GEOMETRIC OPTIMISATION OF CONJUGATE COOLING CHANNELS WITH DIFFERENT CROSS-SECTIONAL SHAPES

Transcription

1 GEOMETRIC OPTIMISATION OF CONJUGATE COOING CHANNES WITH DIFFERENT CROSS-SECTIONA SHAPES By Olabode Thoma OAKOYEJO Prof. T. Bello Ochende, Prof. J. P. Meyer Department of Mechanical and Aeronautical Engineering, Univerity of Pretoria, South Africa 13 : 02 :

2 Outline Introduction Background Motivation/Application Aim/Objective Objective function Methodology Work done Reult/Graph Concluion Future work

3 Introduction Heat generating device and Thermal management Heat generating device, uch a high power electronic equipment and heat exchanger are widely applicable in engineering field e.g electronic chip cooling, power and energy ector. Heat generation can caue overheating problem and thermal tree and may lead to ytem failure. Cooling of heat generating device critical challenge to thermal deign engineer and reearcher. Heat generating device are deigned in uch a way a to optimie the tructural geometry by packing and arranging array of cooling channel into given and available volume contraint without exceeding the allowable temperature limit pecified by the manufacturer. Thi tranlate into the maximiation of heat tranfer denity or the minimiation of overall global thermal reitance, which i a meaure of the thermal performance of the cooling device. H d q Flow W Elemental Volume v el Global Volume V

4 Introduction Modern Heat Tranfer: Geometry and Shape Optimiation Channel geometric deign affect the thermal performance of Heat tranfer Geometry optimization of variou hape and ize H d q Flow W Elemental Volume v el Global Volume V w, h,, dh Convective heat tranfer Heat tranfer Performance Nu h k Characteritic length cale Conductive heat tranfer Geometry Shape Optimation parameter Fig 1. The Nuelt Number (Nu), a meaure of heat tranfer performance

5 Background: Contructal Theory and Deign Bejan and Sciubba (1992),conidered the optimization pacing of board to board of an array of parallel plate that can be fitted in a fixed volume in an electronic cooling ytem Muzychka (2005), analytical optimiation the geometry of circular and noncircular cooling channel. Ordonez (2004), Numerically, conducted a two-dimenional heat tranfer analyi in a heat-generated volume with cylindrical cooling channel and air a the working fluid. d opt 4.683Be 1/ 4 H d q Flow Q * ''' 2 Q k T T n i HW 2 d C Be 3 1/ 2 W Elemental Volume v el n HW d 2 Global Volume V Fig 2. Convectively conducting volume with cooling channel

6 Method of interection of aymptote 0 dh P T in d 0 h When the channel characteritic dimenion cale i mall and ufficiently lender, D 0, D << H d q Flow T in P dh R W Elemental Volume v el Global Volume V When the channel cro-ectional area i large, D R d d 2/3 h h R d h P d h opt T in When the channel cro-ectional area i at optimum 2 h R d d h 0 Fig 3. Method of interection of aymptote d hopt d h

7 Motivation/Application The advent of high denity component ha required invetigation of innovative technique for removing heat from thee device Better and optimal performance Cot minimization Application Electronic cooling Compact heat exchanger, Automotive Nuclear power

8 Aim/Objective Aim : To carry out theoretical and numerical optimization tudie in conjugate heat tranfer in cooling channel with different cro-ection and under varoiu condition Objective : To minimie the dimenionle maximal exce of temperature or global thermal reitance The objective will be conducted in two phae: Analytical (Theory) Analyi Numerical Analyi Optimiation proce by uitable mathematical algorithm

9 Reearch activitie/work done Part 1 : Optimiation of Conjugate Heat Tranfer In Cooling Channel with Internal Heat Generation for Different Cro-ectional Shape Part 2 : Optimiation of aminar-forced Convection Heat Tranfer Through a Vacularied Solid with Cooling Channel Part 3 : Effect of flow orientation on forced convective heat tranfer in cooling channel with internal heat generation

10 PART 1 Optimiation of Conjugate Heat Tranfer In Cooling Channel with Internal Heat Generation for Different Cro-ectional Shape

11 Numerical Modelling: Problem under conideration H W Elemental Volume v el d q Global Volume V Flow H W Elemental Volume v el w c q Global Volume V Flow T in Fluid flow P H W Elemental Volume v el q Global Volume V T in Fluid flow P H W Elemental Volume v el q Global Volume V Fig 4. Three-dimenional parallel channel with different cro ection acro a lab with internal heat generation and forced flow.

12 Problem under conideration Fluid flow T 0 z P T in d h 2 w T y 0 T x 0 T y 0 T z h 0 Fluid flow T 0 z P T in d h 2 w c w T y 0 T x 0 T y 0 T z h T 0 h c y T in P w c Fluid flow y 1 2 z x w T 0 y T 0 x Solid, q' '' T 0 y T 0 h z Fig 5 The three dimenional computational domain Elemental volume with cooling channel P Fluid flow T in h h c 2 /2 d h 1 /2 T 0 z w c w Periodic q Symmetry Periodic T 0 z

13 Objective function and Aumption The objective i the minimiation of the global thermal reitance R k T T max in f q min 2 min R f d, v, T min h opt el opt max min ( P1.1) Aumption Fluid flow and heat tranfer : teady-teady tate condition three dimenional. ingle phae aminar Newtonian fluid with contant propertie (Water) Micro-cale cooling channel

14 Numerical Modelling /Analyi/Optimiation y z x Fig 6: The dicretied 3-D computational domain

15 Numerical Modelling/Analyi Govering Equation u 0 ( P1.2) 2 u u P u ( P1.3) 2 C u T k T f Pf f ( P1.4) Energy equation for a olid region i given a: k 2 T 0 ( P1.5)

16 Numerical Modelling/Analyi Boundary Condition Unit cell uing ymmetry Internal heat generation The continuity of the heat flux at the interface between the olid and the liquid i given a k T n k f u 0 T n A no-lip boundary condition i pecified at the wall of the channel, At the inlet ( x = 0 ) At the outlet ( x = ), zero normal tre P 1 atm out Be u u 0, T T, P P 2 x y in in out At the olid boundarie T 0 ( P1.6) ( P1.7) ( P1.8) ( P1.9) ( P1.10)

17 Numerical Modelling/Analyi Summary of Boundary Condition Fluid flow T 0 z P T in d h 2 w T y 0 T x 0 T y 0 T z h 0 Fluid flow T 0 z P T in d h 2 w c w T y 0 T x 0 T y 0 T z h 0 T in Fluid flow 2 2 T 0 y P y 1 2 h c z x w c w T 0 y T x 0 Solid, q' '' T 0 y T 0 h z Fig 7 The boundary condition of the three dimenional Computational domain of the cooling channel P Fluid flow T in h h c 2 /2 d h 1 /2 T 0 z w c w Periodic q Symmetry Periodic T 0 z

18 Optimiation Contraint An elemental volume contraint i conidered to compoe of elemental cooling channel of hydraulic diameter 2 vel w w dh,, The number of channel in the tructure arrangement can be defined a: ( P1.11) N HW hw ( P1.12) The void fraction or poroity of the unit tructure can be defined a: v v c el The contraint range are: ( P1.13) h y T k q z x z T 0 y T 0 x T 0 y h c 2 w c w T 0 z P T in Fluid flow , 50m w 500 m, 0 d w, 0 w h ( P1.14)

19 Static Temperature ( 0 C) Numerical analyi/ Grid independent tet The numerical olution of the continuity, momentum and energy Equation alongide with boundary condition wa obtained by uing a three dimenional commercial package FUENT that employ a finite volume method. The olution i aid to be converged when the normalized reidual of the ma and momentum equation fall below 10-6 and that of the energy equation i le than Cell Cell Cell Grid independent tet for everal meh refinement were carried out to enure the accuracy of the numerical reult Z The convergence criterion for the overall thermal reitance a the quantity monitored T T max max i T max i i Fig 8 : Grid independent tet ( P1.15)

20 Numerical Reult Finding /Graph T max ( 0 C ) CASE STUDY 1: Cylindrical and quare cooling channel embedded in high-conducting olid Be= 10 8 Pr = 1 k 300 k f Ordonez [15] Preent tudy P = 50kPa 29 T max T max min Poroity Increaing T max min Cyl ( Sqr ( Cyl ( Sqr ( Cyl ( Sqr ( Fig 9a. Thermal reitance curve : preent tudy and ordoenez d h v el ( mm 3 ) Fig 9b Effect of optimied elemental volume on the peak temperature

21 T max ( 0 C ) T max ( 0 C ) Numerical Reult Finding /Graph CASE STUDY 1: Cylindrical and quare cooling channel embedded in high-conducting olid 31 P = 50kPa Cyl ( Sqr ( 31 P = 50kPa Cyl ( 30 Sqr ( Cyl ( 30 Sqr ( T max min Poroity Increaing d ( m ) h ( m ) Fig 10 Effect of optimied hydraulic diameter and pacing on the peak temperature Poroity Increaing Cyl ( Sqr ( Cyl ( Sqr ( Cyl ( Sqr ( T max min

22 T max ( 0 C ) Numerical Reult Finding /Graph T max ( 0 C ) CASE STUDY 2: Truagular cooling channel embedded in highconducting olid 30 I-R Triangle ( Equi Triangle ( I-R Triangle ( Equi Triangle ( 30 I - R Triangle ( Equi Triangle ( I - R Triangle ( Equi Triangle ( 28.5 T max min T max min 28 Poroity Increaing Poroity Increaing d / h v ( mm 3 ) el Fig. 11 Effect of optimied hydraulic diameter and elemental volume on the peak temperature

23 T max ( 0 C ) Numerical Reult Finding /Graph T max ( 0 C ) CASE STUDY 3: Rectangular cooling channel embedded in highconducting olid T max min 27.6 T max min AR c d h / Fig. 12. Effect of optimied apect ratio and hydraulic diameter on the peak temperature

24 Mathematical Optimiation: DYNAMIC-Q Algorithm (by Prof. Snyman) Standard optimization problem T min f x; x, x,... x... X,, x 1 2 i n i x Subject to 0, 1,2,... g x j p j n ( P1.16) ( P1.17) To earch for the: dhopt 0 d h opt 0 k 0, 1,2,... h x k q ( P1.18) R min f d h, opt opt, opt Contraint Poroity 2 vc dh v el w ( P1.19)

25 Mathematical Optimiation DYNAMIC-Q Algorithm Very robut Gradient baed method Penalty function technique Approximation of numerical function by pherical quadratic function Forward differencing for gradient approximation. Automation of the proce Start Initialie the optimiation by pecifying the initial gue of the deign variable xo GAMBIT Journal file Setting deign variable Geometry & meh generation Importing geometry and meh to FUENT FUENT Journal file FUENT Journal file 3-D CFD imulation ( olving model) T T T 1 T f x f x f x x x x x A x x 2 l l l l l 1 T l l l l l l g x g x g x x x x x B x x, i 1,... p i i i i 2 1 T l l l l l l h x h x h x x x x x C x x, j 1,... q j j j j 2 Defining the boundary condition CFD imulation ( olving model) CFD imulation converged? Ye Pot-proceing: data and reult proceing Mathematical optimiation ( Dynamic-Q Algorithm ) No ( P1.20) Optimiation olution converged? Ye Predicted new optimum deign variable and objective function f(x) No Fig. 13. flow chart of numerical imulation Stop

26 Numerical Reult Finding /Graph Cylindrical, quare, triangular and rectangular cooling channel embedded in high-conducting olid 10-3 Cyl ( Sqr ( Cyl ( Sqr ( 10-3 I-T Triangle ( E-T Triangle ( I-T Triangle ( 10-3 Rect ( Rect ( E-T Triangle ( R min 10-4 R min R min Be Be Be Fig. 14 : Effect of dimenionle preure difference on the minimied dimenionle global thermal reitance

27 Numerical Reult Finding /Graph dh opt / dh opt / Numerical Cyl ( Numerical Cyl ( Numerical Sqr ( Numerical Sqr ( Analytical reult Cyl Analytical reult Sqr 10-1 I-T Triangle ( E-T Triangle ( I-T Triangle ( E-T Triangle ( Rect ( Rect ( (d h /) opt Be Be Be Fig. 15 Effect of dimenionle preure difference on optimied dimenionle hydraulic diameter

28 Numerical Reult Finding /Graph I-T Triangle ( (/) opt opt (um)cyl (0.1) 0.01 opt (um)cyl (0.2) opt (um)qr (0.1) opt (um)qr (0.2) Be ( 1 / 2 ) opt Rect ( Rect ( Be ( 1 / 2 ) opt E-T Triangle ( I-T Triangle ( E-T Triangle ( Be Fig. 16 Effect of dimenionle preure difference on optimied dimenionle pacing

29 Analytical Solution Method of interection of aymptote for conjugate channel with internal heat generation EXTREME IMIT 1: SMA CHANNE EXTREME IMIT 2: ARGE CHANNE P P T in T in When the channel characteritic dimenion cale i mall and ufficiently lender, D 0, D << When the channel cro-ectional area i large, D k Tmax Tin d 2 f h R 4P 1 o Be 2 dh q (P1.21) k Tmax Tin 2 / 3 f dh R Be 1/ 3 q 2 (P1.22) The hydraulic diameter become maller, the global thermal reitance increae. The hydraulic diameter become lager, the global thermal reitance increae.

30 The geometric optimiation in term of channel diameter could be achieved by combining Eq. (P1.21) and (P1.22) uing the interection of aymptote method a hown in R P T in R d d 2/3 h h When the channel cro-ectional area i at optimum R d h dh opt P o dh Be 3/8 1/ 4 (P1.23) 2 R dh dh odh opt 1/ 2 3/8 1/ 4 P Be (P1.24) d hopt d h Fig. 17: Interection of aymptote method R 1/ 4 1/ 2 min Po Be dh (P1.25)

31 Comparion of the Theoretical Method and Numerical Optimiation R min 10-4 Numerical Cyl ( Numerical Sqr ( Numerical Cyl ( Numerical Sqr ( Analytical reult Cyl Analytical reult Sqr 10-4 I-T Triangle ( E-T Triangle ( I-T Triangle ( E-T Triangle ( Analytical reult I-T Triangle Analytical reult E-T Triangle 10-4 Rectangle ( Rectangle ( Analytical reult R min R min Be Be Be Fig. 18 : Correlation of the numerical and analytical olution for the minimied global thermal reitance

32 Comparion of the Theoretical Method and Numerical Optimiation dh opt / dh opt / (d h /) opt Numerical Cyl ( Numerical Cyl ( Numerical Sqr ( Numerical Sqr ( Analytical reult Cyl Analytical reult Sqr 10-1 I-T Triangle ( E-T Triangle ( I-T Triangle ( E-T Triangle ( Analytical reult I-T Triangle Analytical reult E-T Triangle 0.02 Rectangle ( Rectangle ( Analytical reult Be Be Be Fig. 19: Correlation between the numerical and analytical olution for the optimied hydraulic diameter

33 P uid flow T in Comparion of the thermal performance of the cooling channel hape tudied h h c 2 /2 R min d h /2 1 T z w c w Periodic q Symmetry Periodic T 0 z Cyl ( Sqr ( I- R Triangle ( Equi Triangle ( Rect ( Cyl ( Sqr ( I - R Triangle ( Equi Triangle ( Rect ( Be Bet Fluid flow T 0 z P T in T 0 y T 0 x T 0 y It wa clearly oberved that the cooling effect wa bet achieved at a higher apect ratio of rectangular channel. However the optimal deign cheme could well lead to a deign that would be impractical at very high channel apect ratio, due to the channel being too thin to be manufactured Fig. 20: Comparion of the thermal performance of the cooling channel hape tudied d h 2 w 2 2 T 0 h c y T in P w c Fluid flow y 1 2 z x w h T 0 z T 0 y T 0 x Solid, q' '' T 0 y Poor T 0 h z

34 Numerical Reult : Temperature ditribution (a) (b) Fig.21. Temperature ditribution on (a) the elemental volume and (b) cooling fluid and inner wall.

35 PART 2 Optimiation of aminar-forced Convection Heat Tranfer Through A Vacularied Solid with Cooling Channel

36 Introduction Material with the property of elf-healing and elf-cooling i becoming more promiing in heat tranfer analyi. The development of vaculariation of the material indicate flow architecture that conduct and circulate fluid at every point within the olid body. Thi olid body (lab) may be performing or experiencing mechanical function uch a mechanical loading, ening and morphing. Thi elf-cooling ability of the vacularied material to bathe at every point of a olid body gave birth to the name mart material. a olid body of fixed global volume, which i heated with uniform heat flux on the right ide; the body i cooled by forcing a ingle-phae cooling fluid (water) from the left ide into the parallel cooling channel Global v olume V Elemental olume v v el q Heating H d w h H h c c P Tin Fluid W flow Fig 22. Three-dimenional parallel quare channel acro a lab with heat flux from one ide and forced flow from the other ide.

37 Objective function and Aumption The objective i the minimiation of the global thermal reitance R min k T T max in f q min R f d, v, T min h opt el opt max min ( P2.1) Aumption a in part 1

38 Numerical Modelling /Analyi y z x Fig. 23: The dicretied 3-D computational domain

39 Numerical Modelling/Analyi Governing Equation and BC a in Part 1 except Energy equation for a olid region i given a: k 2 T 0 ( P2.2) Global v olume V Elemental olume v v el Boundary Condition q Heating H d w h H h c c P Tin Unit cell uing ymmetry Heat flux input at the left ide T 0 y W Fluid flow k T z q ( P2.3) h y T k q z x z T 0 x T 0 y h c 2 w c w T 0 z P Fluid flow T in

40 Optimiation Contraint An elemental volume contraint i conidered to compoe of elemental cooling channel of hydraulic diameter 2 vel w h w w dh N,,, The number of channel in the tructure arrangement can be defined a: HW d 2 h ( P2.4) q Heating ( P2.3) Global v olume V Elemental v olume vel H d w h H h c c P Tin The void fraction or poroity of the unit tructure can be defined a: W Fluid flow 2 v d c h v w el The contraint range are: ( P2.5) h y T k q z x z T 0 y T 0 x T 0 y h c 2 w c w T 0 z P Fluid flow T in , 0.02 w 0.5, 0 d w, 0 w h ( P2.6)

41 T max ( 0 C ) Numerical Reult Finding /Graph T max ( 0 C ) 50 ( ( ( T max min 30 Poroity increaing T max min 25 Poroity increaing ( ( ( d h / v el ( mm 3 ) Fig. 24. Effect of optimied dimenionle hydraulic diameter and elemental volume on the peak temperature

42 Optimiation Reult 10-1 ( ( ( dh opt / DYNAMIC-Q Algorithm 10 0 ( ( ( R min Be Fig. 25 Effect of dimenionle preure difference on the dimenionle thermal reitance and the optimied hydraulic diameter Be

43 T max ( 0 C ) 45 Be = 10 8 dh opt n/ Numerical analyi/reult : Effect of material propertie k r = 10 k r = 100 Be = T max min R min K r 4000 Kr Increaing d / h Be = 10 8 k r At higher thermal conductivity ratio, the thermal conductivity ha negligible effect on minimied thermal reitance and optimied hydraulic diameter K r 4000 Fig. 26. Effect of material propertie on optimied geometry minimied and thermal reitance k r

44 dh opt / opt / Optimiation Reult Effect of material propertie Kr on thermal reitance and optimied geometry K =1( r K =1( r K =10( r K =10( r K =100( r K =100( r K r =1 ( K =1 ( r K =10 ( r K r =10 ( K r =100 ( K =100 ( r 1 K =1 ( r K =1 ( r K =10 ( r K =10 ( r K =100 ( r K =100 ( r R min Be Be Be Fig. 27 Effect of material propertie Kr on thermal reitance and optimied geometry

45 Temperature Profile (a) (b) Fig 28. Temperature ditribution on (a) the elemental volume and (b) cooling fluid and inner wall.

46 Analytical Solution EXTREME IMIT 1: SMA CHANNE EXTREME IMIT 2: ARGE CHANNE P P T in T in When the channel characteritic dimenion cale i mall and ufficiently lender, D 0, D << When the channel cro-ectional area i large, D 2 k f T T 32 d R h Be q max in 1 ( P2.7) R 12 k T T f max in 1 h 0.75 d kr, q (P2.8) A the hydraulic diameter become maller, the global thermal reitance increae. A the hydraulic diameter become larger, the global thermal reitance increae.

47 Analytical Solution The geometric optimiation in term of channel diameter could be achieved by combining Eq. (P2.7) and (P2.8) uing the Interection of aymptote method a hown in Fig. 9. T max P T max d h T in When the channel cro-ectional area i at optimum T d max h opt d h opt kr Be ( P2.9) T d h max 0 k f Tmax Tin min Rmin 2.62 kr Be, q ( P2.10) d hopt Fig. 29: Interection of aymptote method d h

48 Optimiation Reult Effect of material propertie Kr on optimied geometry R min (k r ) 2/ k = 1 r k r = 10 k = 100 r k r = 1 k = 10 r k r = 100 Analytical reult ( dh opt / ) (k r ) -1/ k = 1 r k r = 10 k = 100 r k = 1 r k r = 10 k = 100 r Analytical reult 10-2 ( opt / ) (k r ) -1/ k r = 1 k r = 10 k r = 100 k = 1 r k r = 10 k r = 100 Analytical reult Be Be Be Fig. 30 : Correlation of the numerical and analytical olution for the minimied global thermal reitance

49 PART 3 Effect of flow orientation on forced convective heat tranfer in cooling channel with internal heat generation

50 Introduction : Numerical Anayi d h Symmetry H Flow H Flow Elemental Volume v el d h Elemental Volume v el d h H Flow W Elemental Volume v el W W q Global Volume V q Global Volume V q Global Volume V P T P in T h Fluid flow P in h Fluid flow T in d h T 0 z h Fluid flow d h T 0 z d h T 0 z w w w Periodic Periodic q q q T 0 z Symmetry T 0 z T 0 z Periodic Periodic The array of channel with parallel flow refer a PF-1. The array of channel in which flow of the every other row channel i in counter direction to one another refer a CF-2. The every flow in the array of channel i in counter direction to one another, refer a CF-3 Fig. 31 : Three dimenional parallel circular of PF-1, CF-2 and CF-3

51 Objective function and Aumption The objective i the minimiation of the global thermal reitance R k T T max in f q min 2 min ( P3.1) R f d,, v, T, flow orientation min hopt opt elopt max min Aumption a in part 1

52 Numerical Modelling /Analyi y z x Fig 32. The dicretied 3-D computational domain

53 Numerical Modelling/Analyi Governing Equation a in Part 1 Boundary Condition P T in h Fluid flow d h T 0 z w Symmetry q T 0 z Symmetry Periodic P T in h Fluid flow d h T 0 z w Periodic q T 0 z Periodic P T in h Fluid flow d h T 0 z w Fig. 33 The boundary condition of the three dimenional Computational domain of the cooling channel q T 0 z Periodic

54 Optimiation Contraint An elemental volume contraint i conidered to compoe of elemental cooling channel of hydraulic diameter 2 vel w h w w dh,,, For a fixed length of the channel, the cro-ectional area of the tructure i A The number of channel in the tructure arrangement can be defined a: N The void fraction or poroity of the unit tructure can be defined a: HW HW hw v 4 v The contraint range are: c el v c 4 2 d h ( P3.2) ( P3.3) ( P3.4) ( P3.5) mm 20mm, , 0, 0, 0 el v w d w w h ( P3.6)

55 T max ( 0 C ) T max ( 0 C ) Numerical Reult PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( Poroity increaing d h / T max min Poroity increaing PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( v el ( mm ) T max min Fig. 34 Effect of optimied dimenionle hydraulic diameter and elemental volume on the peak temperature

56 10-3 dh opt / opt / Numerical Reult PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( 0.1 R min PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( Be Be PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( PF-1 ( CF-2 ( CF-3 ( Be Fig. 35 Effect of dimenionle preure difference on the dimenionle thermal reitance and the optimied geometrie

57 Concluion : Part 1 It i all about ize and hape Size and hape ignificant have effect on the thermal performance of heat-generating device. The global thermal reitance i a function of applied dimenionle preure difference number (pumping power) and the channel configuration. Exitence of unique optimal deign variable for a given applied dimenionle preure number for each configuration tudied. Therefore, thermal deigner can pick an optimal olution according to the applied dimenionle preure difference number (Be) available to drive the fluid or thermal reitance required. The cooling effect wa bet achieved at a higher apect ratio of rectangular channel. The performance of the cylindrical channel wa poorer than that of any other channel, it wa a more viable option and more often ued in indutry due to the eae of manufacturability and packaging. The optimal channel pacing ratio ( 1 / 2 ) remain unchanged and inenitive to the performance of the ytem regardle of the preure difference number for the two triangular configuration The optimal deign cheme could well lead to a deign that would be impractical at very high channel apect ratio, due to the channel being too thin to be manufactured

58 Concluion : Part 2 Thi part tudied the numerical optimiation of geometric tructure of quare cooling channel of vacularied material with the localied elf-cooling property ubject to heat flux on one ide in uch a way that the peak temperature i minimied at every point in the olid body. There i exitence of unique optimal deign variable (geometrie) for a given applied dimenionle preure number for fixed poroity. Minimized thermal reitance decreae with increaing Kr and Be. That i the material property and driving force have great influence on the performance of the cooling channel. Therefore, when deigning the cooling tructure of vacularied material, the internal and external geometrie of the tructure, material propertie and pump power requirement are very important parameter to be conidered in achieving efficient optimal deign for the bet performance.

59 Concluion : Part 3 The reult alo how that the flow orientation ha a trong influence on the convective heat tranfer. For pecified applied dimenionle preure difference and poroity, CF-2 and CF-3 orientation perform better than the PF-1 orientation. Therefore, when deigning the cooling tructure of heat exchange equipment, the internal and external geometrie of the tructure, flow orientation and the pump power requirement are very important parameter to be conidered in achieving efficient and optimal deign for the bet performance. The thermal deigner can pick an optimal olution according to the applied dimenionle preure difference number (Be) available to drive the fluid or thermal reitance required.

60 Recommendation for Future work Circular Y-hape cooling channel D 2d D d v v c el R f D, d, 1, 2, w,, min hopt hopt opt opt opt opt opt

61 Recommendation for Future work Multi-cale deign of compact cooling channel Future model Flow H D h q d h Flow W Elemental Volume v el Global Volume V

62 Recommendation for Future work Invetigation of the effect of pin fin of any hape tranverely arranged along the flow channel of the configuration on the temperature ditribution and dimenionle preure difference characteritic with the global objective of minimiing thermal reitance and improving thermal performance. Turbulent and tranient fluid flow. Effect of temperature-dependent of the thermo-phyical propertie of fluid on the minimied thermal reitance. R f ( ( T), ( T), k( T)) min enitive to temperature change due to relatively large variation of working fluid propertie at high heat flux and low Reynold number (Re).

63 it of Publication from the Reearch The following article, book chapter and conference paper were produced during thi reearch. 1. O.T. Olakoyejo, T. Bello-Ochende and J.P Meyer, Mathematical optimiation of laminar forced convection heat tranfer through a vacularied olid with quare channel, International Journal of Heat and Ma Tranfer, Vol. 55, pp , ( Publihed) 2. O.T. Olakoyejo, T. Bello-Ochende and J.P Meyer; Contructal conjugate cooling channel with internal heat generation, International Journal of Heat and Ma Tranfer, Vol. 55, pp , ( Publihed) 3. T. Bello-Ochende, O.T. Olakoyejo and J.P Meyer, Chapter 11, Contructal Deign of Rectangular Conjugate Channel Publihed in the book, Contructal aw and the Unifying Principle of Deign,.A.O Rocha, S. orente and A. Bejan, ed., pp , Springer Publiher, New York, ( Publihed) 4. J.P Meyer, O.T. Olakoyejo, and T. Bello-Ochende; Contructal optimiation of conjugate triangular cooling channel with internal heat generation, International communication of Heat and Ma Tranfer, Vol. 39, pp , (Publihed).

64 it of Publication from the Reearch 5. T. Bello-Ochende, O.T. Olakoyejo, and J.P Meyer; Contructal flow orientation in conjugate cooling channel with internal heat generation, International Journal of Heat and Ma Tranfer, Vol. 57, pp , (Publihed). 6. O.T. Olakoyejo, T. Bello-Ochende and J.P Meyer, Optimiation of circular cooling channel with internal heat generation, Proceeding of the 7 th International Conference on Heat Tranfer, Fluid Mechanic and Thermodynamic, Antalya, Turkey, pp , July ( Preented) 7. O.T. Olakoyejo, T. Bello-Ochende and J.P Meyer, Geometric Optimiation of Forced Convection In Cooling Channel With Internal Heat Generation Proceeding of the 14 th International Heat Tranfer Conference, Wahington D.C, USA, pp , 8-13 Augut ( Preented) 8. O.T. Olakoyejo, T. Bello-Ochende and J.P Meyer, Geometric optimiation of forced convection in a vacularied material, Proceeding of the 8 th International Conference on Heat Tranfer, Fluid Mechanic and Thermodynamic, Pointe Aux Piment, Mauritiu, pp , July, 2011 (Preented and awarded bet paper of the eion).

65 it of Publication from the Reearch 9. O.T. Olakoyejo, T. Bello-Ochende and J.P. Meyer, Contructal optimiation of rectangular conjugate cooling channel for minimum thermal reitance, Proceeding of the Contructal aw Conference, December, 2011, Porto Alegre, Univeridade Federal do Rio Grande do Sul, Brazil. ( Preented) 10. O.T. Olakoyejo, T. Bello-Ochende and J.P Meyer, Optimiation of conjugate triangular cooling channel with internal heat generation, 9 th International Conference on Heat Tranfer, Fluid Mechanic and Thermodynamic, Malta, July, (Preented) 9. O.T. Olakoyejo, T. Bello-Ochende and J.P Meyer, Flow orientation in conjugate cooling channel with internal heat generation, 9 th International Conference on Heat Tranfer, Fluid Mechanic and Thermodynamic, Malta, July 16 18, (Preented).

66 Acknowledgment The Almighty God Supervior : - Prof. T. Bello-Ochende - Prof. J.P. Meyer. Prof eon iebenberg Prof. Bejan and orente Prof. Snyman (Emeritu) Academic and non-academic taff Thermo-fluid reearch tudent Friend. Parent and Sibling

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