diff options
Diffstat (limited to '1752/CH4')
| -rwxr-xr-x | 1752/CH4/EX4.1/exa_4_1.sce | 39 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.10/exa_4_10.sce | 45 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.11/exa_4_11.sce | 21 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.12/exa_4_12.sce | 45 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.13/exa_4_13.sce | 60 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.2/exa_4_2.sce | 41 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.3/exa_4_3.sce | 42 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.4/exa_4_4.sce | 23 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.5/exa_4_5.sce | 19 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.6/exa_4_6.sce | 29 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.7/exa_4_7.sce | 29 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.8/exa_4_8.sce | 28 | ||||
| -rwxr-xr-x | 1752/CH4/EX4.9/exa_4_9.sce | 26 |
13 files changed, 447 insertions, 0 deletions
diff --git a/1752/CH4/EX4.1/exa_4_1.sce b/1752/CH4/EX4.1/exa_4_1.sce new file mode 100755 index 000000000..14298e329 --- /dev/null +++ b/1752/CH4/EX4.1/exa_4_1.sce @@ -0,0 +1,39 @@ +//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.")
+
+
+
+
diff --git a/1752/CH4/EX4.10/exa_4_10.sce b/1752/CH4/EX4.10/exa_4_10.sce new file mode 100755 index 000000000..0a9dc1450 --- /dev/null +++ b/1752/CH4/EX4.10/exa_4_10.sce @@ -0,0 +1,45 @@ +//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")
diff --git a/1752/CH4/EX4.11/exa_4_11.sce b/1752/CH4/EX4.11/exa_4_11.sce new file mode 100755 index 000000000..a25e248ea --- /dev/null +++ b/1752/CH4/EX4.11/exa_4_11.sce @@ -0,0 +1,21 @@ +//Exa 4.11
+clc;
+clear;
+close;
+//given data
+k=40;// in W/m degree C
+d =12*10^-3;// in meter
+t=127;// in degree C
+t_i=877;// in degree C
+t_infinite=52;// in degree C
+h= 20;// in W/m^2 degree C
+rho=7800;// in W/m^2K
+C=600;// in J/kg K
+r=d/2;// in meter
+//l_s = V/A = r/3
+l_s = r/3;
+Bi= h*l_s/k;
+// since Bi < 0.1 , hence lumped heat capacity analysis can be applied
+// (t-t_infinite)/(t_i-t_infinite) = %e^(-h*A*toh /(rho*V*C)) = %e^(-h*toh/(rho*l_s*C)) = %e^(-h*toh/(rho*C*l_s))
+toh = -log((t-t_infinite)/(t_i-t_infinite))*rho*C*l_s/h;// in sec
+disp("Time required for cooling process : "+string(toh)+" seconds or "+string(toh/60)+" minutes")
\ No newline at end of file diff --git a/1752/CH4/EX4.12/exa_4_12.sce b/1752/CH4/EX4.12/exa_4_12.sce new file mode 100755 index 000000000..c98316b32 --- /dev/null +++ b/1752/CH4/EX4.12/exa_4_12.sce @@ -0,0 +1,45 @@ +//Exa 4.12
+clc;
+clear;
+close;
+//given data
+D=10*10^-2;// in m
+b=D/2;
+h= 100;// in W/m^2 degree C
+T_o=418;// in degree C
+T_i=30;// in degree C
+T_infinite=1000;// in degree C
+
+disp(" (A) For copper cylinder ");
+k=350;// in W/mK
+alpha=114*10^-7;// in m^2/s
+Bi= h*b/k;
+theta_0_t = (T_o-T_infinite)/(T_i-T_infinite);
+Fo=18.8;
+// Formula Fo= alpha*t/b^2
+t=Fo*b^2/alpha;
+disp("Time required to reach for the cylinder centreline temperature 418 degree C : "+string(t)+" seconds or "+string(t/3600)+" hours")
+
+// (2) Temperature at the radius of 4 cm
+theta_0_t = 0.985;
+// Formula theta_0_t = (T-T_infinite)/(T_o-T_infinite)
+T= theta_0_t*(T_o-T_infinite)+T_infinite;// in degree C
+disp(T,"Temperature at the radius of 4 cm ")
+disp("It has very less temperature gradients over 4 cm radius")
+
+disp(" (B) For asbestos cylinder ");
+k=0.11;// in W/mK
+alpha=0.28*10^-7;// in m^2/s
+Bi= h*b/k;
+theta_0_t = (T_o-T_infinite)/(T_i-T_infinite);
+Fo=0.21;
+// Formula Fo= alpha*t/b^2
+t=Fo*b^2/alpha;
+disp("Time required to reach for the cylinder centreline temperature 418 degree C : "+string(t)+" seconds or "+string(t/3600)+" hours")
+
+// (2) Temperature at the radius of 4 cm
+theta_x_t = 0.286;
+// Formula theta_x_t = (T-T_infinite)/(T_o-T_infinite)
+T= theta_x_t*(T_o-T_infinite)+T_infinite;// in degree C
+disp(T,"Temperature at the radius of 4 cm ")
+disp("It has large temperature gradients")
diff --git a/1752/CH4/EX4.13/exa_4_13.sce b/1752/CH4/EX4.13/exa_4_13.sce new file mode 100755 index 000000000..2b561fc54 --- /dev/null +++ b/1752/CH4/EX4.13/exa_4_13.sce @@ -0,0 +1,60 @@ +//Exa 4.13
+clc;
+clear;
+close;
+//given data
+D=5*10^-2;// in m
+b=D/2;
+h= 500;// in W/m^2 degree C
+k=60;// in W/m^2K
+rho=7850;// in kg/m^3
+C=460;// in J/kg
+alpha=1.6*10^-5;// in m^2/s
+T_i=225;// in degree C
+T_infinite=25;// in degree C
+t=2;// in minute
+
+// Part(i)
+Bi= h*b/k;
+Fo= alpha*t/b^2;
+theta_0_t = 0.18;
+// Formula theta_0_t = (T_o-T_infinite)/(T_i-T_infinite)
+T_o= theta_0_t*(T_i-T_infinite)+T_infinite;// in degree C
+disp(T_o,"Centreline Temperature of the sphere after 2 minutes of exposure in degree C ") ;
+
+// Part(2)
+depth= 10*10^-3;// in meter
+r=b-depth;// in meter
+rBYb=r/b;
+theta_x_t = 0.95;
+// Formula theta_x_t = (T-T_infinite)/(T_o-T_infinite)
+T= theta_x_t*(T_o-T_infinite)+T_infinite;// in degree C
+disp(T,"The Temperature at the depth of 1 cm from the surface after 2 minutes in degree C ") ;
+
+// Part (3)
+BiSquareFo= Bi^2*Fo;
+QbyQo= 0.8;// in kJ
+A=4/3*%pi*b^3;
+Qo= rho*A*C*(T_i-T_infinite);// in J
+Qo=Qo*10^-3;// in kJ
+// The heat transffered during 2 minute,
+Q= Qo*QbyQo;// in kJ
+disp(Q,"The heat transffered during 2 minutes in kJ")
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/1752/CH4/EX4.2/exa_4_2.sce b/1752/CH4/EX4.2/exa_4_2.sce new file mode 100755 index 000000000..094d15c3c --- /dev/null +++ b/1752/CH4/EX4.2/exa_4_2.sce @@ -0,0 +1,41 @@ +//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
diff --git a/1752/CH4/EX4.3/exa_4_3.sce b/1752/CH4/EX4.3/exa_4_3.sce new file mode 100755 index 000000000..705f00c2e --- /dev/null +++ b/1752/CH4/EX4.3/exa_4_3.sce @@ -0,0 +1,42 @@ +//Exa 4.3
+clc;
+clear;
+close;
+//given data
+k=40;// in W/mK
+rho=8200;// in kg/m^3
+C=400;// in J/kgK
+D=6*10^-3;// in m
+R=D/2;
+t_i=30;// in degree C
+t_infinite1=400;// for 10 sec in degree C
+t_infinite2=20;// for 10 sec in degree C
+h=50;// in W/m^2K
+
+// Part(a)
+//l_s= V/A = R/3
+l_s= R/3;// in m
+//toh= rho*V*C/(h*A) = rho*C*l_s/h
+toh= rho*C*l_s/h;// in sec
+disp(toh,"Time constance in sec")
+
+// Part (b)
+Bi= h*l_s/k;
+// since Bi < 0.1 , hence lumped heat capacity analysis is valid. Now , temperature attained by junction in 10 seconds when exposed to hot air at 400 degree C
+toh=10;// in sec
+// (t-t_infinite1)/(t_i-t_infinite1)= %e^(-h*A*toh/(rho*V*C)) = %e^(-h*toh/(rho*l_s*C))
+t= %e^(-h*toh/(rho*l_s*C))*(t_i-t_infinite1)+t_infinite1;// in degree C
+
+disp("The junction is taken out from hot air stream and placed in stream of still air 20 degree C. The initial temperature in this case will be "+string(t)+" .")
+t_i=t;
+toh=20;// in sec
+t= %e^(-h*toh/(rho*l_s*C))*(t_i-t_infinite2)+t_infinite2;// in degree C
+disp(t,"The temperature attained by junction in degree C");
+
+// Note: In the last, calculation to find the value of t is wrong so Answer in the book is wrong
+
+
+
+
+
+
diff --git a/1752/CH4/EX4.4/exa_4_4.sce b/1752/CH4/EX4.4/exa_4_4.sce new file mode 100755 index 000000000..2a921d740 --- /dev/null +++ b/1752/CH4/EX4.4/exa_4_4.sce @@ -0,0 +1,23 @@ +//Exa 4.4
+clc;
+clear;
+close;
+//given data
+k=8;// in W/mK
+alpha=4*10^-6;// in m^2/s
+h=50;// in W/m^2K
+D=6*10^-3;// in m
+R=D/2;
+T=0.5;// where T = (t-t_infinite)/(t_i-t_infinite)
+//l_s= V/A = R/3
+l_s= R/2;// in m
+Bi= h*l_s/k;
+// since Bi < 0.1 , hence lumped heat capacity analysis can be applied
+// toh= rho*V*C/(h*A) = rho*C*l_s/h = k*l_s/(h*alpha)
+toh= k*l_s/(h*alpha);// in seconds
+disp(toh,"time constant in seconds");
+// It is given that (t-t_infinite)/(t_i-t_infinite) = 0.5 = %e^(-h*A*c /(rho*V*C)) = %e^(-h*c/(rho*l_s*C)) = %e^(-h*alpha*c/(l_s))
+// or (t-t_infinite)/(t_i-t_infinite) = %e^(-h*alpha*c/(l_s);
+c= -log(T)*l_s/(h*alpha);// in sec
+disp(c,"The time required to temperature change to reach half of its initial value in seconds");
+
diff --git a/1752/CH4/EX4.5/exa_4_5.sce b/1752/CH4/EX4.5/exa_4_5.sce new file mode 100755 index 000000000..b8f768bbb --- /dev/null +++ b/1752/CH4/EX4.5/exa_4_5.sce @@ -0,0 +1,19 @@ +//Exa 4.5
+clc;
+clear;
+close;
+//given data
+//t=450-500*x+100*x^2+150*x^3 at any instant, so
+// dtBYdx= -500+200*x+450*x^2
+
+L=0.5;// thickness of the wall in meter
+k=10;// in W/mK
+// Rate of heating entering in the wall per unit area, at
+x=0;
+//q1= -k*dtBYdx
+q1= -k*(-500+200*x+450*x^2);// in W/m^2
+// Rate of heat going out of the wall per unit area , at
+x=L;
+q2= -k*(-500+200*x+450*x^2);// in W/m^2
+E=q1-q2;// in W/m^2
+disp(E,"Heat energy stored per unit area in W/m^2")
diff --git a/1752/CH4/EX4.6/exa_4_6.sce b/1752/CH4/EX4.6/exa_4_6.sce new file mode 100755 index 000000000..aabca8fc0 --- /dev/null +++ b/1752/CH4/EX4.6/exa_4_6.sce @@ -0,0 +1,29 @@ +//Exa 4.6
+clc;
+clear;
+close;
+//given data
+k=385;// in W/mK
+h=100;// in W/m^2K
+delta =2*10^-3;// thickness of plate in meter
+A=25*25;// area of plate in square meter
+rho=8800;// kg/m^3
+C=400;// J/kg-K
+// l_s= V/A= L*B*delta/(2*L*B) = delta/2
+l_s= delta/2;// in meter
+Bi= h*l_s/k;
+// since Bi < 0.1 , hence lumped heat capacity analysis can be applied
+
+// Part(i)
+// toh= rho*V*C/(h*A) = rho*C*l_s/h
+toh= rho*C*l_s/h;// in second
+disp(toh,"Time constant in seconds");
+
+// Part(ii)
+t_i=400;// in degree C
+t=40;// in degree C
+t_infinite=25;// in degree C
+// (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*C*l_s/h;// in sec
+disp(toh,"The time required for the plate to reach the temperature of 40 degree C in seconds");
+
diff --git a/1752/CH4/EX4.7/exa_4_7.sce b/1752/CH4/EX4.7/exa_4_7.sce new file mode 100755 index 000000000..b60250c65 --- /dev/null +++ b/1752/CH4/EX4.7/exa_4_7.sce @@ -0,0 +1,29 @@ +//Exa 4.7
+clc;
+clear;
+close;
+//given data
+k=380;// in W/mK
+delta =6*10^-2;// thickness of plate in meter
+rho=8800;// kg/m^3
+C=400;// J/kg-K
+// l_s= V/A = delta/2
+l_s= delta/2;// in meter
+t=80;// in degree C
+t_i=200;// in degree C
+t_inf=30;// in degree C
+hw= 75;// in W/m^2K
+ha= 10;// in W/m^2K
+
+// Part(i)
+// ha*A*(t-t_inf_a)+ hw*A*(t-t_inf_w) = -rho*V*C*dtBYdtho, since t_ini_a = t_inf_w = t_inf = 30 degree C
+// (ha+hw)*A*(t-t_inf)= -rho*V*C*dtBYdtho
+// (ha+hw)/(rho*C*V)*A*dtoh = -dt/(t-t_inf)
+// integrate('(ha+hw)/(rho*V*C)*A','toh',0,toh) = integrate('1/(t-t_inf)','t',t_i,t)
+toh= -rho*l_s*C/(ha+hw)*log((t-t_inf)/(t_i-t_inf));
+disp("Time required to cool plate to 80 degree C is : "+string(toh)+" seconds = "+string(toh/60)+" minutes");
+
+// Part (ii)
+t= -rho*l_s*C/(2*ha)*log((t-t_inf)/(t_i-t_inf));
+disp("Time required to cool plate in only air is : "+string(t)+" seconds = "+string(t/60)+" minutes");
+
diff --git a/1752/CH4/EX4.8/exa_4_8.sce b/1752/CH4/EX4.8/exa_4_8.sce new file mode 100755 index 000000000..039f0899a --- /dev/null +++ b/1752/CH4/EX4.8/exa_4_8.sce @@ -0,0 +1,28 @@ +//Exa 4.8
+clc;
+clear;
+close;
+//given data
+k=45;// in W/m degree C
+d =0.1;// in meter
+l =0.30;// in meter
+t=800;// in degree C
+t_i=100;// in degree C
+t_infinite=1200;// in degree C
+h= 120;// in W/m^2 degree C
+alpha=1.2*10^-5;// in meter
+rhoC= k/alpha;
+V=%pi/4*d^2*l;// in m^3
+A= %pi*d*l + 2*%pi/4*d^2;// in m^2
+// l_s= V/A = (%pi/4*d^2*l)/(%pi*d*l + 2*%pi/4*d^2) = d*l/(4*l+2*d^2)
+l_s = d*l/(4*l+2*d^2);
+Bi= h*l_s/k;
+// since Bi < 0.1 , hence lumped heat capacity analysis can be applied
+// (t-t_infinite)/(t_i-t_infinite) = %e^(-h*A*toh /(rho*V*C)) = %e^(-h*toh/(rho*l_s*C)) = %e^(-h*toh/(rhoC*l_s))
+toh = -log((t-t_infinite)/(t_i-t_infinite))*rhoC*l_s/h;// in sec
+
+// So, the velocity of ingot passing through the furnace
+FurnaceLength = 8*100;// in cm
+time = toh;
+Velocity = FurnaceLength/time;// in cm/sec
+disp(Velocity,"Maximum speed in cm/sec")
diff --git a/1752/CH4/EX4.9/exa_4_9.sce b/1752/CH4/EX4.9/exa_4_9.sce new file mode 100755 index 000000000..516bbffcc --- /dev/null +++ b/1752/CH4/EX4.9/exa_4_9.sce @@ -0,0 +1,26 @@ +//Exa 4.9
+clc;
+clear;
+close;
+//given data
+rho=8500;// in kg/m^3
+C=400;// J/kgK
+toh=1;// in sec
+h= 400;// in W/m^2 degree C
+t=198;// in degree C
+t_i=25;// in degree C
+t_infinite=200;// in degree C
+
+// Part (1)
+// toh =rho*V*C/(h*A) = rho*C*l_s/h
+l_s= toh*h/(rho*C);
+// l_s = V/A = r/3
+r=3*l_s;// in m
+r=r*10^3;// in mm
+d=2*r;// in m
+disp(d,"Junction diameter needed for the thermocouple in mili miter");
+
+// Part(ii)
+// toh= -rho*V*C/(h*A)*log((t-t_infinite)/(t_i-t_infinite))
+toh = -toh*log((t-t_infinite)/(t_i-t_infinite));
+disp(toh,"Time required for the thermocouple junction to reach 198 degree C in seconds");
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