Major: All Engineering Majors. Authors: Autar Kaw, Luke Snyder

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1 Nolr Rgrsso Mjor: All Egrg Mjors Auhors: Aur Kw, Luk Sydr hp://urclhodsgusfdu Trsforg Nurcl Mhods Educo for STEM Udrgrdus 3/9/5 hp://urclhodsgusfdu

2 Nolr Rgrsso hp://urclhodsgusfdu

3 Nolr Rgrsso So populr olr rgrsso odls: Epol odl: ( y Powr odl: b ( y ) 3 Suro growh odl: y b + 4 Polyol odl: ( y ) b ) 3 hp://urclhodsgusfdu

4 Nolr Rgrsso Gv d pos (, y), (, y),, (, y) bs f y f () o h d, whr f () s olr fuco of (, y ) ( (, y, y ) ( ), y ) y f ( ) y f () Fgur Nolr rgrsso odl for dscr y vs d 4 hp://urclhodsgusfdu

5 Rgrsso Epol Modl 5 hp://urclhodsgusfdu

6 Epol Modl Gv (, y), (, y ),, (, y ) bs f y b o h d (, y ) b y (, y ) y b (, y ) (, y ) Fgur Epol odl of olr rgrsso for y vs d 6 hp://urclhodsgusfdu

7 Fdg Coss of Epol Modl Th su of h squr of h rsduls s dfd s S r ( ) b y Dffr wh rspc o d b S r ( b )( ) b y S r b ( b y )( ) b 7 hp://urclhodsgusfdu

8 Fdg Coss of Epol Modl Rwrg h quos, w ob + b b y b b y hp://urclhodsgusfdu 8

9 Fdg coss of Epol Modl Subsug bck o h prvous quo b b b b y y Th cos b c b foud hrough urcl hods such s bsco hod b b y Solvg h frs quo for ylds hp://urclhodsgusfdu 9

10 Epl -Epol Modl My ps g cocrd wh s volvs jco of rdocv rl For pl for scg gllblddr, fw drops of Tchu-99 soop s usd Hlf of h Tchu-99 would b go bou 6 hours I, howvr, ks bou 4 hours for h rdo lvls o rch wh w r posd o dy-o-dy cvs Blow s gv h rlv sy of rdo s fuco of Tbl Rlv sy of rdo s fuco of (hrs) γ hp://urclhodsgusfdu

11 Epl -Epol Modl co Th rlv sy s rld o by h quo γ A λ Fd: ) Th vlu of h rgrsso coss A d λ b) Th hlf-lf of Tchu-99 c) Rdo sy fr 4 hours hp://urclhodsgusfdu

12 Plo of d hp://urclhodsgusfdu

13 Coss of h Modl Th vlu of λ s foud by solvg h olr quo ( ) f λ λ λ λ γ γ λ A λ λ γ A λ γ hp://urclhodsgusfdu 3

14 Sg up h Equo MATLAB ( ) f λ λ λ λ γ γ λ (hrs) γ hp://urclhodsgusfdu 4

15 Sg up h Equo MATLAB ( ) f λ λ λ λ γ γ λ [ ] g[ ] sys ld susu(g**p(ld*)); susu(g*p(ld*)); su3su(p(*ld*)); su4su(*p(*ld*)); fsu-su/su3*su4; 5 λ hp://urclhodsgusfdu 5

16 Clculg h Ohr Cos Th vlu of A c ow b clculd A 6 6 γ λ λ 9998 Th pol rgrsso odl h s γ hp://urclhodsgusfdu

17 Plo of d d rgrsso curv γ hp://urclhodsgusfdu

18 Rlv Isy Afr 4 hrs Th rlv sy of rdo fr 4 hours γ Ths rsul pls h oly ( 4) 637% rdocv sy s lf fr 4 hours 8 hp://urclhodsgusfdu

19 Howork Wh s h hlf-lf of Tchu-99 soop? Wr progr h lgug of your choc o fd h coss of h odl Copr h coss of hs rgrsso odl wh h o whr h d s rsford Wh f h odl ws γ λ? 9 hp://urclhodsgusfdu

20 THE END hp://urclhodsgusfdu hp://urclhodsgusfdu

21 Polyol Modl Gv ( ) (, y), (, y),, (, y o gv d s ) bs f (, y ) y (, y ) (, y ( ), y ) y f ( ) y Fgur Polyol odl for olr rgrsso of y vs d hp://urclhodsgusfdu

22 Polyol Modl co Th rsdul ch d po s gv by y E Th su of h squr of h rsduls h s ( ) r y E S hp://urclhodsgusfdu

23 Polyol Modl co To fd h coss of h polyol odl, w s h drvvs wh rspc o whr ( ) ( ) ( ) ) ( ) ( ) ( r r r y S y S y S,, qul o zro hp://urclhodsgusfdu 3

24 Polyol Modl co Ths quos r for r gv by + + y y y Th bov quos r h solvd for,,, hp://urclhodsgusfdu 4

25 Epl -Polyol Modl Rgrss h hrl pso coffc vs prur d o scod ordr polyol Tbl D pos for prur vs Tprur, T ( o F) Coffc of hrl pso, α (// o F) α Thrl pso coffc, α (// o F) 7E-6 6E-6 5E-6 4E-6 3E-6 E-6 E Tprur, o F 5 Fgur D pos for hrl pso coffc vs prur hp://urclhodsgusfdu

26 Epl -Polyol Modl co T T α + + W r o f h d o h polyol rgrsso odl T T T T T T T T T T α α α Th coffcs,, r foud by dffrg h su of h squr of h rsduls wh rspc o ch vrbl d sg h vlus qul o zro o ob hp://urclhodsgusfdu 6

27 Epl -Polyol Modl co 7 Th cssry suos r s follows Tbl D pos for prur vs α 5 Tprur, T ( o F) Coffc of hrl pso, α (// o F) T 3 T 4 T 7 α T α 6978 T α hp://urclhodsgusfdu

28 Epl -Polyol Modl co Usg hs suos, w c ow clcul,, Solvg h bov sys of sulous lr quos w hv Th polyol rgrsso odl s h α + T + T T 8 T 8 hp://urclhodsgusfdu

29 Trsforo of D To fd h coss of y olr odls, rsuls solvg sulous olr quos For hcl covc, so of h d for such odls c b rsford For pl, h d for pol odl c b rsford As show h prvous pl, y chcl d physcl procsss r govrd by h quo, b y Tkg h url log of boh sds ylds, l y l + b L z l y d l W ow hv lr rgrsso odl whr (plyg) o wh b z + 9 hp://urclhodsgusfdu

30 Trsforo of d co Usg lr odl rgrsso hods, z z z Oc, o r foud, h orgl coss of h odl r foud s b hp://urclhodsgusfdu 3

31 THE END hp://urclhodsgusfdu 3 hp://urclhodsgusfdu

32 Epl 3-Trsforo of d My ps g cocrd wh s volvs jco of rdocv rl For pl for scg gllblddr, fw drops of Tchu- 99 soop s usd Hlf of h Tchu-99 would b go bou 6 hours I, howvr, ks bou 4 hours for h rdo lvls o rch wh w r posd o dy-o-dy cvs Blow s gv h rlv sy of rdo s fuco of Tbl Rlv sy of rdo s fuco of (hrs) γ Rlv sy of rdo, γ 5 5 T, (hours) 3 Fgur D pos of rlv rdo sy vs hp://urclhodsgusfdu

33 Epl 3-Trsforo of d co Fd: ) Th vlu of h rgrsso coss A d λ b) Th hlf-lf of Tchu-99 c) Rdo sy fr 4 hours Th rlv sy s rld o by h quo γ A λ 33 hp://urclhodsgusfdu

34 Epl 3-Trsforo of d co Epol odl gv s, γ A λ ( γ ) l( A) + λ z lγ, l( A) l Assug o d λ w ob z + Ths s lr rloshp bw z d 34 hp://urclhodsgusfdu

35 Epl 3-Trsforo of d co, Usg hs lr rloshp, w c clcul d z z λ A z whr 35 hp://urclhodsgusfdu

36 Epl 3-Trsforo of D co Suos for d rsforo r s follows Tbl Suo d for Trsforo of d odl γ z lγ z Wh z 6 6 z hp://urclhodsgusfdu

37 Epl 3-Trsforo of D Clculg, ( 899) ( 5)( 8778) 6( 65) ( 5) co 6 55 Sc lso l A ( A) 65 5 ( 55) λ hp://urclhodsgusfdu

38 Epl 3-Trsforo of D co Rsulg odl s γ γ Rlv Isy of Rdo, 5 5 T, (hrs) Fgur Rlv sy of rdo s fuco of prur usg rsforo of d odl 38 hp://urclhodsgusfdu

39 Epl 3-Trsforo of D co Th rgrsso forul s h γ b) Hlf lf of Tchu-99 s whγ l 6 48 hours ( 5) 55( ) ( 99974) γ 39 hp://urclhodsgusfdu

40 Epl 3-Trsforo of D co c) Th rlv sy of rdo fr 4 hours s h 55( 4 γ ) Ths pls h oly 636% of h rdocv rl s lf fr 4 hours 4 hp://urclhodsgusfdu

41 Coprso Coprso of pol odl wh d whou d Trsforo: Tbl Coprso for pol odl wh d whou d Trsforo Wh d Trsforo (Epl 3) Whou d Trsforo (Epl ) A λ Hlf-Lf (hrs) Rlv sy fr 4 hrs hp://urclhodsgusfdu

42 Addol Rsourcs For ll rsourcs o hs opc such s dgl udovsul lcurs, prrs, book chprs, ulpl-choc ss, workshs MATLAB, MATHEMATICA, MhCd d MAPLE, blogs, rld physcl probls, pls vs hp://urclhodsgusfdu/opcs/olr_r grssohl

43 THE END hp://urclhodsgusfdu

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