7-84. Chapter 7 External Forced Convection
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1 Chapter 7 External Frced Cnvectin 7-99 Wind i blwing ver the rf f a hue. The rate f heat tranfer thrugh the rf and the ct f thi heat l fr -h perid are t be deterined. Auptin Steady perating cnditin exit. The critical eynld nuber i e cr = 0. 3 Air i an ideal ga with cntant prpertie. The preure f air i at. pertie Auing a fil teperature f 0C, the prpertie f air are (Table A W/. C Air Analyi The eynld nuber i e L L - / (60000/ 3600 /( /.3380 Ty = 00 K which i greater than the critical eynld nuber. Thu we have cbined lainar and turbulent flw. Then the Nuelt nuber and the heat tranfer cefficient are deterined t be hl Nu (0.037e L 87 [0.037( ]( W/. C h Nu ( W/. C L 0 In teady peratin, heat tranfer fr the r t the rf (by cnvectin and radiatin ut be equal t the heat tranfer fr the rf t the urrunding (by cnvectin and radiatin, which ut be equal t the heat tranfer thrugh the rf by cnductin. That i, Q Q Q Q r t rf, cnv+rad rf, cnd rf t urrunding, cnv+rad Taing the inner and uter urface teperature f the rf t be T,in and T,ut, repectively, the quantitie abve can be expreed a Q h A ( T T A ( T T ( W/. C(300 (0T C Q r t rf,cnv+rad Q rf,cnd A rf t urr,cnv+rad T h, in i L r, in (0.9(300 (.670 T A ( T, ut, ut (0.9(300 (.670 r 8, in T, in T, ( W/. C( T urr A ( T 8, ut W/.K (0 73K T urr W/.K ( T Slving the equatin abve iultaneuly give Q 8,0 W 8.03W, T in 0.6C, andt,, ut ut 73K ( T (00K, in 73K (3.0 W/. C(300 ( T 3. C, ut The ttal aunt f natural ga cnuptin during a -hur perid i Q Q ttal t (8.03J/(3600 ther Qga.7 ther ,00J Finally, the ney lt thrugh the rf during that perid i Mney lt (.7 ther( $0.60/ ther $9. = 60 /h T = 0C, ut, in 0 C Q Tin = 0C 7-8
2 Chapter 7 External Frced Cnvectin 7-00 Stea i flwing in a tainle teel pipe while air i flwing acr the pipe. The rate f heat l fr the tea per unit length f the pipe i t be deterined. Auptin Steady perating cnditin exit. Air i an ideal ga with cntant prpertie. 3 The preure f air i at. pertie Auing a fil teperature f 0C, the prpertie f air are (Table A W/. C,.60 - /, and Analyi The uter diaeter f inulated pipe i D =.6+3.=.6 c = 0.6. The eynld nuber i Steel pipe D (/(0.6 Di = D = c e 3.0 D =.6 c.60 / Inulatin The Nuelt nuber fr flw acr a cylinder i deterined fr = 0.3 Nu and 0.6e 0.3 / 0. / 0.6(3.0 ( / 3 / 0. / h D 3 / e 8,000 / / , W/C Nu ( W/ C 0.6 Area f the uter urface f the pipe per length f the pipe i A D L ( 0.6( 0.36 / / In teady peratin, heat tranfer fr the tea thrugh the pipe and the inulatin t the uter urface (by firt cnvectin and then cnductin ut be equal t the heat tranfer fr the uter urface t the urrunding (by iultaneu cnvectin and radiatin. That i, Q Q Q pipe and inulatin urface t urrunding Uing the theral reitance netwr, heat tranfer fr the tea t the uter urface i expreed a cnv, i 0.099C/W h A (80 W/. C (0.0 ( and Q pipe inulatin pipe andin i i ln( r / r ln(.3 / 0.00C/W L ( W/. C( ln( r3 / r ln(.8 / C/W L (0.038W/. C( cnv, i T T pipe inulatin Heat tranfer fr the uter urface can be expreed a Q h A ( T T A ( T T urfacet urr,cnv+rad urr (0.3(0.36 (0T C ( C/W (.670 urr 8 W/.K ( T (.0W/. C( K ( T (3 73K 3 C Slving the tw equatin abve iultaneuly, the urface teperature and the heat tranfer rate per length f the pipe are deterined t be T 9.9C and Q 60. W (per length D i Air 3C, / Stea, 0C D 7-8
3 Chapter 7 External Frced Cnvectin 7-0 A pherical tan filled with liquid nitrgen i exped t wind. The rate f evapratin f the liquid nitrgen due t heat tranfer fr the air i t be deterined fr three cae. Auptin Steady perating cnditin exit. adiatin effect are negligible. 3 Air i an ideal ga with cntant prpertie. The preure f air i at. pertie The prpertie f air at at preure and the free trea teperature f 0C are (Table A- 0.0W/. 96 C g/. g/ Analyi (a When there i n inulatin, D = D i =, and the eynld nuber i (0000/3600/ ( e D / The Nuelt nuber i deterined fr Nu - 6 / 6 0.e 0.06e / 3 0. / / 6 6 / ( (.93 0 ( W/. C and h Nu ( W/. C D The rate f heat tranfer t the liquid nitrgen i Q ha ( T T h( D ( T T (.66 W/. C[ ( ] The rate f evapratin f liquid nitrgen then bece Q 9. J/ Q h 0.80 g/ h 98J/g.030 (0 ( 96 C 9,00W (b Nte that after inulatin the uter urface teperature and diaeter will change. Therefre we need t evaluate dynaic vicity at a new urface teperature which we will aue t be -00C. At -00C,.890 e D Nu g/.. Nting that D = D 0 =., the Nuelt nuber bece (0000/3600/ ( e e / / / / 6 6 / ( ( ( W/. C and h Nu (90.7W/. C D. The rate f heat tranfer t the liquid nitrgen i Wind 0C 0 /h.890 Inulatin 6 D i D Nitrgen tan -96C 7-86
4 A D (..8 T T,tan T T,tan Q inulatin r r cnv r r ha [0 ( 96] C (.0 (0.03W/. C(.0 ( (.7W/. C(.8 The rate f evapratin f liquid nitrgen then bece Q 7.36J/ Q h g/ h 98J/g Chapter 7 External Frced Cnvectin 736W (c We ue the dynaic vicity value at the new etiated urface teperature f 0C t be.790 e D Nu g/.. Nting that D = D 0 =.0 in thi cae, the Nuelt nuber bece (0 000/3600/( e e / / / / 6 6 / ( (.96 0 ( W/. C and h Nu ( W/. C D.0 The rate f heat tranfer t the liquid nitrgen i A D (.0.8 T T,tan T T,tan Q inulatin r r cnv r r ha [0 ( 96] C (.0 (0.0000W/. C(.0 ( (0.73W/. C(.8 The rate f evapratin f liquid nitrgen then bece Q 0.07J/ Q h.38 0 h 98J/g - g/ W 7-87
5 Chapter 7 External Frced Cnvectin 7-0 A pherical tan filled with liquid xygen i exped t abient wind. The rate f evapratin f the liquid xygen due t heat tranfer fr the air i t be deterined fr three cae. Auptin Steady perating cnditin exit. adiatin effect are negligible. 3 Air i an ideal ga with cntant prpertie. 7 The preure f air i at. pertie The prpertie f air at at preure and the free trea teperature f 0C are (Table A- 0.0W/. 83C g/. g/ Analyi (a When there i n inulatin, D = D i =, and the eynld nuber i (0000/3600/ ( e D / The Nuelt nuber i deterined fr Nu - / 6 0.e 0.06e / 3 0. / / 6 6 / ( (.93 0 ( W/. C and h Nu (0 3.9 W/. C D The rate f heat tranfer t the liquid xygen i Q ha ( T T h( D ( T T (3.9W/. C[ ( ] The rate f evapratin f liquid xygen then bece Q. J/ Q h g/ h 3J/g.00 (0 ( 83 C,37W (b Nte that after inulatin the uter urface teperature and diaeter will change. Therefre we need t evaluate dynaic vicity at a new urface teperature which we will aue t be -00C. At -00C,.890 g/.. Nting that D = D 0 =., the Nuelt nuber bece e D Nu (0000/3600/ ( e e / / / / 6 6 / ( ( ( W/. C and h Nu (90.7W/. C D. The rate f heat tranfer t the liquid nitrgen i Wind 0C 0 /h.890 Inulatin D i D Oxygen tan -83C 7-88
6 A D (..8 T T,tan T T,tan Q inulatin r r cnv r r ha [0 ( 83] C (.0 (0.03W/. C(.0( (.7W/. C(.8 The rate f evapratin f liquid nitrgen then bece Q 6.98J/ Q h 0.03 g/ h 3J/g Chapter 7 External Frced Cnvectin 698W (c Again we ue the dynaic vicity value at the etiated urface teperature f 0C t be.790 e D Nu g/.. Nting that D = D 0 =.0 in thi cae, the Nuelt nuber bece (0 000/3600/( e e / / / / 6 6 / ( (.96 0 ( W/. C and h Nu ( W/. C D.0 The rate f heat tranfer t the liquid nitrgen i A D (.0.8 T T,tan T T,tan Q inulatin r r cnv r r ha [0 ( 83] C (.0 (0.0000W/. C(.0 ( (0.73W/. C(.8 The rate f evapratin f liquid xygen then bece Q 0.08J/ Q h. 0 h 3J/g - g/ W 7-89
7 Chapter 7 External Frced Cnvectin 7-03 A circuit bard hue 80 clely paced lgic chip n ne ide. All the heat generated i cnducted acr the circuit bard and i diipated fr the bac ide f the bard t the abient air, which i frced t flw ver the urface by a fan. The teperature n the tw ide f the circuit bard are t be deterined. Auptin Steady perating cnditin exit. The critical eynld nuber i e cr = 0. 3 adiatin effect are negligible. Air i an ideal ga with cntant prpertie. 7 The preure f air i at. pertie Auing a fil teperature f 0C, the prpertie f air are (Table A W/. C Analyi The eynld nuber i e L L / (00/ 60 /( / which i le than the critical eynld nuber. Therefre, the flw i lainar. Uing the prper relatin fr Nuelt nuber, heat tranfer cefficient i deterined t be hl Nu 0.66e L 0.66(7.0 0 ( W/. C h Nu (8. 3.3W/. C L 0.8 The teperature n the tw ide f the circuit bard are Q Q ha ( T T T T ha ( W 30C 39.8C (3.3W/. C(0. (0.8 A QL Q ( T T T T L A ( W( C 39.C (6 W/. C(0. (0.8 T =30C 00 /in T T 7-90
8 Chapter 7 External Frced Cnvectin 7-0E The equivalent wind chill teperature f an envirnent at 0F at variu wind peed are = 0 ph: T 9. ( 9. T ( equiv abient ( 0 F ( 0 ph ph 9F = 0 ph: T equiv ( 0 F ( 0 ph ph.9 F = 30 ph: T equiv ( 0 F ( 30 ph ph 33. F = 0 ph: T equiv ( 0 F ( 0 ph ph 37.7 F In the lat 3 cae, the pern need t be cncerned abut the pibility f freezing. 7-9
9 Chapter 7 External Frced Cnvectin 7-0E "!POBLEM 7-0E" "ANALYSIS" T_equiv=9.-(9.-T_abient*( *el+0.30*qrt(el el [ph] Tabient [F] Tequiv [F]
10 Chapter 7 External Frced Cnvectin F Tequiv [F] F 0 F el [ph] Deign and Eay ble 7-93
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