From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001 From: priyanka Date: Wed, 24 Jun 2015 15:03:17 +0530 Subject: initial commit / add all books --- 1752/CH4/EX4.1/exa_4_1.sce | 39 ++++++++++++++++++++++++++++ 1752/CH4/EX4.10/exa_4_10.sce | 45 +++++++++++++++++++++++++++++++++ 1752/CH4/EX4.11/exa_4_11.sce | 21 ++++++++++++++++ 1752/CH4/EX4.12/exa_4_12.sce | 45 +++++++++++++++++++++++++++++++++ 1752/CH4/EX4.13/exa_4_13.sce | 60 ++++++++++++++++++++++++++++++++++++++++++++ 1752/CH4/EX4.2/exa_4_2.sce | 41 ++++++++++++++++++++++++++++++ 1752/CH4/EX4.3/exa_4_3.sce | 42 +++++++++++++++++++++++++++++++ 1752/CH4/EX4.4/exa_4_4.sce | 23 +++++++++++++++++ 1752/CH4/EX4.5/exa_4_5.sce | 19 ++++++++++++++ 1752/CH4/EX4.6/exa_4_6.sce | 29 +++++++++++++++++++++ 1752/CH4/EX4.7/exa_4_7.sce | 29 +++++++++++++++++++++ 1752/CH4/EX4.8/exa_4_8.sce | 28 +++++++++++++++++++++ 1752/CH4/EX4.9/exa_4_9.sce | 26 +++++++++++++++++++ 13 files changed, 447 insertions(+) create mode 100755 1752/CH4/EX4.1/exa_4_1.sce create mode 100755 1752/CH4/EX4.10/exa_4_10.sce create mode 100755 1752/CH4/EX4.11/exa_4_11.sce create mode 100755 1752/CH4/EX4.12/exa_4_12.sce create mode 100755 1752/CH4/EX4.13/exa_4_13.sce create mode 100755 1752/CH4/EX4.2/exa_4_2.sce create mode 100755 1752/CH4/EX4.3/exa_4_3.sce create mode 100755 1752/CH4/EX4.4/exa_4_4.sce create mode 100755 1752/CH4/EX4.5/exa_4_5.sce create mode 100755 1752/CH4/EX4.6/exa_4_6.sce create mode 100755 1752/CH4/EX4.7/exa_4_7.sce create mode 100755 1752/CH4/EX4.8/exa_4_8.sce create mode 100755 1752/CH4/EX4.9/exa_4_9.sce (limited to '1752/CH4') 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"); -- cgit