Hea ansfe asis Febua 7, 7 Hea ansfe asis a Caeo Mehanial Engineeing 375 Hea ansfe Febua 7, 7 Engineeing ediaion CSUN has aedied pogams in Civil, Eleial, Manufauing and Mehanial Engineeing Naional aediing a eviews all engineeing pogams in US Fall 7 eaediaion visi equies olleion of suden wo un in all ou noes, quies design poje and eams a end of semese You an ge hem ba in lae fall 7 ssessmen esuls 9 sudens ompleed assessmen 7 ae OK o bee wih Eel sills 5 ae OK o bee wih Malab sills Couse ompleion daa: Mah 8(, ECE (, ME 39(5, ME 37(9, ME 39(, ME 7(, MSE 3( 5 go 3 d / C (6 missed C go d(e a e a 3 ssessmen esuls II 3 go hemo poblem oe Q Q/m p d fo onsan P Wih onsan p, q p ( 5 go inepolaion ( go paial edi ( 3 go poblem o find Δh fo dh/d / fom 5 o (8 go paial edi h dh d [ ] h Ouline eview Definiions eview las wee Hea eaion Geneal eneg balane and geome Simplified ases: sead, onedimensional, no hea eaion, onsan hemal onduivi nale one dimensional ases Consan and vaiable hemal onduivi Consan hea eaion em 5 Q is he oal hea ansfe wih eneg unis of J o u Q is he hea ansfe ae in powe unis J/s W o u/h Hea flu: q Figue - fom Çengel, Hea and ansfe 6 ME 375 Hea ansfe
Hea ansfe asis Febua 7, 7 eview Conduion Fouie aw q / (D: d/d is hemal onduivi (W/m K o u/h f of depends on empeaue; ma be assumed onsan fo small empeaue ange Fo onsan ( ( q o q 7 onv h ( s s h hea ansfe oeffiien (W/m K o u/h f of Equaion assumes dieion of hea ansfe is fom solid o fluid eview Conveion V Figue -3 fom Çengel, Hea and ansfe 8 eview adiaion adiaion fom sufae o sufae ad, Fσ( F is shape-emissivi fao σ, Sefan olmann onsan 5.67-8 W/m K.7-8 u/h f is he absolue empeaue!!! la bod is pefe adiao Emissivi is faion of bla bod emied b aual sufae bsobivi is inoming faion absobed 9 Vaious phenomena in solids an eae hea Define as he hea eaed pe uni volume pe uni ime Hea Geneaion Figue - fom Çengel, Hea and ansfe Find fo a Wie wih Cuen he definiion of is he hea eaed pe uni volume pe uni ime Eleial esisane podues a hea dissipaion of I I / in was whee I is he uen in amps is he eleial esisivi (ohm m is he lengh of he wie in m is oss seional aea of he wie, π, in m Find an equaion fo in ems of he vaiables shown hee Find fo a Wie wih Cuen he definiion of is he hea eneg eaed pe uni volume pe uni ime Eleial esisane podues an eneg dissipaion of I I / in was whih is eneg pe uni ime Divide his b he wie volume, V o ge I I I I J V π J uen densi (/m ME 375 Hea ansfe
Hea ansfe asis Febua 7, 7 ME 375 Hea ansfe 3 3 Find fo a Wie wih Cuen ppl he equaion jus found o find fo a oppe wie (.7-8 ohm m a o C wih a diamee of mm (. m and a uen of ampees ( ( ( 3 6 8.788..7 m W W ohm m m ohm D I I e π π eangula Eneg alane Figue - fom Çengel, Hea and ansfe Eneg balane: Soed eneg hea inflow hea ouflow hea eaed Soage p Δ Δ Δ 5 eangula Eneg alane p e q q q hea eaed Soed eneg hea inflow hea ouflow p e Uses Fouie aw ξ ξ q 6 Eneg alane Dimensions p e E M E M Θ Θ 3 3 p ξ ξ E E Θ Θ 3 ll ems have dimensions of eneg pe uni volume pe uni ime E denoes eneg unis dimensions: dimensions: 7 Eneg alane Simplifiaions p e fo sead hea ansfe p e fo no hea eaion 8 Eneg alane Simplifiaions p e fo one dimensional hea ansfe p e Fo onsan hemal onduivi,
Hea ansfe asis Febua 7, 7 Simples Cases p e fo sead hea ansfe fo one dimensional hea ansfe fo no hea eaion dq q C Consan d d C d d d d d q Figue -3 fom q d q Çengel, d Hea and ansfe d q d d d φ 9 Fo onsan : q ( Clindial Coodinaes p φ φ p φ φ Sead -D Clinde d d d d e Fo no hea eaion d d d d d d Clindial adial hea ansfe C q π πc Clindial Shell Q π Figue -5 fom Çengel, Hea and ansfe q d π πc d d C π d π d d Figue - 5 fom Çengel, Hea and ansfe Clindial Shell II Q π d Fo onsan π π 3 ( Figue - 5 fom Çengel, Hea and ansfe Sample Poblem π Insulaion (. W/m K is o be added o a pipe wih a.5 m diamee, a sufae empeaue of o C, and a hea loss pe uni lengh of 5 W/m. Wha hiness of insulaion, δ, is equied if he empeaue of he oue insulaion sufae is o C? Given: o C and o 5W C m (.5 m /.75 m, and Find: δ ME 375 Hea ansfe
Hea ansfe asis Febua 7, 7 Sample Poblem Soluion Given: o C, o C,.75 m,. W/m K and 5 W m π Q π o o.w C C π.8 o m C 5W.8 e (.75 m e m.676 m δ.676 m.75 m.96 m 5.8 Figue -3 fom Çengel, Hea and ansfe Spheial Coodinaes p sin θ sin θ θ θ sin θ φ φ 6 Sead -D Sphee p sin θ sin θ θ θ sin θ φ φ e Fo no hea eaion d d d d d C d 7 d C d Spheial Shell d q π πc d Q d π π d Fo onsan π ( π 8 Sead, -D, Consan, eangula ( Q Clindial shell ( ( π π ( Spheial shell π ( π 9 Sead, -D, Vaiable, eangula Clindial shell π π Spheial shell π Q d d ( d ( q 3 d d ME 375 Hea ansfe 5
Hea ansfe asis Febua 7, 7 veage hemal Conduivi ll he equaions on he pevious ha had an inegal of hemal onduivi ha is in he eal fom of an aveage If ( hen avg, he aveage value of beween and, is pplied o hemal onduivi, his eal esul is avg avg 3 d d Sead, -D, Vaiable, ( eangula d q Clindial shell π π ( d ( ( Spheial shell π π ( Q d he fomulas ae he same as hose fo onsan if a suiable aveage is used 3 -D, eangula, Hea Geneaion p e fo sead hea ansfe d d fo one dimensional hea ansfe d d e ed C d d [ d C ] d C d 33 -D, eangula, Hea Geneaion [ d C ] d C d How do we find C and C? Have o mah bounda ondiions (a and given in a paiula poblem Can speif empeaue a,, o boh Can speif q d/d a o, bu no boh Can speif d/d h( - a,, o boh Can speif ombinaions of above ondiions oo a onsan and hee 3 -D, eangula, Hea Geneaion Fo onsan and we an inegae he pevious equaion wo imes d [ d C ] d C e C d [ C ] d C C C How do we ge C and C if we now a and a? [ ] C 35 -D, eangula, Hea Geneaion Fo a we mus have C C C Fo a we mus have C C C C ( C C 36 ME 375 Hea ansfe 6
Hea ansfe asis Febua 7, 7 -D, eangula, Hea Geneaion Subsiue C and C ino eal soluion C C ( ( 37 -D, eangula, Hea Geneaion Wie las equaion in ems of dimensionless empeaue aio and / ( ( ( Define dimensionless H e hea eaion ( H H 38 empeauediffeene aio Plo of ( - /( - fo Hea Geneaion in a Slab.8.6...8.6.. e H (...3..5.6.7.8.9 / H H. H. H H H 5 H 39 -D, eangula, Hea Geneaion Compue he hea flu fom he boed empeaue equaion on ha 3 q d d q ( ( ( ( Veif Hea alane (Hea in a (Hea eaed (Hea ou a Q E oo a a slab wih hiness,, and oss seional aea,, giving a volume ( ( q ( q E ( q Wha if ( ( ( q Seing in eal equaions above gives ( e q ME 375 Hea ansfe 7
Hea ansfe asis Febua 7, 7 Manipulaions Seing q and solving fo gives loaion of maimum empeaue eall ha q d/d so d/d if q Find ha / fo maimum empeaue ma 8 Dimensionless empeaue esuls and ma See deivaion slides a end of leue 3 /...8.6.. Slab Wih Hea Geneaion oh bounda empeaues...3..5.6.7.8.9 Dimensionless Disane, / H H H. H. H H H 5 H Ohe Geomeies Can find simila esuls wih hea eaion fo solid lindes and sphees, spheial shells and lindial shells Same eal appoah, bu diffeen esuls fo eah pe of geome See pined noes o ge esuls fo vaious geomeies empeaue, hea flow, maimum empeaue, ondiions fo maimum empeaue 5 Solid Clinde solid linde wih adius,, onsan hea eaion and onsan, has a maimum empeaue a is ene ma sufae Cha 6 eample had hea eaion of.788 6 W/m 3 fo a. m diamee oppe wie wih a uen of. Wha is ma sufae fo his wie? 6 Soluion ae 3 W/m K a o C 6.788 W (.5 m 3 m K 3W m K Can ombine equaions fo ma and ma sufae. I I ma sufae ma sufae I π 7 ddiional Chas he esuls shown in ha 37 ae deived in he following slides hese has show he algebai deails fo he following esuls oaion of he maimum empeaue Value of he maimum empeaue Dimensionless foms of he empeaue equaion ddiional vesion of he ma sufae equaion is also pesened 8 ME 375 Hea ansfe 8
Hea ansfe asis Febua 7, 7 Cha 37 Manipulaion Deails Sa wih basi esul fom ha 36 Divide b and mulipl ems on lef b / o / hen eaange o ge e e 9 Cha 37 Manipulaion Deails II Se d/d in ha 36 equaion d q d ( ma e ma Subsiue his value ino equaion o ge he maimum empeaue 8 5 Cha 37 Manipulaion Deails III Compae / and ma / equaions ma ma 8 ma ma 5 Moe on ma sufae as equaion on ha ma sufae I Weidemann-Fan aw (appoimae fo meals: /.5-8 ohm W/K is alled he oen onsan Epeimenal daa agee o bee han % 8.5 ohm W I I K ma sufae 5 ME 375 Hea ansfe 9