HW 5 solution - MANE-4400 Nuclear Power Systems...

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MANE-4400 Nuclear Power Systems Engineering, Spring 2007 HW 5, due: 3/23/07 1 Problem 5.1 Saturated water is heated by a 0.001 m radius copper wire. The system is at 1 atm. The temperature of the wire is T wire . a) Calculate the heat flux at Δ T = T wire -T sat = 1,3,4,5 10, 20 , 300 and 1000 o C. b) Find the point of interception between natural convection and boiling. c) Calculate the critical heat flux q max (CHF). d) Calculate the minimal heat flux. e) Plot as much of the boiling curve as you can on log q vs. log Δ T coordinates. SOLUTION: First I calculated Δ T = T wire -T sat = 1,3,4,5 10, 20 "Problem Saturated water is heated by a 0.001 m radius copper wire. The system is at 1 atm. The temperature of the wire is Twire . a) Calculate the heat flux at T = Twire -Tsat = 1,3,4,5 10, 20 , 300 and 1000 oC. b) Find the point of interception between natural convection and boiling.” "Properties" Tsat=T_sat(water,P=100) h_l=enthalpy('water', p=100, x=0) h_g=enthalpy('water', p=100, x=1) h_lg=h_g-h_l k_l=CONDUCTIVITY('water', p=100, x=0) rho_l=density('water', p=100, x=0) rho_g=density('water', p=100, x=1) C_p=SPECHEAT('water', p=100, x=0) Pr_l=PRANDTL ('water', p=100, x=0) sigma_w=SURFACETENSION ('water', T=Tsat) alpha=k_l/(rho_l*C_p) mu=VISCOSITY('water', p=100, x=0) nu=mu/rho_l betha=750/1e6 D=0.001 Tw=100+dT "Natural Convection and Boiling" Ra_D=9.81*betha*(Tw-Tsat)*D^3/(nu*alpha) Nusselt_conv=0.36+0.518*Ra_D^.25/(1+(0.559/Pr_l)^(9/16))^(4/9) "or we can use:" Nusselt_conv2=(0.6+0.378*Ra_D^(1/6)/(1+(0.559/Pr_l)^(9/16))^(8/27))^2 h_conv=k_l/D*Nusselt_conv q_conv=h_conv*(Tw-Tsat)
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MANE-4400 Nuclear Power Systems Engineering, Spring 2007 HW 5, due: 3/23/07 2 "Boiling" "Nu=Ja^2/(C^3*Pr_l^m)" L_c=sqrt(sigma_w/((rho_l-rho_g)*9.81)) C=0.013 m=2 Ja=(C_p*(Tw-Tsat))/h_lg Nusselt_boiling=Ja^2/(C^3*Pr_l^2) h_boiling=k_l/L_c*Nusselt_boiling q_boiling=h_boiling*(Tw-Tsat) alpha=1.645E-07 betha=0.00075 C=0.013 C_p=4217 D=0.001 dT=30 h_boiling=120857 h_conv=2596 h_g=2.675E+06 h_l=417402 h_lg=2.258E+06 Ja=0.05676 k_l=0.6649 L_c=0.002505 m=2 mu=0.000283 nu=2.952E-07 Nusselt_boiling=455.3 Nusselt_conv=3.904 Nusselt_conv2=3.85 Pr_l=1.795
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HW 5 solution - MANE-4400 Nuclear Power Systems...

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