ME 315 Exam 2 Wednesday, November 11, 2015 CIRCLE YOUR DIVISION

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1 ME 315 Exa edneday, Nveber 11, 015 Thi i a cled-bk, cled-nte exainatin. There i a frula heet rvided. Yu are al allwed t bring yur wn ne-age letter ize, dubleided crib heet. Yu ut turn ff all cunicatin device befre tarting thi exa, and leave the ff fr the entire exa. Pleae write legibly and hw all wrk fr yur wn benefit. State all autin. Pleae arrange all yur heet in the crrect rder. Nae: at Firt CIRCE YOUR DIVISION Div. 1 (8:30 a) Div. (9:30 a) Div. 3 (11:30 a) Div. 4 (3:30 ) Prf. Naik Prf. Ruan Prf. Pan Prf. Marcnnet Yur Aigned # : (Only alicable t Div. 3) Prble 1 (30 Pint) (40 Pint) 3 (30 Pint) Ttal (100 Pint) Scre 1

2 Prble 1 (30 t) (a) (6 t) Cnider a lainar flw ver a flat late. The hae f theral bundary layer (δ t ) and velcity bundary layer (δ) are given in the figure. The Prandtl nuber (Pr) huld be. A: Pr > 1 B: Pr 1 C: Pr < 1 D: Inufficient Infratin Briefly jutify yur chice. n Pr 1/3 1 Pr 1 t Prandtl nuber i the rati f vicu diffuin rate cared t vicu diffuin rate i higher, Prandtl nuber i greater than ne theral diffuin rate; ince (b) (7 t) The btt urface f tw identical cu f water (A and B) are heated t T,A = 15C and T,B = 300C. The biling curve fr aturated water at atheric reure i given belw. Nte: the exce teerature T e i defined a T T at, wheree T at fr water at atheric reure i 100C. hich cu f water ha a higher rate f evaratin?? Qualitatively jutify yur anwer uing the biling curve, yur undertanding f the bilingg regie, and/r arriate equatin. N calculatin are required. Fr the l biling curve: T ea, near critical heat flux rviding very high rate f heat tranfer T e,b 5 C nucleate biling regin 00 C fil biling regin near iniu heat flux (eidenfrt int) rviding ignificantly le rate f heat tranfer Cu A ha higher rate f evaratin

3 (c) (7 t) A ht rectangular late, f length a and width b with a > b, i hung vertically in air and cled by free cnvectin.. The vertical ide can be either alng b (Cae 1) r a (Cae ), a illutrated. Aue the bundary layer fr free cnvectin i lainar. Recall that the crrelatin f average Nuelt nuber in lainar regin ha the fr: h 1/4 Nu CRa, wheree C i a cntant. k Briefly exlain whether the rientatin f the late will affect the cling rate. 3/4 1/4 1/4 3/4 1/4 Nu Ra Gr h average heat tranfer cefficient decreae with increae in length f the late with hrter ide (b)) alng the vertical will rvide fater cling rate Bundary layer grw alng the vertical ide. ith the lnger ide (a) alng the vertical, a thicker bundary layer will reult in lwer value f heatt tranfer cefficient with hrterr ide (b) alng the vertical will rvide fater cling rate (d) (10 t) A cncentric-tube heat exchanger i deigned t wrk with a ht liquid and a cld liquid with knwn inlet teerature. It can be erated in either arallel-flw Overall heat tranfer cefficient: U = 100 /( K); Area: A = 1 r cunter- whichh flw cnfiguratin will be re effective. flw cnfiguratin. The heat exchanger ha the fllwing araeter: Heat Caacity Rate: C h = C c = 100 /K Calculate the effectivene (ε) f arallel flw and cunter-flw cnfiguratin and identify UA NTU C in Fr arallel flw: HE Figure 11.10, Fr cunter-flw: H Figure K 100 K HEX PF 1.11 HEX,CF EX, PF 0.4 HEX,CF 0.5 cunter-flw arrangeent i re effective C 1 and Cr C 1 ex NTU 1 C NTU 1 NTU 1 r 0.5 in ax C r 100 K K

4 Prble (40 t) Cnider a chilly, autun day at Purdue with wind velcity f U = / and an abient teerature f T = 10 C. Yu frget yur jacket at he and yur frear are exed t the cld air. Fr the air, aue k = 0.06 /(-K), Pr = 0.7, and the vicity given by the table. Recall that α = k / ρc = ν / Pr. [ /] 10 C C C Fr thi rble, arxiate yur frear a a lng cylinder, with diaeter D = 75, in cr-flw f air with a urface teerature f T = 37 C. (a) (13 t) Calculate the rate f heat l er unit area fr yur ar. T T Fil teerature: Tfil 3.5 C ud Reynld nuber: Re D air / /3 Fr cylinder in cr-flw with air: NuD CReDPr 0.193ReD Pr hd h7510 NuD 50.4 h 17.5 k air K -K qcnv h T T K Rate f heat l er unit area: -K qcnv 47.5 (b) (0 t) Nw yu run thrugh the funtain utide f ME and yur ar are cated unifrly with a thin layer f water (D AB = /, h fg = J/kg). Aue the urrunding air ha a relativity huidity f ϕ = 80%. Calculate the ttal rate f heat er unit area fr yur wet frear. Schidt nuber: Sc ρ at,var [kg/ 3 ] 10 C C C air 0.7 DAB

5 Aue heat and a tranfer analgy i alicable 1/ /3 Sh CRe Sc 0.193Re Sc 50.4 D D D 3 hd h7510 ShD 50.4 h DAB h k e 1; n 1/3 DAB Pr DAB 5 h DABe K -K h h 5 1/ Rate f evaratin f water var fr the urface: h A h A T T kg eva - Rate f evarative heat l er unit area: 4 kg 6 J qeva evahfg kg Ttal rate f heat l er unit area: qttal qcnv qeva qttal eva A, A, A, at A, at 3 kg (c) (7 t) Nw cnider that yu were wearing a jacket f lw theral cnductivity aterial that fit nugly ver yur frear adding an effective theral reitance f R = K/. Aue yur ar and jacket are dry and that the thickne f yur jacket de nt change the cnvective heat tranfer cefficient ignificantly fr art (a). Find the rate f heat l er unit area fr yur ar with the jacket. 1 -K Theral reitance due t cnvectin: R cnv h Ttal theral reitance due t cnvectin and cnductin thrugh the jacket: -K -K Rttal R Rcnv T T K Rate f heat l er unit area with the jacket: qcnv, new Rttal -K q 5.3 cnv, new 5

6 Prble 3 (30 t) A fluid f ecific heat C, theral cnductivity k, and vicity flw teadily thrugh a circular tube f diaeter D and length. The a flw rate i and the fluid enter with a ean teerature f T i,. The flw i turbulent and fully-develed ver the entire length f the tube. The tube urface (wall) i ubjected t a heat flux that decreae linearly fr inlet t x utlet a: q q1 where q 0 i knwn. q = q 1 x T C T i, C,, k, C T dt qpdx D (a) (4 t) Uing an arriate crrelatin, write an exrein fr cnvective heat tranfer cefficient h inide the tube nly in ter f knwn araeter. hd Fr turbulent, fully-develed flw with fluid heating: NuD 0.03ReD Pr k ud D 4 C C ReD and Pr D D k k 4 6

7 (b) (10 t) Derive an exrein fr variatin f the ean fluid teerature ter f knwn araeter. Cnidering energy balance fr the cntrl vlue: E in E ut E gen E t T x x qp x dt 1 dx C, i Ti, 0 C T q Pdx C T dt 0 C dt q Pdx qp x Integrating: T x T x C T ; P D x nly in (c) (6 t) Derive an exrein fr the ttal rate f heat tranfer q t the fluid nly in ter f knwn araeter. Ttal rate f heat tranfer: q C T, T, i qp qp qp T, Ti, Ti, q C T, i T, i qp C C C q q D x x q q Pdx q D dx q D x q D q D 7

8 (d) (5 t) Derive an exrein fr variatin f the urface (wall) teerature ter f knwn araeter. q Cnidering heat flux at any ectin: q h T x T x Tx Tx h qp x q x TxT, i x 1 C h T x nly in (e) (5 t) Derive an exrein fr the axial lcatin x ax at which the urface (wall) teerature i axiu. dt qp qpx ax q Fr axiu urface teerature: 0 dx C C h P xax P 1 C C h C xax C fr Dh Dh 8

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