Chapter 3, Solution 1C.

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1 COSMOS: Cmplete Onlne Slutns Manual Organzatn System Chapter 3, Slutn C. (a If the lateral surfaces f the rd are nsulated, the heat transfer surface area f the cylndrcal rd s the bttm r the tp surface area f the rd, A s πd / 4. (b If the tp and the bttm surfaces f the rd are nsulated, the heat transfer area f the rd s the lateral surface area f the rd, A πd. Chapter 3, Slutn C. In steady heat cnductn, the rate f heat transfer nt the wall s equal t the rate f heat transfer ut f t. Als, the temperature at any pnt n the wall remans cnstant. Therefre, the energy cntent f the wall des nt change durng steady heat cnductn. Hwever, the temperature alng the wall and thus the energy cntent f the wall wll change durng transent cnductn. Chapter 3, Slutn 3C. The temperature dstrbutn n a plane wall wll be a straght lne durng steady and ne dmensnal heat transfer wth cnstant wall thermal cnductvty. Chapter 3, Slutn 4C. The thermal resstance f a medum represents the resstance f that medum aganst heat transfer. Chapter 3, Slutn 5C. The cmbned heat transfer ceffcent represents the cmbned effects f radatn and cnvectn heat transfers n a surface, and s defned as h cmbned h cnvectn h radatn. It ffers the cnvenence f ncrpratng the effects f radatn n the cnvectn heat transfer ceffcent, and t gnre radatn n heat transfer calclatns. Chapter 3, Slutn 6C. Yes. The cnvectn resstance can be defned as the nverse f the cnvectn heat transfer ceffcent per unt surface area snce t s defned as cnv /( ha. Heat and Mass Transfer: A Practcal Apprach, 3/e, Yunus A. Çengel 007 The McGraw-Hll Cmpanes.

2 COSMOS: Cmplete Onlne Slutns Manual Organzatn System Chapter 3, Slutn 7C. The cnvectn and the radatn resstances at a surface are parallel snce bth the cnvectn and radatn heat transfers ccur smultaneusly. Chapter 3, Slutn 8C. Fr a surface f A at whch the cnvectn and radatn heat transfer ceffcents are h and h, the sngle equvalent heat transfer ceffcent s h h h when the cnv rad medum and the surrundng surfaces are at the same temperature. Then the equvalent thermal resstance wll be /( h A. eqv eqv eqv cnv rad Chapter 3, Slutn 9C. The thermal resstance netwrk asscated wth a fve-layer cmpste wall nvlves fve sngle-layer resstances cnnected n seres. Chapter 3, Slutn 0C. Once the rate f heat transfer Q & s knwn, the temperature drp acrss any layer can be determned by multplyng heat transfer rate by the thermal resstance acrss that layer, ΔT layer layer Chapter 3, Slutn C. The temperature f each surface n ths case can be determned frm ( T Ts / s Ts T ( Q & s ( T T / T T ( Q & where s s s s s the thermal resstance between the envrnment and surface. Chapter 3, Slutn C. Yes, t s. Heat and Mass Transfer: A Practcal Apprach, 3/e, Yunus A. Çengel 007 The McGraw-Hll Cmpanes.

3 COSMOS: Cmplete Onlne Slutns Manual Organzatn System Chapter 3, Slutn 3C. The wndw glass whch cnssts f tw 4 mm thck glass sheets pressed tghtly aganst each ther wll prbably have thermal cntact resstance whch serves as an addtnal thermal resstance t heat transfer thrugh wndw, and thus the heat transfer rate wll be smaller relatve t the ne whch cnssts f a sngle 8 mm thck glass sheet. Chapter 3, Slutn 4C. Cnvectn heat transfer thrugh the wall s expressed as has ( Ts T. In steady heat transfer, heat transfer rate t the wall and frm the wall are equal. Therefre at the uter surface whch has cnvectn heat transfer ceffcent three tmes that f the nner surface wll experence three tmes smaller temperature drp cmpared t the nner surface. Therefre, at the uter surface, the temperature wll be clser t the surrundng ar temperature. Chapter 3, Slutn 5C. The new desgn ntrduces the thermal resstance f the cpper layer n addtn t the thermal resstance f the alumnum whch has the same value fr bth desgns. Therefre, the new desgn wll be a prer cnductr f heat. Chapter 3, Slutn 6C. The blanket wll ntrduce addtnal resstance t heat transfer and slw dwn the heat gan f the drnk wrapped n a blanket. Therefre, the drnk left n a table wll warm up faster. Chapter 3, Slutn 36. The wall f a refrgeratr s cnstructed f fberglass nsulatn sandwched between tw layers f sheet metal. The mnmum thckness f nsulatn that needs t be used n the wall n rder t avd cndensatn n the uter surfaces s t be determned. Assumptns Heat transfer thrugh the refrgeratr walls s steady snce the temperatures f the fd cmpartment and the ktchen ar reman cnstant at the specfed values. Heat transfer s ne-dmensnal. 3 Thermal cnductvtes are cnstant. 4 Heat transfer ceffcents accunt fr the radatn effects. Heat and Mass Transfer: A Practcal Apprach, 3/e, Yunus A. Çengel 007 The McGraw-Hll Cmpanes.

4 COSMOS: Cmplete Onlne Slutns Manual Organzatn System Prpertes The thermal cnductvtes are gven t be k 5. W/m C fr sheet metal and W/m C fr fberglass nsulatn. Analyss The mnmum thckness f nsulatn can be determned by assumng the uter surface temperature f the refrgeratr t be 0 C. In steady peratn, the rate f heat transfer thrugh the nsulatn refrgeratr wall s cnstant, and thus heat transfer between the rm and the refrgerated space s equal t the heat transfer between the rm and the uter mm surface f the refrgeratr. Cnsderng a unt surface area, mm Q & h A( T T rm s, ut (9 W/m C(m (5 0 C 45 W Usng the thermal resstance netwrk, heat transfer between the rm and the refrgerated space can be expressed as Trm Trefrg ttal Trm Trefrg / A h k k Substtutng, 45 W/m 9 W/m metal nsulatn h T rm (5 3 C 0.00 m C 5. W/m C W/m ns 3 C 4 W/m Slv ng fr, the mnmum thckness f nsulatn s determned t be m 0.45 cm C T refrg Chapter 3, Slutn 59. A cmpste wall cnssts f several hrzntal and vertcal layers. The left and rght surfaces f the wall are mantaned at unfrm temperatures. The rate f heat transfer thrugh the wall, the nterface temperatures, and the temperature drp acrss the sectn F are t be determned. Assumptns Heat transfer s steady snce there s n ndcatn f change wth tme. Heat transfer thrugh the wall s ne-dmensnal. 3 Thermal cnductvtes are cnstant. 4 Thermal cntact resstances at the nterfaces are dsregarded. Heat and Mass Transfer: A Practcal Apprach, 3/e, Yunus A. Çengel 007 The McGraw-Hll Cmpanes.

5 COSMOS: Cmplete Onlne Slutns Manual Organzatn System Prpertes The thermal cnductvtes are gven t be k A k F, k B 8, k C 0, k D 5, k E 35 W/m C. Analyss (a The representatve surface area s A m. The thermal resstance netwrk and the ndvdual thermal resstances are T T md, md, ttal A B D E F C A B D E F 0.0m 0.04 C/W ( W/m C(0. m C T T ttal md, 0.05 m 0.06 C/W (0 W/m C(0.04 m 0.05 m 0.6 C/W (8 W/m C(0.04 m 0.m 0. C/W (5 W/m C(0.06 m 0.m 0.05 (35 W/m C(0.06 m C/W 0.06 m 0.5 C/W ( W/m C(0. m 4 0. md, md, ( C 57 W C/W md, C/W 0.05 C/W C/W (fr a 0. m m sectn Then steady rate f heat transfer thrugh entre wall becmes Q & ttal (5 m(8 m (57 W m 5 W (b The ttal thermal resstance between left surface and the pnt where the sectns B, D, and E meet s ttal md, C/W Then the temperature at the pnt where the sectns B, D, and E meet becmes T T Q & T T Q & ttal 300 C (57 W(0.065 C/W 63 C ttal (c The temperature drp acrss the sectn F can be determned frm ΔT Q & ΔT Q & F (57 W(0.5 C/W 43 C F Chapter 3, Slutn 66C. Heat and Mass Transfer: A Practcal Apprach, 3/e, Yunus A. Çengel 007 The McGraw-Hll Cmpanes.

6 COSMOS: Cmplete Onlne Slutns Manual Organzatn System When the dameter f cylnder s very small cmpared t ts length, t can be treated as an nfntely lng cylnder. Cylndrcal rds can als be treated as beng nfntely lng when dealng wth heat transfer at lcatns far frm the tp r bttm surfaces. Hwever, t s nt prper t use ths mdel when fndng temperatures near the bttm and the tp f the cylnder. Chapter 3, Slutn 67C. Heat transfer n ths shrt cylnder s ne-dmensnal snce there wll be n heat transfer n the axal and tangental drectns. Chapter 3, Slutn 68C. N. In steady-peratn the temperature f a sld cylnder r sphere des nt change n radal drectn (unless there s heat generatn. Chapter 3, Slutn 79E. A steam ppe cvered wth -n thck fberglass nsulatn s subjected t cnvectn n ts surfaces. The rate f heat lss frm the steam per unt length and the errr nvlved n neglectng the thermal resstance f the steel ppe n calculatns are t be determned. Assumptns Heat transfer s steady snce there s n ndcatn f any change wth tme. Heat transfer s ne-dmensnal snce there s thermal symmetry abut the center lne and n varatn n the axal drectn. 3 Thermal cnductvtes are cnstant. 4 The thermal cntact resstance at the nterface s neglgble. Prpertes The thermal cnductvtes are gven t be k 8.7 Btu/h ft F fr steel and k 0.00 Btu/h ft F fr fberglass nsulatn. Analyss The nner and uter surface areas f the nsulated ppe are A πd π (3.5 / ft(ft 0.96 ft A πd π (8 / ft(ft.094 ft The ndvdual resstances are ppe nsulatn T T Heat and Mass Transfer: A Practcal Apprach, 3/e, Yunus A. Çengel 007 The McGraw-Hll Cmpanes.

7 COSMOS: Cmplete Onlne Slutns Manual Organzatn System h A ttal h A nsulatn ppe (30 Btu/h.ft. F(0.96 ft ln( r / r ln( / h F/Btu πk π (8.7 Btu/h.ft. F(ft ln( r3 / r ln(4 / 5.56 h F/Btu πk π (0.00 Btu/h.ft. F(ft (5 Btu/h.ft. F(.094 ft h F/Btu h F/Btu h F/Btu Then the steady rate f heat lss frm the steam per ft. ppe length becmes T Q & T ttal ( F 69.9Btu/h 5.65 h F/Btu If the thermal resstance f the steel ppe s neglected, the new value f ttal thermal resstance wll be ttal h F/Btu Then the percentage errr nvlved n calculatns becmes errr % whch s nsgnfcant. ( h F/Btu % 5.65 h F/Btu Heat and Mass Transfer: A Practcal Apprach, 3/e, Yunus A. Çengel 007 The McGraw-Hll Cmpanes.

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