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authorpriyanka2015-06-24 15:03:17 +0530
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treeab291cffc65280e58ac82470ba63fbcca7805165 /1309/CH7
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+clc;
+clear;
+printf("\t\t\tChapter7_example1\n\n\n");
+printf("\t\t\tSolution to part (a)\n");
+// determination of boundary layer growth with length
+// properties of air at 27 degree celsius from appendix table D.1
+rou=1.177; // density in kg/cu.m
+v=15.68e-6; // viscosity in sq.m/s
+L=0.5; // length in m
+V_inf=1; // air velocity in m/s
+Re= (V_inf*L)/v; // Reynolds Number
+printf("The Reynolds Number is %.2e ",Re);
+// Reynolds Number is less than 5e5 hence the flow is laminar and Blasius Solution applies
+x=[0 0.125 0.25 0.375 0.5]; // distances in m where boundary layer growth is determined
+[n,m]=size(x);
+for i=1:m
+ delta(i)=5*x(i)^0.5/(V_inf/v)^0.5;
+end
+subplot(211);
+plot(x,delta);
+a=gca();
+newTicks=a.x_ticks;
+newTicks(2)=[0;0.125;0.25;0.375;0.5];
+newTicks(3)=['0';'0.125';'0.25';'0.375';'0.50'];
+a.x_ticks=newTicks;
+title('Boundary-layer growth with distance');
+xlabel('x, m');
+ylabel('delta, m^(1/2)');
+printf("\n\t\t\tSolution to part (b)\n");
+// produce graph of velocity distribution at x=0.25 m
+eta=0:5;
+[p,q]=size(eta);
+f=[0 0.32979 0.62977 0.84605 0.95552 0.99155];//value for f for corresponding eta value from Table 7.1
+for j=1:q
+ y(j)=eta(j)*(v*0.25)^0.5;
+end
+printf("\n\t\t\tResults of Calculations for Example 7.1\n");
+printf("\teta\t\ty,m\t\t\tf=vx, m/s\n");
+for i=1:q
+printf("\t%d\t\t%.2e\t\t%.5f\n",eta(i),y(i),f(i));
+end
+subplot(212);
+plot(f,y);
+b=gca();
+newTicks1=b.x_ticks;
+newTicks1(2)=[0;0.25;0.5;0.75;1.0];
+newTicks1(3)=['0';'0.25';'0.5';'0.75';'1.0'];
+b.x_ticks=newTicks1;
+newTicks2=b.y_ticks;
+newTicks2(2)=[0;0.0025;0.005;0.0075;0.010];
+newTicks2(3)=['0';'0.0025';'0.005';'0.0075';'0.010'];
+b.y_ticks=newTicks2;
+title('Velocity Distribution at x=0.25 m');
+xlabel('Vx, m/s');
+ylabel('y, m');
+printf("\t\t\tSolution to part (c)\n");
+// calculation of absolute viscosity
+gc=1;
+mu=rou*v/gc;
+printf("\nThe absolute viscosity is %.3e N.s/sq.m",mu);
+b=1; // width in m
+Df=0.664*V_inf*mu*b*(Re)^0.5;
+printf("\nThe skin-drag is %.2e N",Df);
+printf("\nThe skin-drag including both sides of plate is %.2e N",2*Df);
diff --git a/1309/CH7/EX7.10/Result7_10.pdf b/1309/CH7/EX7.10/Result7_10.pdf
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+clc;
+clear;
+printf("\t\t\tChapter7_example10\n\n\n");
+// Calculation of the pressure drop for the air passing over the tubes and the heat transferred to the air.
+// properties of air at 70 + 460 = 530 degree R = 540 degree R from appendix table D1
+rou= 0.0735; // density in Ibm/cu.ft
+cp=0.240; // specific heat BTU/(lbm-degree Rankine)
+v= 16.88e-5; // viscosity in sq.ft/s
+kf = 0.01516 ; // thermal conductivity in BTU/(hr.ft.degree Rankine)
+a = 0.859; // diffusivity in sq.ft/hr
+Pr = 0.708; // Prandtl Number
+// specifications of 3/4 standard type K copper tubing from appendix table F2
+OD=0.875/12; // outer diameter in ft
+ID=0.06208; // inner diameter in ft
+A=0.003027; // cross sectional area in sq.ft
+L=2;
+sL=1.5/12;
+sT=1.3/12;
+V_inf=12; // velocity of air in ft/s
+V1=(sT*V_inf)/(sT-OD); // velocity at area A1 in ft/s
+printf("\nVelocity at area A1 is %.1f ft/s",V1);
+sD=((sL)^2+(sT/2)^2)^0.5; // diagonal pitch in inch
+printf("\nThe diagonal pitch is %.2f in",sD*12);
+V2=(sT*V_inf)/(2*(sD-OD));
+printf("\nVelocity at area A2 is %.1f ft/s",V2);
+if V1>V2 then
+ Vmax=V1;
+ else Vmax=V2;
+end
+Re_D=Vmax*OD/v; // Reynolds Number
+printf("\nThe Reynolds number is %.2e ",Re_D);
+sT_OD=1.3/0.875;
+sT_sL=1.3/1.5;
+printf("\nThe values of parameters are sT/Do=%.2f and sT/sL=%.2f",sT_OD,sT_sL);
+f1=0.35; //value of f1 for above values of sT/Do and Re
+f2=1.05; //Corresponding value of f2 for above values of sT/sL and Re
+gc=32.2;
+N=7;
+dP=N*f1*f2*(rou*Vmax^2/(2*gc));
+printf("\nThe pressure drop is %.2f lbf/ft^2 = %.4f psi",dP, dP/147);
+sL_Do=sL/OD;
+C1=0.438; //value of C1 for above values of sT/Do and sL/Do
+C2=0.97; //value of C2 for above values of sT/Do and sL/Do
+m=0.565; //value of m for above values of sT/Do and sL/Do
+hc=kf*1.13*C1*C2*(Re_D)^m*(Pr)^(1/3)/OD; // The convection coefficient
+printf("\nThe convection coefficient is %.1f BTU/(hr.sq.ft.degree Rankine)",hc);
+As=70*%pi*OD*L; // outside surface area of 70 tubes
+printf("\nThe outside surface area of 70 tubes is %.1f sq.ft",As);
+Tw=200; // outside surface temeperature in degree F
+T_inf=70; // air temperature in degree F
+q=hc*As*(Tw-T_inf);// heat transferred
+printf("\nThe heat transferred is %.2e BTU/hr",q);
diff --git a/1309/CH7/EX7.2/Figure7_2.jpeg b/1309/CH7/EX7.2/Figure7_2.jpeg
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+clc;
+clear;
+printf("\t\t\tChapter7_example2\n\n\n");
+// determination of temperature profile
+// properties of water at (40 + 100)/2 = 70°F = 68°F from appendix table C11
+rou= 62.4; // density in Ibm/ft^3
+cp=0.9988; // specific heat BTU/(lbm-degree Rankine)
+v= 1.083e-5; // viscosity in sq.ft/s
+kf = 0.345 ; // thermal conductivity in BTU/(hr.ft.degree Rankine)
+a = 5.54e-3; // diffusivity in sq.ft/hr
+Pr = 7.02; // Prandtl Number
+V=1.2; // velocity in ft/s
+x=[1 2]; // distances from plate entry in ft
+for i=1:2
+Re(i)=(V*x(i))/v; // Reynolds Number at x=1 ft
+printf("\nThe Reynolds Number at x=%d ft is %.3e",i,Re(i));
+// since Reynolds Number is less than 5*10^5, the flow is laminar
+hL(i)=0.664*Pr^(1/3)*Re(i)^0.5*kf/x(i);
+printf("\nThe average convection coefficient at x=%d is %.1f BTU/(hr. sq.ft. degree Rankine)",i,hL(i));
+Tw=100; // temperature of metal plate in degree fahrenheit
+T_inf=40; // temperature of water in degree fahrenheit
+A(i)=x(i)*18/12; // cross sectional area for 1 ft length
+q(i)=hL(i)*A(i)*(Tw-T_inf);
+printf("\nThe heat transferred to water over the x=%d ft is %.3e BTU/hr",i,q(i));
+end
+eta=0:0.2:1.2;
+[n m]=size(eta);
+theta=[1 .75 .51 .31 .17 .08 0.01]; // values of dimensionless temperature from figure 7.7 corresponding to eta value taken
+for i=1:m
+y(i)=eta(i)*(v*x(1)/V(1))^0.5;
+T(i)=theta(i)*(Tw-T_inf)+T_inf;
+end
+printf("\nSolution Chart for example 7.2\n");
+printf("\teta\t\ttheta\t\ty, ft\t\t\tT, degree F\n");
+for i=1:m
+printf("\t%.1f\t\t%.2f\t\t%.1e\t\t\t%.1f\n",eta(i),theta(i),y(i),T(i));
+end
+plot(T,y);
+a=gca();
+newTicks=a.x_ticks;
+newTicks(2)=[100; 90; 80; 70; 60;50; 40];
+newTicks(3)=['100'; '90'; '80'; '70'; '60';'50'; '40'];
+a.x_ticks=newTicks;
+newTicks1=a.y_ticks;
+newTicks1(2)=[0; 0.001; 0.002; 0.003; 0.004];
+newTicks1(3)=['0'; '0.001'; '0.002'; '0.003'; '0.004'];
+a.y_ticks=newTicks1;
+a.axes_reverse=["on","off"];
+xgrid(1);
+title('Temperature variation (at x = 1 ft) within the boundary layer for the water');
+xlabel('T, degree Fahrenheit');
+ylabel('y, ft');
diff --git a/1309/CH7/EX7.3/Result7_3.pdf b/1309/CH7/EX7.3/Result7_3.pdf
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+clc;
+clear;
+printf("\t\t\tChapter7_example3\n\n\n");
+// Determination of the average convection coefficient and the total drag force exerted on the plate.
+// properties of air at (300 + 400)/2 = 350 K from appendix table D1
+rou= 0.998; // density in kg/cu.m
+cp= 1009; // specific heat in J/(kg*K)
+v= 20.76e-6; // viscosity in sq.m/s
+Pr = 0.697; // Prandtl Number
+k= 0.03003; // thermal conductivity in W/(m.K)
+a = 0.2983e-4; // diffusivity in sq.m/s
+L=1; // Length of plate in m
+V=5; // velocity of air in m/s
+b=0.5; // width in m
+Re=V*L/v; // Reynolds number at plate end
+printf("\nThe Reynolds number is %.2e",Re);
+// Since the flow is laminar at plate end, The average convection coefficient is calculated with Equation Nu=h*L/k= 0.664 Re^(1/2)Pr^(1/3)
+h=k*0.664*Re^(1/2)*Pr^(1/3)/L; // The average convection coefficient in W/(sq.m.K)
+printf("\nThe average convection coefficient is %.2f W/(sq.m.K)",h);
+Df=0.664*V*rou*v*b*(Re)^0.5; // drag force in N
+printf("\nThe drag force is %.2e N",Df);
+hx=(1/2)*h; // local convective coefficient
+printf("\nThe local convective coefficient is %.2f W/(sq.m.K)",hx);
+delta=5*L/(Re)^0.5; // The boundary-layer thickness at plate end
+printf("\nThe boundary-layer thickness at plate end is %.2f cm",delta*100);
+delta_t=delta/(Pr)^(1/3);
+printf("\nThe thermal-boundary-layer thickness is %.2f cm",delta_t*100);
diff --git a/1309/CH7/EX7.4/Result7_4.pdf b/1309/CH7/EX7.4/Result7_4.pdf
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+clc;
+clear;
+printf("\t\t\tChapter7_example4\n\n\n");
+// Determination of the maximum heater-surface temperature for given conditions
+// fluid properties at (300 degree R + 800 degree R)/2 = 550 degree R=540degree R from Appendix Table D.6
+rou= 0.0812; // density in Ibm/ft^3
+cp=0.2918; // specific heat BTU/(lbm-degree Rankine)
+v= 17.07e-5; // viscosity in ft^2/s
+kf = 0.01546 ; // thermal conductivity in BTU/(hr.ft.degree Rankine)
+a = 0.8862; // diffusivity in ft^2/hr
+Pr = 0.709; // Prandtl Number
+qw=10/(1.5*10.125)*(1/.2918)*144; // The wall flux
+printf("\nThe wall flux is %d BTU/(hr. sq.ft)",qw);
+V_inf=20; // velocity in ft/s
+L=1.5/12; // length in ft
+Re_L=V_inf*10*L/v; // Reynolds number at plate end
+printf("\nThe Reynolds number at plate end is %.2e",Re_L);
+// So the flow is laminar and we can find the wall temperature at plate end as follows
+T_inf=300; // free stream temperature in degree Rankine
+Tw=T_inf+(qw*L*10/(kf*0.453*(Re_L)^0.5*(Pr)^(1/3)));
+printf("\nThe maximum heater surface temperature is %d degree Rankine",Tw);
diff --git a/1309/CH7/EX7.5/Result7_5.pdf b/1309/CH7/EX7.5/Result7_5.pdf
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+clc;
+clear;
+printf("\t\t\tChapter7_example5\n\n\n");
+// validation of the equation st.(Pr)^(2/3)=Cd/2 where St: Stanton Number Pr:Prandtl Number Cd: Drag Coefficient
+// values of parameters from example 7.4
+rou= 0.0812; // density in Ibm/ft^3
+cp=0.2918; // specific heat BTU/(lbm-degree Rankine)
+v= 17.07e-5; // viscosity in ft^2/s
+kf = 0.01546 ; // thermal conductivity in BTU/(hr.ft.degree Rankine)
+a = 0.8862; // diffusivity in ft^2/hr
+Pr = 0.709; // Prandtl Number
+Tw=469; // maximum heater temperature in degree Rankine
+T_inf=300; // free-stream temperature in degree Rankine
+qw=324; // The wall flux in BTU/(hr.ft^2)
+V_inf=20; // velocity in ft/s
+hx=qw/(Tw-T_inf); // The convection coefficient
+printf("\nThe convection coefficient is %.2f BTU/(hr.sq.ft.degree R)",hx);
+LHS=(hx/3600)*(Pr)^(2/3)/(rou*cp*V_inf);
+printf("\nThe value of left hand side of the equation is %.2e",LHS);
+Re_L=1.46e+005; // Reynolds number at plate end
+RHS=0.332*(Re_L)^(-0.5);
+printf("\nThe value of left hand side of the equation is %.2e",RHS);
+err=(LHS-RHS)*100/LHS;
+printf("\nThe error is %d percent",err);
+printf("\nSince the error is only %d percent, the agreement is quite good",err);
diff --git a/1309/CH7/EX7.6/Result7_6.pdf b/1309/CH7/EX7.6/Result7_6.pdf
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+clc;
+clear;
+printf("\t\t\tChapter7_example6\n\n\n");
+// Estimation of the drag due to skin friction
+// properties of water at 68°F from Appendix Table C.11
+rou= 62.4; // density in Ibm/cu.ft
+v= 1.083e-5; // viscosity in sq.ft/s
+V_inf=5*.5144/.3048; // barge velocity in ft/s using conversion factors from appendix table A1
+printf("\nThe barge velocity is %.2f ft/s",V_inf);
+L=20; // Length of barge in ft
+Re_L=V_inf*L/v; // Reynolds number at plate end
+printf("\nThe Reynolds number at plate end is %.2e",Re_L);
+Cd=0.003; //value of Cd corresponding to the Reynolds number from figure 7.11
+gc=32.2;
+b=12; // width in ft
+Df=(Cd*rou*V_inf^2*b*L)/(2*gc);
+printf("\nThe drag force is %d lbf",Df);
diff --git a/1309/CH7/EX7.7/Result7_7.pdf b/1309/CH7/EX7.7/Result7_7.pdf
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+clc;
+clear;
+printf("\t\t\tChapter7_example7\n\n\n");
+// Determination of wattage requirement
+// properties of carbon dioxide at a film temperature of (400+600)/2 = 500 K from appendix table D2
+rou= 1.0732; // density in kg/m^3
+cp= 1013; // specific heat in J/(kg*K)
+v= 21.67e-6; // viscosity in m^2/s
+Pr = 0.702; // Prandtl Number
+k= 0.03352; // thermal conductivity in W/(m.K)
+a = 0.3084e-4; // diffusivity in m^2/s
+V_inf=60; // carbon dioxide velocity in m/s
+x_cr=(5e5)*v/V_inf; // The transition length in m
+printf("\nThe transition length is %.1f cm",x_cr*100);
+w=4; // width of each heater in cm
+b=.16; // effective heating length in m
+Tw=600; // temperature of heater surface in K
+T_inf=400; // temperature of carbon dioxide in K
+r=pmodulo(x_cr*100,w);
+n=(x_cr*100+r)/w; // number of heater where transition occurs
+printf("\nThe transition thus occur at %dth heater",n);
+m=6; // number of heater strips
+q=zeros(m+1,1);
+x=[0.04 0.08 0.12 0.16 0.20 0.24];
+for i=1:n-1 // transition occurs at 5th heater, so laminar zone equation is followed till then
+ h(i)=(0.664*k)*(V_inf/v)^0.5*(Pr)^(1/3)/x(i)^0.5;
+ printf("\n\nThe convective coefficient for heater no. %d is %d W/(sq.m.K)",i,h(i));
+ q(i+1)=h(i)*x(i)*b*(Tw-T_inf);
+ dq(i)=q(i+1)-q(i);
+ printf("\nThe heat transferred by heater no. %d is %d W",i,dq(i));
+end
+// Turbulent zone exists from 5th heater onwards so the following equation is followed Nu=h*x/kf=[0.0359*(Re_L)^(4/5)-830]*(Pr)^(1/3)
+for i=5:6
+ Re_L(i)=V_inf*x(i)/v;
+ h(i)=(k/x(i))*[0.0359*(Re_L(i))^(4/5)-830]*(Pr)^(1/3)
+ printf("\n\nThe Reynolds number for heater no. %d is %.2e",i,Re_L(i));
+ printf("\nThe convective coefficient for heater no. %d is %.1f W/(sq.m.K)",i,h(i));
+ q(i+1)=h(i)*x(i)*b*(Tw-T_inf);
+ dq(i)=q(i+1)-q(i);
+ printf("\nThe heat transferred by heater no. %d is %d W",i,dq(i));
+end
+
diff --git a/1309/CH7/EX7.8/Result7_8.pdf b/1309/CH7/EX7.8/Result7_8.pdf
new file mode 100755
index 000000000..ce33b8313
--- /dev/null
+++ b/1309/CH7/EX7.8/Result7_8.pdf
Binary files differ
diff --git a/1309/CH7/EX7.8/ch7_8.sce b/1309/CH7/EX7.8/ch7_8.sce
new file mode 100755
index 000000000..ca71853dd
--- /dev/null
+++ b/1309/CH7/EX7.8/ch7_8.sce
@@ -0,0 +1,30 @@
+clc;
+clear;
+printf("\t\t\tChapter7_example8\n\n\n");
+// Estimation of force exerted on the pole
+// properties of air at given conditions from appendix table D1
+rou= 0.0735; // density in Ibm/ft^3
+v= 16.88e-5; // viscosity in ft^2/s
+V=20*5280/3600; // flow velocity in ft/s
+printf("\nThe flow velocity is %.1f ft/s",V);
+D=12/12; // diameter of pole in ft
+L=30;// length of pole in ft
+gc=32.2;
+Re_D=V*D/v; // Reynolds Number for flow past the pole
+printf("\nThe Reynolds Number for flow past the pole is %.2e ",Re_D);
+Cd_cylinder=1.1; // value of Cd for smooth cylinder from figure 7.22
+A_cylinder=D*L; // frontal area of pole
+printf("\nThe frontal area of pole is %d sq.ft",A_cylinder);
+Df_cylinder=Cd_cylinder*(1/2)*rou*V^2*A_cylinder/gc;
+printf("\nThe Drag force exerted on only the pole is %.1f lbf",Df_cylinder);
+D_square=2/12; // length of square part of pole
+L_square=4;
+Re_square=V*D_square/v; // Reynolds Number for square part of pole
+printf("\nThe Reynolds Number for square part of pole is %.1e",Re_square);
+Cd_square=2; // Corresponding value of Cd for square part from figure 7.23
+A_square=D_square*L_square; // projected frontal area of square part
+printf("\nThe frontal area of square part of pole is %.3f sq.ft",A_square);
+Df_square=Cd_square*(1/2)*rou*V^2*A_square/gc;
+printf("\nThe Drag force exerted on cross piece of the pole is %.2f lbf",Df_square);
+Df_total=Df_cylinder+Df_square;
+printf("\nThe total drag force on the pole is %.1f lbf",Df_total);
diff --git a/1309/CH7/EX7.9/Result7_9.pdf b/1309/CH7/EX7.9/Result7_9.pdf
new file mode 100755
index 000000000..05273af03
--- /dev/null
+++ b/1309/CH7/EX7.9/Result7_9.pdf
Binary files differ
diff --git a/1309/CH7/EX7.9/ch7_9.sce b/1309/CH7/EX7.9/ch7_9.sce
new file mode 100755
index 000000000..0c440c728
--- /dev/null
+++ b/1309/CH7/EX7.9/ch7_9.sce
@@ -0,0 +1,30 @@
+clc;
+clear;
+printf("\t\t\tChapter7_example9\n\n\n");
+// determination of required current
+// properties of air at film temperature (300 + 500)/2 = 400 K from appendix table D1
+rou= 0.883; // density in kg/cu.m
+cp= 1014; // specific heat in J/(kg*K)
+v= 25.90e-6; // viscosity in sq.m/s
+Pr = 0.689; // Prandtl Number
+kf= 0.03365; // thermal conductivity in W/(m.K)
+a = 0.376e-4; // diffusivity in sq.m/s
+V_inf=1; // velocity in m/s
+D=0.00013; // diameter in m
+L=1/100; // length of wire in cm
+Re_D=V_inf*D/v; // The Reynolds number of flow past the wire
+printf("\nThe Reynolds number of flow past the wire is %.3f",Re_D);
+C=0.911; //value of C for cylinder from table 7.4
+m=0.385; //value of m for cylinder from table 7.4
+hc=kf*C*(Re_D)^m*(Pr)^(1/3)/D; // the convection coefficient in W/(m^2.K)
+printf("\nThe convection coefficient is %d W/(sq.m.K)",hc);
+Tw=500; // air stream temperature in K
+T_inf=300; // wire surface temperature in K
+As=%pi*D*L; // cross sectional area in sq.m
+qw=hc*As*(Tw-T_inf); // The heat transferred to the air from the wire
+printf("\nThe heat transferred to the air from the wire is %.3f W",qw);
+resistivity=17e-6; // resistivity in ohm cm
+Resistance=resistivity*(L/(%pi*D^2)); // resistance in ohm
+printf("\nThe resistance is %.3f ohm",Resistance/100);
+i=(qw*100/Resistance)^0.5; // current in ampere
+printf("\nThe current is %.1f A",i);