volume of plate
+Lc=V/As;// m characteristic length of plate
+h=20000;//kJ/m^2.h.C
+k=370;//W/m.C
+rho=3000;// kg/m^3
+C=0.8;//kJ/kg.C
+t=-70;// degree C
+ta=-183;// degree C
+ti=200;// degree C
+Bi=h*Lc/k;// biot number
+if (Bi< 0.1)
+disp("Bi is less than 0.1 hence lumped heat capacity method can be applied")
+end
+disp("Temperature distribution is given by : (t-ta)/(ti-ta) = exp((-h*As*tau)/rho*V*C)")
+m= (t-ta)/(ti-ta);
+x=-h/(Lc*rho*C);
+tau=3600*(log(m))/x;
+disp("sec",tau,"time required to attend the temperature is ")
diff --git a/965/CH4/EX4.20/20.sci b/965/CH4/EX4.20/20.sci new file mode 100644 index 000000000..6b94fe4f1 --- /dev/null +++ b/965/CH4/EX4.20/20.sci @@ -0,0 +1,17 @@ +clc;
+clear all;
+disp("time required")
+x=12/1000;//m
+a=1.2*10^(-5);//m^2/s
+ti=745;// degree C
+ta=20;// degree C
+t=595;// degree C
+
+
+T1=(t-ta)/(ti-ta);
+erfM=T1;
+M=0.9;// from tables
+tau=((x/M)^2)/(4*a);
+disp("seconds",tau,"Tau =")
+
+
diff --git a/965/CH4/EX4.21/21.sci b/965/CH4/EX4.21/21.sci new file mode 100644 index 000000000..8b231d397 --- /dev/null +++ b/965/CH4/EX4.21/21.sci @@ -0,0 +1,18 @@ +clc;
+clear all;
+disp("to find Depth")
+a=2.75*10^(-3);//m^2/h
+ti=5.4;// degree C
+ta=-6;// degree C
+t=0;// degree C
+tau=9.5;// hours
+
+
+T1=(t-ta)/(ti-ta);
+erfM=T1;
+M=0.5;// from tables
+x=2*M*(a*tau)^0.5;
+disp("m",x,"x =")
+
+
+
diff --git a/965/CH4/EX4.22/22.sci b/965/CH4/EX4.22/22.sci new file mode 100644 index 000000000..b6e69e9fb --- /dev/null +++ b/965/CH4/EX4.22/22.sci @@ -0,0 +1,19 @@ +clc;
+clear all;
+disp("Time and Temperature")
+L=60/1000;// m
+a=1.22*10^(-5);//m^2/s
+ti=30;// degree C
+ta=110;// degree C
+tau=1.5*60;// seconds
+
+taumax=L^2/(4*a*0.25);
+disp("s",taumax,"maximum time that the slab be treated asa semi infinite body taumax=")
+x=L/2;
+M=x/(2*(a*tau)^0.5);
+//erfM=0.47=T1;
+T1=0.47;
+t=ta+T1*(ti-ta);
+disp("degree C",t,"temperature at the centre of slab T =")
+
+
diff --git a/965/CH4/EX4.23/23.sci b/965/CH4/EX4.23/23.sci new file mode 100644 index 000000000..ad029ad64 --- /dev/null +++ b/965/CH4/EX4.23/23.sci @@ -0,0 +1,22 @@ +clc;
+clear all;
+disp("Temperature & heat rate")
+x=80/1000;// m
+a=1.6*10^(-3);//m^2/h
+ti=25;// degree C
+ta=340;// degree C
+k=0.94;// W/(m.C)
+tau=8;//hours
+
+M=x/(2*(a*tau)^0.5);
+M
+//erfM=0.37=T1;
+T1=0.37;
+
+t=ta+T1*(ti-ta);
+disp("degree C",t,"temperature at the centre of slab T =")
+
+Q=k*(ti-ta)*(exp(-M*M))/(3.1416*a*tau)^0.5;
+disp("W/m^2",Q,"instantaneous heat flow rate Q =")
+ Qs=k*(ti-ta)/(3.1416*a*tau)^0.5;
+disp("W/m^2",Qs,"heat flow rate at the surface Qs =")
diff --git a/965/CH4/EX4.24/24.sci b/965/CH4/EX4.24/24.sci new file mode 100644 index 000000000..06b67e43d --- /dev/null +++ b/965/CH4/EX4.24/24.sci @@ -0,0 +1,17 @@ +clc;
+clear all;
+disp("Time Required")
+x=0;// m
+gradT=400;// C/m
+a=0.42;//m^2/h
+ti=120;// degree C
+ta=6;// degree C
+k=0.94;// W/(m.C)
+tau=8;//hours
+
+//Qs=k*gradT=k*(ti-ta)/(3.1416*a*tau)^0.5;
+//gradT=(ti-ta)/(3.1416*a*tau)^0.5
+tau=(((ti-ta)/gradT)^2)/(3.1416*a);
+disp("seconds",tau*3600,"time required Tau =")
+
+
diff --git a/965/CH4/EX4.25/25.sci b/965/CH4/EX4.25/25.sci new file mode 100644 index 000000000..0fef49ef0 --- /dev/null +++ b/965/CH4/EX4.25/25.sci @@ -0,0 +1,21 @@ +clc;
+clear all;
+
+disp("Maximum temperature rise")
+a=1.25*10^(-5);//m^2/s
+k=54;// W/(m.C)
+A=4*360*10^(-4);//m^2
+m=1600;//kg
+v=90;// km/h
+tau=9;//seconds
+
+KE=0.5*m*v*v*(1000/3600)^2;
+Q=KE/tau;
+Qs=Q;
+disp("W",Q,"heat flow rate at surface Qs =")
+//Qs=-k*(ti-ta)/(3.1416*a*tau)^0.5;
+delT=Qs*((3.1416*a*tau)^0.5)/(k*A);
+
+disp("degree C",delT,"temperature rise ta-ti =")
+
+
diff --git a/965/CH4/EX4.26/26.sci b/965/CH4/EX4.26/26.sci new file mode 100644 index 000000000..67e503075 --- /dev/null +++ b/965/CH4/EX4.26/26.sci @@ -0,0 +1,24 @@ +clc;
+clear all;
+disp("Time and Temperature")
+R=300/1000;//m
+a=1.12*10^(-4);//m^2/s
+ti=20;//degree C
+ta=480;// degree C
+t=350;// degree C
+tau=3*60;//seconds
+
+M=a*tau/R^2;
+erfM=0.32;
+T1=erfM;
+
+t=ta+T1*(ti-ta);
+disp("degree C",t,"temperature at the centre of surface T=")
+t=350;//
+T1=(t-ta)/(ti-ta);
+M=0.23;
+tau=M*(R^2)/a;
+
+disp("sec",tau,"time required Tau =")
+
+
diff --git a/965/CH4/EX4.27/27.sci b/965/CH4/EX4.27/27.sci new file mode 100644 index 000000000..f599e5dde --- /dev/null +++ b/965/CH4/EX4.27/27.sci @@ -0,0 +1,15 @@ +clc;
+clear all;
+disp("The Time lag")
+x=300/1000;//m
+rho=1600;// kg/m^3
+k=0.65;//W/(m.C)
+c=440;// J/(kg.C)
+n=1/24;// h^-1
+n
+a=k*3600/(rho*c);
+a
+deltau = (x/2)*(1/(3.1416*a*n)^(0.5));
+
+disp("h",deltau,"time lag =")
+
diff --git a/965/CH4/EX4.28/28.sci b/965/CH4/EX4.28/28.sci new file mode 100644 index 000000000..c3a448aef --- /dev/null +++ b/965/CH4/EX4.28/28.sci @@ -0,0 +1,9 @@ +clc;
+clear all;
+disp("Depth and Temperature")
+a=0.044;//m^2/h
+n=1400*60;// h^-1
+theta=2/100;
+
+x=-((a/(3.1416*n))^0.5)*log (theta);
+disp("mm",x*1000,"depth x =")
diff --git a/965/CH4/EX4.29/29.sci b/965/CH4/EX4.29/29.sci new file mode 100644 index 000000000..c8404ab54 --- /dev/null +++ b/965/CH4/EX4.29/29.sci @@ -0,0 +1,35 @@ +clc;
+clear all;
+disp("Heat rate & energy")
+A=5;//m^2
+k=1.2;// W/(m.C)
+a=1.77*10^(-3);//m^2/h
+//t =(120-100*x+24*x^2+40*x^3-30*x^4
+//gradT=-100+48*x+120*x*x-120*x^3;
+//d2T=48+240*x-360*x*x
+
+x=0;
+t=120-100*x+24*x^2+40*x^3-30*x^4;
+gradT=-100+48*x+120*x*x-120*x^3;
+Qin=-k*A*gradT;
+disp("W",Qin," heat entering the slab Qin =")
+x=0.5;
+gradT=-100+48*x+120*x*x-120*x^3;
+Qout=-k*A*gradT;
+disp("W",Qout," heat leaving the slab Qout =")
+
+Qs=Qin-Qout;
+disp("W",Qs," heat stored in the unit time Qs =")
+
+x=0;
+d2T=48+240*x-360*x*x;
+Tt=a*d2T;
+disp("C/h",Tt,"rate of temperature change at inlet =")
+
+x=0.5;
+d2T=48+240*x-360*x*x;
+Tt=a*d2T;
+disp("C/h",Tt,"rate of temperature change at outlet =")
+//d3T =240-720x =0
+x=240/720;//m
+disp("m",x,"point where rate of heating/cooling is maximum x =")
diff --git a/965/CH4/EX4.3/3.sci b/965/CH4/EX4.3/3.sci new file mode 100644 index 000000000..280eb7335 --- /dev/null +++ b/965/CH4/EX4.3/3.sci @@ -0,0 +1,21 @@ +clc;
+clear all;
+disp("required temperature calculation")
+D=0.1;//m dimeter
+R=D/2;//m radius
+As=4*%pi*(R^2);// m^2 surface area of sphere
+V=4*%pi*(R^3)/3;// m^3 volume of sphere
+Lc=V/As;// m characteristic length of sphere
+h=200; //W/m^2/C
+k=386;//W/m.C
+rho=8954;// kg/m^3
+C=383;//J/kg.C
+ta=50;// degree C
+ti=250;// degree C
+tau = 5*60;//sec
+Bi=h*Lc/k;// biot number
+if (Bi< 0.1)
+disp("Bi is less than 0.1 hence lumped heat capacity method can be applied")
+disp("Temperature distribution is given by : (t-ta)/(ti-ta) = exp((-h*As*tau)/(rho*V*C))")
+t = ta+(ti-ta)*exp((-h*As*tau)/(rho*V*C));
+disp("degree C",t,"the temperature attained is ")
diff --git a/965/CH4/EX4.30/30.sci b/965/CH4/EX4.30/30.sci new file mode 100644 index 000000000..a0e36eda3 --- /dev/null +++ b/965/CH4/EX4.30/30.sci @@ -0,0 +1,25 @@ +clc;
+clear all;
+disp("Temperautre and rate")
+R=50/1000;//m
+ti=900;// degree C
+ta=30;//degree C
+h=20;// W/(m^2.C)
+rhos=7800;//kg/m^3
+cs=460;// J/kg.C
+tau=30;//s
+k=40;//W/(m.C)
+
+
+Lc=R/3;//m
+Bi=h*Lc/k;
+As=4*3.1416*R^2;
+V=4/3*3.1416*R^3;
+X=h*As*tau/(rhos*V*cs);
+M=exp(-X);
+t=ta+(ti-ta)*M;
+disp("degree C",t," temperature of ball after 30 sec, t =")
+
+gradT=(ti-ta)*M*(-X/tau);
+disp("C/min",gradT*60," rate of cooling after 30 seconds =")
+
diff --git a/965/CH4/EX4.31/31.sci b/965/CH4/EX4.31/31.sci new file mode 100644 index 000000000..5fbbc1621 --- /dev/null +++ b/965/CH4/EX4.31/31.sci @@ -0,0 +1,23 @@ +clc;
+clear all;
+disp("Time for cooling")
+L=20/1000;//m
+ti=150;// degree C
+ta=30;//degree C
+hw=100;// W/(m^2.C)
+ha=20;// W/(m^2.C)
+t=90;// degree C
+rho=8800;//kg/m^3
+c=400;// J/kg.C
+k=360;//W/(m.C)
+
+As=4*3.1416*R^2;
+Lc=L/2;//m
+Bi=h*Lc/k;
+
+C=120;
+tau=-rho*L*c*log((t-ta)/(ti-ta))/C
+disp("minutes",tau/60," time, Tau =")
+
+
+
diff --git a/965/CH4/EX4.32/32.sci b/965/CH4/EX4.32/32.sci new file mode 100644 index 000000000..2ce6fe94a --- /dev/null +++ b/965/CH4/EX4.32/32.sci @@ -0,0 +1,16 @@ +clc;
+clear all;
+disp("contact surface temperature")
+disp("The rate of heat flow at a surface x =0 is given by")
+disp(" Q = -k*A*delT/(%pi*a*tau)^0.5")
+disp("Heat received by each unit area of contact surface from the body at a temperature t1 is")
+disp("Q = -k1*A*(t1-ts)/(%pi*a1*tau)^0.5")
+disp("Heat received by each unit area of contact surface from the body at a temperature t2 is")
+disp("Q = -k2*A*(ts-t2)/(%pi*a2*tau)^0.5")
+disp(" The contact surface will remain at a constant temperature if ")
+disp("-k1*A*(t1-ts)/(%pi*a1*tau)^0.5 = -k2*A*(ts-t2)/(%pi*a2*tau)^0.5")
+disp("-k1*A*(t1-ts)/(tau)^0.5 = -k2*A*(ts-t2)/(tau)^0.5")
+disp("ts(k1*a2^0.5+k2*a1^0.5)= k1*t1*a2^0.5+k2*t2*a1^0.5")
+disp("ts =(k1*t1*a2^0.5+k2*t2*a1^0.5)/(k1*a2^0.5+k2*a1^0.5)")
+disp("dividing numerator and denomenator by (a1*a2)^0.5,")
+disp("ts =(k1*t1/a1^0.5+k2*t2/a2^0.5)/(k1/a1^0.5+k2/a2^0.5)")
diff --git a/965/CH4/EX4.4/4.sci b/965/CH4/EX4.4/4.sci new file mode 100644 index 000000000..1af28d192 --- /dev/null +++ b/965/CH4/EX4.4/4.sci @@ -0,0 +1,17 @@ +clc;
+clear all;
+disp("heat transfer coefficient")
+L=0.04;//m length of plate
+Lc=L/2;// m characteristic length of plate
+k=386;//W/m.C
+rho=9000;// kg/m^3
+C=380;//J/kg.C
+t=165;//degree C
+ta=90;// degree C
+ti=200;// degree C
+tau = 4.5*60;//sec
+disp("Temperature distribution is given by : (t-ta)/(ti-ta) = exp((-h*As*tau)/(rho*V*C))")
+m = (t-ta)/(ti-ta);
+x=(-tau)/(rho*Lc*C);
+h=(log(m))/x;
+disp("W/m^2.C",h,"the heat transfer coefficient is ")
diff --git a/965/CH4/EX4.5/5.sci b/965/CH4/EX4.5/5.sci new file mode 100644 index 000000000..ebaaba41f --- /dev/null +++ b/965/CH4/EX4.5/5.sci @@ -0,0 +1,17 @@ +clc;
+clear all;
+disp("heat transfer coefficient")
+R=12.5/2000;//m radius of sphere
+Lc=R/3;// m characteristic length of sphere
+k=386;//W/m.C
+rho=8850;// kg/m^3
+C=400;//J/kg.C
+t=54;//degree C
+ta=28;// degree C
+ti=65;// degree C
+tau = 1.15*60;//sec
+disp("Temperature distribution is given by : (t-ta)/(ti-ta) = exp((-h*As*tau)/(rho*V*C))")
+m = (t-ta)/(ti-ta);
+x=(-tau)/(rho*Lc*C);
+h=(log(m))/x;
+disp("W/m^2.C",h,"the heat transfer coefficient is ")
diff --git a/965/CH4/EX4.6/6.sci b/965/CH4/EX4.6/6.sci new file mode 100644 index 000000000..6bc58b726 --- /dev/null +++ b/965/CH4/EX4.6/6.sci @@ -0,0 +1,17 @@ +clc;
+clear all;
+disp("Initial cooling rate ")
+R=25/1000;//m radius of steel ball
+rho=7800;//kg/m^3
+c=2;//kJ/kg.K
+ti=900;// degree C
+ta=30;// degree C
+tau=1*60;//seconds
+h=30;// W/m^2.C
+
+//(t-ta)/(ti-ta)=exp(-h*As*tau/(rho*V*cp))
+t=ta+(ti-ta)*exp(-h*3*tau/(rho*R*c*1000));
+disp("degree C", t,"temperature t =")
+R=ti-t;
+disp("C/min",ceil(R),"Rate of cooling =")
+
diff --git a/965/CH4/EX4.7/7.sci b/965/CH4/EX4.7/7.sci new file mode 100644 index 000000000..42f361787 --- /dev/null +++ b/965/CH4/EX4.7/7.sci @@ -0,0 +1,25 @@ +clc;
+clear all;
+disp("Ingot velocity ")
+D=10/100;//m Diameter of cylindrical ingot
+L=30/100;//m
+ti=1250;// degree C
+t=800;// degree C
+ta=90;// degree C
+k=40;// W/m.C
+h=100;// W/m^2.C
+a=1.16*10^(-5);//m^2/s
+Lc=D*L/(4*L+2*D);//m
+Lc
+Bi=h*Lc/k;
+disp(Bi,"Bi =")
+//(t-ta)/(ti-ta)=exp(-a*h*As*tau/(k*V))
+//h*As/rho*V*c =-a*h*As/(k*V)=-a*h*tau/(k*Lc)
+X=-a*h/(k*Lc);
+////(t-ta)/(ti-ta)=exp(X*tau)
+tau=(1/X)*log((t-ta)/(ti-ta));
+disp("S", tau,"time required tau =")
+Lf=6;//m furnace length
+vel=Lf/tau;
+disp("m/s",vel,"velocity of ingot passing through furnace =")
+
diff --git a/965/CH4/EX4.8/8.sci b/965/CH4/EX4.8/8.sci new file mode 100644 index 000000000..569b25de9 --- /dev/null +++ b/965/CH4/EX4.8/8.sci @@ -0,0 +1,29 @@ +clc;
+clear all;
+disp("sphere exposed to airflow ")
+R=15/2000;//m radius of steel sphere
+ti=550;// degree C
+t=90;// degree C
+ta=20;// degree C
+k=42;// W/m.C
+h=120;// W/m^2.C
+a=0.045;//m^2/h
+Lc=R/3;//m
+rho=7850;// kg/m^3
+c=475;// J/kg.C
+As=4*3.1416*R^2;
+V=4*3.1416*(R^3)/3;
+Bi=h*Lc/k;
+disp(Bi,"Bi =")
+//Fo=a*tau/Lc^2;
+//(t-ta)/(ti-ta)=exp(Bi*Fo))
+X=-log((t-ta)/(ti-ta))
+Fo=X/Bi;
+disp(Fo,"Fo =")
+tau=Fo*Lc*Lc/(a/3600);
+disp("s",tau,"time required tau =")
+Fo=7200*0.0333;
+Qi=-h*As*(ti-ta)*(exp(-1*Bi*Fo));
+disp("W",Qi,"Instantaneous heat transfer rate 2 minutes after the start of cooling Qi =")
+Q = rho*V*c*(ti-ta)*((exp(-Bi*Fo))-1);
+disp("W",Q,"Total heat energy transfer from sphere during firsh 2 minutes Q =")
diff --git a/965/CH4/EX4.9/9.sci b/965/CH4/EX4.9/9.sci new file mode 100644 index 000000000..c177318d8 --- /dev/null +++ b/965/CH4/EX4.9/9.sci @@ -0,0 +1,31 @@ +clc;
+clear all;
+disp("time for cooling")
+D=10/1000;//m Diameter of plastic sphere
+ti=75;// degree C
+t=35;// degree C
+ta=23;// degree C
+V=10;// m/s
+//for copper
+kcu=400;// W/m.K
+rhocu=8933;// kg/m^3
+ccu=380;// J/kg.C
+//for air at 23 degree C
+mu=18.16*10^(-6);// N.s/m^2
+v=15.36*10^(-6);//m^2/s
+ka=0.0258;// W/m.K
+Pr=0.709
+mus=19.78*10^(-6);// N.s/m^2 at 35 degree C
+
+Re=V*D/v
+l=Re^0.5;
+m=Re^(2/3);
+n=Pr^0.4;
+p=(mu/mus)^0.25;
+Nu=2+(0.4*l+0.06*m)*n*p
+h=ka*Nu/D;
+X=(t-ta)/(ti-ta);
+Y=-h*6/(rhocu*ccu*D);
+tau=(log (X))/Y;// sec
+disp("s",tau,"time taken to cool tau =")
+
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