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authorpriyanka2015-06-24 15:03:17 +0530
committerpriyanka2015-06-24 15:03:17 +0530
commitb1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch)
treeab291cffc65280e58ac82470ba63fbcca7805165 /1309/CH6
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diff --git a/1309/CH6/EX6.1/Result6_1.pdf b/1309/CH6/EX6.1/Result6_1.pdf
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+clc;
+clear;
+printf("\t\t\tChapter6_example1\n\n\n");
+// Determination of the fluid outlet tetnperature and the tube-wall temperature at the outlet.
+// properties of ethylene glycol at 20 degree celsius from appendix table C5
+Cp_20=2382;
+rou_20=1.116*1000;
+v_20=19.18e-6;
+kf_20=.249;
+a_20=.939e-7;
+Pr_20=204;
+// specifications of 1/2 standard type M seamless copper water tubing from appendix table F2
+OD=1.588/100;
+ID=1.446/100;
+A=1.642e-4;
+Q=3.25e-6;
+V=Q/A;
+printf("\nThe average flow velocity is %.1f m/s",V*100);
+// calculation of Reynold's Number to check flow regime
+Re=V*ID/v_20;
+printf("\nThe Reynolds Number is %.1f",Re);
+// since Re>he 2100, the flow regime is laminar and the hydrodynamic length can be calculated as
+Z_h=0.05*ID*Re;
+printf("\nThe hydrodynamic length is %.1f cm",Z_h*100);
+Tbi=20; // bulk-fluid inlet temperature in degree celsius
+qw=2200; // incident heat flux in W/m^2
+L=3; // Length of copper tube in m
+R=ID/2; // inner radius in m
+Tbo=Tbi+(2*qw*a_20*L)/(V*kf_20*R);
+printf("\nThe bulk-fluid outlet temperature is %.1f degree celsius",Tbo);
+// This result is based on fluid properties evaluated at 20°C. taken as a first approximation
+Z_t=0.05*ID*Re*Pr_20;
+printf("\nThe thermal entry length is %.1f m",Z_t);
+Two=Tbo+(11*qw*ID)/(48*kf_20); // The wall temperature at outlet in degree celsius
+printf("\nThe wall temperature at outlet is %.1f degree celsius",Two);
+//The result is based on first approximation based on flow properties evaluated at the fluid inlet temperature.
diff --git a/1309/CH6/EX6.2/Result6_2.pdf b/1309/CH6/EX6.2/Result6_2.pdf
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+clc;
+clear;
+printf("\t\t\tChapter6_example2\n\n\n");
+// determination of average convection coefficient
+T_avg=(140+70)/2;
+printf("\nThe average bulk temperature is %d degree celsius",T_avg);
+// properties of water at average bulk temperature from appendix table C11
+rou=.994*62.4;
+kf=.363;
+cp=.9980;
+a=5.86e-3;
+v=0.708e-5;
+Pr=4.34;
+// specifications of 1 standard type M copper tube from appendix table F2
+OD=1.125/12; // outer diameter in ft
+ID=0.8792; // inner diameter in ft
+A=0.006071 // cross sectional area in sq.ft
+m_flow=1.5; // mass flow rate in lbm/s
+V=m_flow*3600/(rou*A); // velocity in ft/hr
+printf("\nThe velocity is %d ft/hr",V);
+L=20;
+Tw=240;
+Tbo=140;
+Tbi=70;
+hL=-(rou*V*ID*cp*log((Tw-Tbo)/(Tw-Tbi)))/(4*L);
+printf("\nThe average convective coefficient is %d BTU/(hr. sq.ft.degree Rankine)",hL);
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+clc;
+clear;
+printf("\t\t\tChapter6_example3\n\n\n");
+// Determination of the variation of wall temperature with length up to the point where the flow becomes fully developed.
+// properties of milk
+kf=0.6; // thermal conductivity in W/(m-K)
+cp=3.85*1000; // specific heat in J/(kg*K)
+rou=1030; // density in kg/m^3
+mu=2.12e3; // viscosity in N s/m^2
+// specifications of 1/2 standard type K tubing from appendix table F2
+OD=1.588/100; // outer diameter in m
+ID=1.340/100; // inner diameter in m
+A=1.410e-4 // cross sectional area in m^2
+rou=1030;
+V=0.1;
+mu=2.12e-3
+// determination of flow regime
+Re=rou*V*ID/(mu);
+printf("\nThe Reynolds Number is %d",Re);
+// The flow being laminar, the hydrodynamic entry length is calculated as follows
+ze=0.05*ID*Re;
+printf("\nThe hydrodynamic entry length is %.1f cm",ze*100);
+Tbo=71.7; // final temperature in degree celsius
+Tbi=20; // initial temperature in degree celsius
+L=6; // heating length in m
+qw=rou*V*ID*cp*(Tbo-Tbi)/(4*L);
+printf("\nThe heat flux is %d W/sq.m",qw);
+q=qw*%pi*ID*L;
+printf("\nThe power required is %.1f W",q);
+printf("\nA 3000 W heater would suffice");
+Pr=(cp*mu)/kf; // Prandtl Number
+printf("\nThe Prandtl Number is %.1f",Pr);
+zf=0.05*ID*Re*Pr;
+printf("\nThe length required for flow to be thermally developed is %.1f m",zf);
+// calculations of wall temperature of the tube
+reciprocal_Gz=[0.002 0.004 0.01 0.04 0.05];// values of 1/Gz taken
+[n m]=size(reciprocal_Gz);
+Nu=[12 10 7.5 5.2 4.5]; //Enter the corresponding value of Nusselts Number from figure 6.8
+for i=1:m
+ z(i)=ID*Re*Pr*reciprocal_Gz(i);
+ h(i)=kf*Nu(i)/ID;
+ Tbz(i)=20+(8.617*z(i));
+ Twz(i)=Tbz(i)+(11447/h(i));
+end
+printf("\nSummary of Calculations to Find the Wall Temperature of the Tube");
+printf("\n\t1/Gz\t\tNu\t\tz (m)\t\th W/(sq.m.K)\t\tTbz (degree celsius)\t\tTwz (degree celsius)");
+for i=1:m
+printf("\n\t%.3f\t\t%.1f\t\t%.3f\t\t%d\t\t\t%.1f\t\t\t\t%.1f",reciprocal_Gz(i),Nu(i),z(i),h(i),Tbz(i),Twz(i));
+end
+subplot(211);
+plot(z,Tbz,'r--d',z,Twz,'r-'); // our first figure
+a1 = gca();
+h1=legend(["Tbz";"Twz"]);
+subplot(212)
+plot(z,h, 'o--'); // our second figure
+hl=legend(['h'],2);
+title('Variation of temperature and local convection coefficient with axial distance for the constant- wall-flux tube');
+a2 = gca();
+a2.axes_visible = ["off", "on","on"];
+a2.y_location ="right";
+
+a1.axes_bounds=[0 0 1 1]; // modify the first figure to occupy the whole area
+a2.axes_bounds=[0 0 1 1]; // modify the second figure to occupy the whole area too
+
+a1.data_bounds=[0,0;6,140];
+a2.data_bounds=[0,0;6,700];
+
+a1.x_ticks = tlist(["ticks", "locations", "labels"], (0:6)', ["0";"1";"2";"3";"4";"5";"6"]);
+a1.x_label
+a1.y_label
+x_label=a1.x_label;
+x_label.text=" z,m"
+a2.x_label
+a2.y_label
+y_label=a1.y_label;
+y_label.text="T, degree celsius"
+y_label=a2.y_label;
+y_label.text="h, W/(sq.m.K)"
+xgrid(1);
+a2.filled = "off";
diff --git a/1309/CH6/EX6.4/Figure6_4.jpg b/1309/CH6/EX6.4/Figure6_4.jpg
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diff --git a/1309/CH6/EX6.4/ch6_4.sce b/1309/CH6/EX6.4/ch6_4.sce
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+clc;
+clear;
+printf("\t\t\tChapter6_example4\n\n\n");
+// The average bulk temperature of the Freon-12 is [-4O +(-4)]/2 = -22°F
+// properties of Freon-12 at average bulk temperature
+kf=0.04; // thermal conductivity in BTU/(hr.ft.°R)
+cp=0.2139; // specific heat in BTU/(lbm-°R)
+rou= 1.489*(62.4); // density in lbm/cu.ft
+v=0.272e-5; // viscosity in sq.ft/s
+a=2.04e-3; // diffusivity in sq.ft/hr
+Pr=4.8; // Prandtl Number
+// specifications of 3/8 standard type K copper tubing from appendix table F2
+OD=0.5/12; // outer diameter in ft
+ID=0.03350; // inner diameter in ft
+A=0.0008814 // cross sectional area in sq.ft
+// Laminar conditions are asssumed
+z=5;
+Tw=32;
+Tbo=-4;
+Tbi=-40;
+L=5;
+i=1;
+V_assumed(i)=100; //assumed value for velocity
+for i=1:6
+ inv_Gz(i)=(z*a)/(V_assumed(i)*ID^2);
+ Nu=[4.7 5.8 6.2 6.3 6.4 6.4]; // corresponding Nusselt numbers from fig. 8.8:
+ hL(i)=Nu(i)*kf/ID;
+ V(i)=-(2*a*L*hL(i))/((kf*ID/2)*log((Tw-Tbo)/(Tw-Tbi)));
+ V_assumed(i+1)=V(i);
+end
+printf("\nSummary of Results\n");
+printf("Assmued V (ft/hr)\t1/Gz\tNu(fig 8.8)\thL BTU/(hr. sq.ft. degree R)\tV (ft/hr)\n");
+for j=1:6
+printf("\t%d\t\t%.4f\t%.1f\t\t%.2f\t\t\t\t%d\n",V_assumed(j),inv_Gz(j),Nu(j),hL(j),V(j));
+end
+V_final=V(i-1);
+hL_final=hL(i-1);
+printf("\nThe final velocity is %d ft/hr = %.4f ft/s",V_final,V_final/3600);
+printf("\nThe final convective coefficient is %.2f BTU/(hr. sq.ft. degree R)",hL_final);
+// checking the laminar-flow assumption by calculating the Reynolds number
+Re=(V_final/3600)*ID/v;
+printf("\nThe Reynolds number is %d",Re);
+// The flow is laminar
+m_Fr=rou*A*V_final/3600;
+printf("\nThe mass flow rate of Freon-12 is %.2e lbm/s = %.2f lbm/hr",m_Fr,m_Fr*3600);
+As=%pi*ID*L;
+q=hL_final*As*[(Tw-Tbo)-(Tw-Tbi)]/(log((Tw-Tbo)/(Tw-Tbi)));
+printf("\nThe heat gained by Freon-12 is %.1f BTU/hr",q);
+q_check=m_Fr*cp*(Tbo-Tbi);
+printf("\nOn checking the heat transferred we find almost equal to the heat gained by Freon-12");
+rou_water=1.002*62.4; // density of water in lbm/ft^3 from appendix table C11
+m_water=rou_water*L*(2/12)*(3/12);
+printf("\nThe mass of water in the prescribed volume is %.1f lbm",m_water);
+// to remove 144 BTU/lbm of water, the time required is caalculated as below
+t=144*m_water/q;
+printf("\nThe required time is %.1f hr",t);
+inv_Gz1=[0.001 0.004 0.01 0.015 0.02 0.0271]; // guess values of 1/Gz
+Nu_D=[19.3 12.1 8.9 7.7 7.1 6.4]; //corresponding Nusselt number from fig. 6.8
+[n m]=size(inv_Gz1);
+for j=1:m
+ Z(j)=ID*Re*Pr*(inv_Gz1(j));
+ hz(j)=Nu_D(j)*kf/ID;
+ Tbz(j)=32-72*exp(-0.01812*Z(j)*hz(j));
+end
+printf("\nSummary of Data for Example 6.4 ");
+printf("\n\t1/Gz\tNu_D\tz (ft)\thz, BTU/(hr. sq.ft.degree R)\tTbz,degree F\n");
+for p=1:m
+ printf("\t%.4f\t%.1f\t%.2f\t%.2f\t\t\t\t%.1f\n",inv_Gz1(p),Nu_D(p),Z(p),hz(p),Tbz(p));
+end
+subplot(211);
+plot(Z,Tbz,'r--d',Z,Tw,'r-'); // your first figure
+a1 = gca();
+hl=legend(['Tbz';'Tw'],4);
+subplot(212)
+plot(Z,hz, 'o--'); // your second figure
+a2 = gca();
+hl=legend(['hz'],1);
+a2.axes_visible = ["off", "on","on"];
+a2.y_location ="right";
+
+a1.axes_bounds=[0 0 1 1]; // modify the first figure to occupy the whole area
+a2.axes_bounds=[0 0 1 1]; // modify the second figure to occupy the whole area too
+a2.filled = "off";
+a1.data_bounds=[-2,-40;5,40];
+a2.data_bounds=[-2,0;5,30];
+x_label1=a1.x_label;
+x_label1.text="z, ft";
+y_label2=a2.y_label;
+y_label2.text="hz, BTU/(hr.sq.ft.degree R)";
+y_label=a1.y_label;
+y_label.text="T, degree F";
+newticks1=a1.y_ticks;
+newticks1(2)=[-40;-30;-20;-10;0;10;20;30;40];
+newticks1(3)=['-40';'-30';'-20';'-10';'0';'10';'20';'30';'40'];
+a1.y_ticks=newticks1;
+newticks2=a2.y_ticks;
+newticks2(2)=[0;5;10;20;30];
+newticks2(3)=['0';'5';'10';'20';'30'];
+a2.y_ticks=newticks2;
+newticks=a1.x_ticks;
+newticks(2)=[-2;-1;0;1;2;3;4;5];
+newticks(3)=['-2';'-1';'0';'1';'2';'3';'4';'5'];
+a1.x_ticks=newticks;
+
+title('Graphical summary of the solution to the constant-wall-temperature tube of Example 6.4');
diff --git a/1309/CH6/EX6.5/Result6_5.pdf b/1309/CH6/EX6.5/Result6_5.pdf
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+clc;
+clear;
+printf("\t\t\tChapter6_example5\n\n\n");
+// Determination for the power required for heating and the wall temperature at the outlet.
+// The liquid properties are evaluated at the mean temperature of (80 + 20)/2 = 50°C.
+// specifications of 1 standard type K copper water tubing from appendix table F2
+OD = 2.858/100; // outer diameter in m
+ID = 2.528/100; // inner diameter in m
+A = 5.019e-4; // cross sectional area in sq.m
+// 1 oz = 2.957e-5 m^3
+Q=80*2.957e-5/120; // The volume flow rate of water (at 20°C) in cu.m/s
+printf("\nThe volume flow rate of water (at 20°C) is %.2e cu.m/s",Q);
+p_20= 1.000*1000; // density of water at 20°C in kg/cu.m
+// properties of water at 50°C from appendix table C11
+p_50= 0.990*(1000); // density in kg/m3
+cp= 4181; // specific heat in J/(kg*K)
+v = 0.586e-6; // viscosity in sq.m/s
+kf = 0.640; // thermal conductivity in W/(m.K)
+a = 1.533e-7; // diffusivity in sq.m/s
+Pr = 3.68; // Prandtl number
+mass_flow=p_20*Q; // mass flow rate through the tube in kg/s
+printf("\nmass flow rate through the tube is %.4f kg/s",mass_flow);
+L=3; // length of tube in m
+As=%pi*ID*L;
+Tbo=80; // final temperature in °C
+Tbi=20; // initial temperature in °C
+qw=mass_flow*cp*(Tbo-Tbi)/(As);
+q=qw*As;
+A=%pi*(ID/2)^2;
+printf("\nThe power required in %.3e W/sq.m = %d W",qw,q);
+V=mass_flow/(p_50*A); // average velocity at 50 °C
+printf("\nThe average velocity at 50°C is %.2e m/s",V);
+Re=(V*ID)/v; // Reynold's Number
+printf("\nThe Reynolds Number for the flow is %d",Re);
+// The flow is laminar so we can use Figure 6.12 to obtain the information needed on Nusselt number and to find hz
+inv_Gz=L/(Re*ID*Pr); // The inverse Graetz number at tube end, based on 50°C conditions
+printf("\nThe inverse Graetz number at tube end, based on 50°C conditions is %.4f",inv_Gz);
+Nu=6.9; //value of corresponding Nusselts Number from figure 6.12
+hz=(Nu*kf)/ID;
+printf("\nThe local convection coefficient is %.1f W/(sq.m.K)",hz);
+Two=(qw/hz)+Tbo; // The outlet wall temperature in °C
+printf("\nThe outlet wall temperature is %d °C",Two);
diff --git a/1309/CH6/EX6.6/Result6_6.pdf b/1309/CH6/EX6.6/Result6_6.pdf
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diff --git a/1309/CH6/EX6.6/ch6_6.sce b/1309/CH6/EX6.6/ch6_6.sce
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+clc;
+clear;
+printf("\t\t\tChapter6_example6\n\n\n");
+// determibation of heat gained
+// air properties to be calculated at T=(72+45)/2=58.5 degree Fahrenheit
+// properties at T=58.5 degree fahrenheit from appendix table D1
+p = 0.077; // density in lbm/ft^3
+cp = 0.240; // specific heat in BTU/(lbm.degree Rankine)
+v = 15.28e-5; // viscosity in ft^2/s
+kf = 0.0146; // thermal conductivity in BTU/(hr.ft."R)
+a = 0.776; // diffusivity in ft^2/hr
+Pr = 0.711; // prandtl number
+D=7/12; // diameter in ft
+L=40; // length in ft
+Tbo=72; // outlet temperature in degree Fahrenheit
+Tbi=45; // inlet temperature in degree Fahrenheit
+A=%pi*(D^2)/4; // cross sectional area of duct in ft^2
+// density at outlet temperature in lbm/ft^3
+rou_o=.0748;
+V=10; // average velocity in ft/s
+mass_flow=rou_o*A*V;
+printf("\nThe mass flow rate is %.1f lbm/s",mass_flow);
+// average velocity evaluated by using the average bulk temperature
+V_avg=mass_flow/(p*A);
+printf("\nThe average velocity evaluated by using the average bulk temperature is %.2f ft/s",V_avg);
+Re=(V_avg*D)/v;
+printf("\nThe Reynolds number for the flow is %.3e ",Re);
+// the flow is in turbulent regime
+q=mass_flow*cp*(Tbo-Tbi);
+printf("\nThe heat gained by air is %.3f BTU",q);
+hc=1; // convection coefficient between the outside duct wall and the attic air in BTU/(hr. sq.ft.degree Rankine).
+T_inf=105; // The temperature of attic air surrounding the duct in degree Fahrenheit
+hz=(0.023*Re^(4/5)*Pr^0.4)*kf/D; // The local coefficient at the duct end is %.2f BTU/(hr. sq.ft.degree Rankine)
+printf("\nThe local coefficient at the duct end is %.2f BTU/(hr. sq.ft.degree Rankine)",hz);
+qw=(T_inf-Tbo)/((1/hc)+(1/hz)); // wall flux in BTU/(hr. sq.ft.degree Rankine)
+printf("\nThe wall flux is %.1f BTU/(hr. sq.ft.degree Rankine)",qw);
+Two=qw*(1/hz)+Tbo; // The wall temperature at exit in degree Fahrenheit
+printf("\nThe wall temperature at exit is %.1f degree Fahrenheit",Two);