an experimental study of convective heat transfer from...
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Ind ian Journal o f Enginecring & Mate ri a ls Scic llccs Vol. 9. December 2002, pp. 464-471
An experimental study of convective heat transfer from flat and ribbed surfaces t
Anda llib Tariq, S K Swain & P K Panigrahi
Dcparlme nt o f Mechanica l Eng ineering, Indi an Institute of Technology, Kanpur 208 016, India
Received 13 Decell/ber 2001: accepled 23 Seplell/ber 2002
Heat tran sfc r and fricti on cha raclCri stics of fl ow in a rec tangular channe l with a so lid rib mo unted on the bottom surface of the channc l ha ve becn in vestiga ted cxpcrimentally . Thc experime nts have been carried out at Rey no lds num ber (based on hydraulic di amete r o f the channel ) rangc o f 12 ,800 to 29,400. The skin fri c tio n coeffic ie nt, Nu ssclt number, ve loc ity and temperalllrc profile result s are presented. T he surface temperature images obta ined with the he lp of liquid c rystal thermography supple ment the undcrstanding o f fl ow phys ics with qua litative explanation. The ave rage Nusselt number for the ri bbed !low case is highe r in compari son to that fo r the fl at surface. The inc rease in skin friction coeffi c ient fo r the ribbed fl ow case is comparati ve ly less than the Nusselt number increase, indicating the e ffec ti veness o f the ribbed surface in hea t transfer e nhancemcnt app licat ions. The liquid c rystal the rmography images show the flow in the downstream reg ion o f the rib to bc two dirm:ns ional in naturc. The rec ircul ati on and rcattachme nt reg ion for the ribbed flow case and th e ir ro le in heattransfc r e fTec ti veness is clearl y vis ible in the liq uid crystal images.
Fl ow interruptio n created in fl ow passages at period ic inte rvals is a popular means fo r heat trans fe r en hancement. The flow passages (which may be of vari ous geometri es , for example tubular or rec tangular) or surfaces o f dev ices such as heat exchangers, ad vanced gas-coo led reactor fu e l c le ments, and e lectronic coo ling dev ices are usually roug hened or dimpl ed to improve the convective heat transfer. The ro ughness breaks up the viscou s sublayer and promotes loca l wall turbul ence. There is an incrcase in heat tran ~ fer fro m bo th the rough and smooth surfaces w ith s imu ltaneous increase in the pressure drop. Thus, it is o f inte rest to finrl out a roughness geometry that wi ll y ie ld hi gh heat transfer aug mcntati on with minimum pressure penalty . The rib tu rb ul ators have been inves ti gated by many in vest igators as a poss ibl e means for heat tran sfe r enhancement. These ribs increase the hea t tran sfer in the channel fl ows by increasing the heat transfer area (fin effec t) and by di sturbing the lami nar sub-layer (roughness effect).
Sunden r has presented an overview o f heat transfe r and fluid fl ow in rib-roughened rec tangular ducts. Geometric parameters such as channe l aspect ratio (II !?), rib he ig ht-to-passage hydrauli c diameter e/D" or blockage ra ti o, rib ang le of attack (a) , the manner in whi ch the ri bs are pos itio ned re lati ve to o ne another,
t pres..:nted at the 2S 'h National Co nfercnce 0 11 Fluid Mechanics & Flui d Power. he ld at Punj ab Engince ring Coll ege , C handi ga rh, du ring 13- 15 December 200 I
rib pitch-to-he ight ratio (s/e), rib shape and config uration have pronounced effects o n both local and overall heat trans fer coefficients. Some of these effects have been studi ed by many investigators2
.8
.
Investigations in the past2.4 mainly concerned the
overall pressure drop or friction factor and the average heat transfer coefficient or Nusselt number. Mo re recent studi es5
.8 have used new techniques, i.e.
laser Doppler ve loc itimetry , laser ho lographic inte rferometry and liquid crysta l thermog raphy to study the deta il s of the fl ow patte rn and temperature fi e ld. Improvements on the understand ing of the physical processes have been made.
The present inves tigations attempt to improve the physical understanding o f the flo w in a rib roughened channe l by simultaneous quantitative representation o f friction characte ri sti cs, heat transfe r characterist ics, ve loc ity profiles and temperature pro fil es. Liqui d c rys ta l the rmography has been used to visua lize the temperature field of the botto m surface o f the channel. Liquid crystal thermography uses liq uid c rysta ls, which ex ist between the solid and iso tropic liquid ph ase of some organic compounds. Inc ident light is scatte red selec ti vely and the change in the ir colour is observed depending on the temperature . The change in color is moni tored by image processi ng syste m and is used as a measure of the temperature fi e ld . One of the important advantages of th is no n-intrusive the rmography technique is to ill ustrate the fl ow footp rints and local va lues of temperature/heat transfer coefficient on the surface under in vestigation.
TARIQ el al.: CONVECTI VE HEAT TRANSFER FROM FLAT AN D RIB BED SURFACES 465
Liquid crysta l !ilee ts
Air g»p (3mm)
Square AI . ri b (13 X 13 mm)
Aluminum pl. te (3 mm)
o Bakel ite (25.4 mm)
II] B.kellte (1 3.0)
Air
----
Fig . I- Schematic d iagram of fl ow system, coordinate sys tem and instrumentati on
Thi s simultaneous "tlow visualization" enhances the understanding of underl ying physics and helps the investi gator in interpretation of the resul ts.
Experimental Procedure Fig. I shows the sketch of the ex perimental set up
used in thi s work. The ex perimental fac ility comprises of a fl ow circuit, an image process ing system, the traverse mechanism and the heating secti on. Velocity measurements have been carri ed out using a pitot static tube connected to a digital mi cromanometer (FCO 12 - Furness Contro ls Limited, England). Temperature in the thermal boundary layer is measured using a K-type thermocouple connected to a digital multi meter. Wall temperature di stributi ons have been recorded with liquid crystal sheets, ex posed to two 50 W tungs ten-halogen lamps, prov iding an excell ent co lour renderi ng even in the long run , a reasonab le hi gh effi cacy, hi gh luminance and compact size as descri bed by de Boer and Fi scher').
Flow circuit
The ex peri ments are perfo rmed in an open-loop airfl ow system. The air is sucked into the tes t secti on through a honey comb sec ti on, five anti-turbulence screens and a 3: I contrac ti on cone. The tes t sec ti on is fo llowed by a fl ow straightener to minimi ze the
intluence of blower noise in the test secti on. Speed of the blower is controlled by a speed controller (V ictor G 1000) supplied by Kirloskar Electric Co. Ltd ., India. The test channel is 3300 mm long with an aspect ra tio of 1.8: I, (298x 160 mm2 in the verti cal pl ane) and IS
made of perspex sheet of 12 mm thick ness .
Heating section
A single aluminium plate (680x298x3 mm\ heated by stainless steel foil from underneath , acts as heat transfer surface. Six stainl ess stainless steel fo il s of dimension 690x47xO.045 mm3 connected in series are cemented onto the 25 mm thick bakelite sheet. A vari ac is used to contro l the power supply, i.e. heati ng level. The aluminium plate is hi ghl y poli shed in order to minimize emi ss ivity and hence the radi ati ve losses. In addition, to minimize the conducti ve heat losses, lower surface of the bakelite board is insul ated using a 13 mm th ick plate of bakelite with a 2 mm air gap in between.
The heat transfer surface is instrumented with thi rteen calibrated thermocouples of the chromelalumel type, along the centerline and spanwi se direction of the heated plate in order to measure the pl ate temperature and check the spanwise temperatu re uni formity respecti ve ly. Conduction losses to the bottom surface of the heating secti on through the
466 INDI AN J. ENG. MATER. SC I. , DECEMBER 2002
bakelit e arc est imated by mounting the thermocouples onto it at several locati ons.
Tme colour imagc processing system
The image acquisition and processing system used in the present inves ti gation consists of a high reso lution 768 (hori zontal)xS74 (vertical) pixels CCD video camera (SONY XC-OOJP) w ith 16 mm foca l length lens (VCL-1 6WM ), a 24-bit co lour frame grabber board (Imaging Technology) and a high speed Pc. The current 24-bit true colour image processing board from Imaging Technology, USA, can be program med for co lour analys is uSing base level Cprograms.
Thermochromic liquid crystals (TLCs)
T LCs are available in different bandwidths, which deri ne the temperature range in which they acti vely refl ec t visible li ght. In the present inves ti gati on, the heating sur face is coated w ith a thin layer of TLCs sheet (Hall cres t, Inc.: R3SCSW ). This means the activati on o f the red co lour of thi s parti cular TLC beg ins at 3SoC and the bandwidth is SoC wide. The prefabri ca ted LC sheets were ca librated ill Sill! under the no fl ow condition, keeping identica l illuminati on and i mag i ng characteri sti cs throughout the experiment. The relationship between hue and temperature was obtained for inverting the liquid crys tal images.
Uncertainty and measurcmcnt crrors •
Errors in the ex perimental data arc associated with measuring temperature by K-type thermocouples, l"I uc tuating supply vo ltage at the variac and the rocussed power source for li ghting the liquid crys tals. Errors related 'to K-type thermocouple effects have been found to be quite small. M ost of the experiments were conducted several ti mes to check temperature measurement. The local Nusselt number and average Nusselt number were found to be in good agreement w ith theoretical correlati ons. The calibration process was repeated thri ce. The results were found to be repeatable. The image acqu ired during the transient state tes t and the steady state tes t al so showed good repeatability.
Data Ana lysis
Hydrodynamic boundary-layer
The experimental ve loc ity profile between 1/ / U ~
and v / 8 has been compared w ith the !lat. plate :
laminar and turbul ent profil e, where, 1/. is the
streamwise veloc ity, U~ is the free stream velocity,
y is the wall normal distance and 8 is the boundary
layer thickness. The laminar profile has been obtained using Blasius so lution lo. The law of the wall is used for the turbulent veloc ity profile given aslO :
II' =2.44 111 .1"+5.0 ... ( I )
where,
; II / U ~ II
~Cf l2
Y + yU~~Cf /2
Y
The basic unknown In Eq.( I ) is wall sk in f ri cti on
coefficients Cf (or T,, ) which can be inferred by
using the boundary condition ; @y=c5, II = U~ where, 0
and U ~ are the hydrodynamic boundary layer
thi ckness and free stream ve loc ity respectively . For the laminar flow, the variati on of (8 / x ) as a functi on of local Reynolds number is obtai ned on the bas is of Blasius solution lo as:
8 5.0
~- ~Re,
For turbulent flow, it is calculatedusing l l :
(j - -'- = 0.37 Re, 5
.r
... (2)
. . . (3)
The sk in friction coe ffi cient in laminar fl ow over flat I . b ' d f 10 P ate IS 0 talne rom :
I
Cf
= 0.664 Re,- "2 ... (4
In turbulent fl ow, the skin fri ct ion coefficient is b . df . 11 o tal ne rom uSlIlg :
I
C1 = 0 .0592 Re ,- ":\ fo r 5x l 05 < Re, < 107 . .. (5)
The skin friction coefficient can be cletermined by measuring the velocity gradient in the near wa ll region of the channel from using:
TARIQ el (II.: CONVECTIVE HEAT TRANSFER FROM FLAT AND RIBB ED SURFACES 467
c = ~I(dll/dv) L=o I I '
- pU -2 =
... (6)
where, the wall velocity gradient is determined from the quad rat ic curve fitting th rough the near-wall va1ues of veloc ity.
Thermal boundary-layer
The non-dimensional temperature B is defined as:
e = T,, (.r) - T (.r, v)
T,, (.r) - T~ ... (7)
where. T:, (.r) is the local temperature of the plate, T~ is
the free stream temperature and T(x. y) is the
temperature inside the now fi eld . The theoretical nondimensional temperature variation for laminar flow is obtained from Blasius solution l O The laws of the wall for turbulent flow temperature profil e can be
d ill ex presse as :
/ + =2.075 111 / +3.9
where,
f ' = (T,,(X)-T(X,y))B
q,,jp CI,
+ yU~JC7i y = . y
... (8)
Here the wall shear stress, T" is obtained as earlier by
Eq .( I). Therefore , basic unknow n in the Eq.(8) is q",
which can be obtained by applying the boundary cond iti on; @y 'c,o'[; T= T= where, aT and T= are the
thermal boundary layer thickness and free stream temperature respec ti vely. Thus, using Eq.(8) it IS
possible to get the plot of B(x,)I) as a
function of y / Or .
The variation of Or / X versus Reyno lds number
compar ison for laminar now uses:
Dr - ~ -= S63 IRe, -
X ... (9)
The above relation is inferred from Eq.(2) by using
0/0, = PrY. . For turbulent flow, the thermal
boundary layer thickness variation is ex pressed as:
... ( 10) x
The above relation is obtained from Eq.(3) and
0/ Or = p/;X, where P/~ is the turbulent Prandtl
n um ber 10.
The local convective heat transfer coefficient of the heated surface is presented in terms of the local
Nusselt number NUr and is defined as:
- x dT Nil =----
x T (x) - T i " . = (,)' 1'=11
... ( II )
Here the air temperature gradi ent df / dyl,=o is
determined by fitting quadratic fun ction through the near wall values of temperature. The correlation for the local Nusselt number for laminar now is given bylll:
Nu, = 0.332Re/-; PrX for 0.6 < P r < 50 . .. ( 12)
The correlation for the local N usselt number for turbulent nows is":
Nll x = 0.0296Re,Ys PrX for R er < 108 ( 13)
The properties of air are calculated at the film
temperature, TI = (~, ex) + T=)) / 2 .
Results and Discussion The now and heat transfer test results are presented
here along with the respective laminar and turbulent profiles in order to study the influence of two dimensional rib of square cross secti on on the wall parameters. In addition , liquid crystal images are used to assist in interpreting the influence of rib in now modul ati on and heat transfer enhancement.
Velocity field
Figs 2 and 3 compare the experimental dimensionless transverse coord inate ()' / 0) versus
the dimensionless local velocity ( u / U = ) profil e
468 INDI AN J. ENG. M ATER. SCI., DECEMBER 2002
without and with rib respecti vely with flat plate lam inar and turbul ent profile. The velocity profil e in Fig. 2 indicates the fl ow on the flat surface to be lam inar. The ve loc ity profiles in Fi g. 3 are seen to be turbulent in nature due to the presence of the rib .
Figs 4 and 5 show the variati on of the dimensionless boundary-layer thi ckness ( (5/ X) as a
functi on of local Reynolds number ( Rel" )' Fig. 4
supports the earlier observati on that the flat surface veloc ity profile is laminar. The boundary layer thi ck ness for the rib roughened surface is larger than the laminar and turbulent boundary layer (Fig. 5).
The Rey nolds number dependence of skin fricti on
coeffi cient, Cr is shown in Figs 6 and 7. At the
in l"\() w plane for smooth surfaces, there is about 8-IO(Yc) deviati on from the lami nar correlation which dimini shes well as the Rey nolds number increases . For ribbed surfaces, the skin fricti on coeffi cient does not have a systematic variation. Th is indicates the
08
"" 8 :J "3
0 '
02
08
06
D.
q=336.0 t 5.0 % W/m2
,.-.----
0
x
c f o e 0
i . ~
0
xo • ! . 0
• e II: c;: ~ ~
v
e . •
02
. 00
0
e 9 v:
-; - .o---·: - :·~ :li~f· \( ! o 0 ~ • i o. . ;0
~ ~ i~ )( 0 ~ 0 ~ .. 0 R,~. _ 4 1U\!
• f ; (J 0
•
Re.'~J6 )( n ... lIlfl4
He , - ' ij IJo
lie, 1O:'~!I
Ihl, - HJ91 flf!,1;;/61
lie . ' !4{4
He. ' 11 4fi..1 V
Ilo!, 751Y.>1 0
n.,, - "l%f1 H .. " J]II~J 0 R ... · ~ HI:, 41:.6 1
R",441 "1'}
He, ' !>lo<1f 0 Re,.'5 14: , e R ... : S9SBI 0
lamlflllrh 'rbulenl
0 4 06 0.8
y/8
Fig. 2- Yeloc ity profil es of fl ow over a flat surface
q=336.0 , 5.0 % W/m2
..
02 0.4 06
y/8
Rex::: 2 1083 + ReJ[::: 26638 Rex = 36107 Rex ::: 32565 Re. = 44046 Rex = 59702 Re:o; ::: 45435 Rex =61 453 6
Re~ :: 832Q7 lammar
turbulent ------
08
Fig. 3- Veloc ity profi les of fl ow over a fl at surface wi th a ri b
complexity of the rib roughened surfaces III
compari son to fl at surface.
Thermal field
Figs 8 and 9 compare the temperature profile of the fl at surface and ribbed surface respec ti vely with the laminar and turbu lent profile of a flat plate. The measured fl at surface temperature profil e in Fig. 8 is similar to the flat plate turbulent profil e indicating the temperature profile to be turbulent in nature. 1n comparison to the flat surface (Fig. 8), Fig. 9 shows the temperature profile to be turbul ent in nature for the rib roughened surface. Figs 10 and II show the variation between the dimensionless thermal boundary-layer thickness and the local Reynolds number. From Fi g. 10, the temperatu re profil e is observed to be close to laminar in nature. The trend shown for the ribbed surface in Fig. I I is different from that of the flat surfaces shown in Fig. \0 .
The local Nusselt number versus the local Reynolds number plot is shown in Figs 12 and 13 for smooth
X ;;0
0.12
0.1
008
006
004
002
, D
[aminar-
q=336.0' 5.0 % W/m2 R. (D ,/~'~~;ci .. .. -. laminar :OIx·· =5~ORex-: 112 -._. ·· ~,:··m ~ ~ ~~gg
turbulentOlx =O.37Re;"; ~; m.J: ~~gg
o ............... ~ . ....L.~~~.....J o 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
Re,
Fi g. 4- Yari ation of the hydrodynami c boundary layer thickness fo r fl ow over a fl at surface
0 " r-'~"'-~"'-~"""""""~""""'~""""'~""""'~""""~""""~""" laminar -
q=336.0 ! 5.0 % W/m2 Re (D.J'~'~~~o~ .. o 12 .... ....... • ....... _ ..... _ ._. - - .. - ··Iamiflar:o/x. =5.ORe)(·- l!? ·· ~~m ~ : j~~g
turbulent:OIx =O.37Rex·lIS ~: Ig~: ~~gg • 0.1
0 04
G02
o I .~......J........ ..........
o 10000 200('() 30000 40000 50000 60000 70000 80000 9 0000 100000
Re,
Fig. 5- Variati on of the hydrodynamic boundary layer thickness fo r flow over a fl at surface with a rib
TARIQ el al .: CONV ECTIVE HEAT TRANSFER FROM FLAT AND RIBBED SURFACES 469
o 0 1·~
00 12
00 '
0.008
r5 0006
0004
0001
0 0 10000
. _ laminar --
q=336.0 t 5.0 % W/m2 He (O t->'~t:~;~ .. laminar : Cfx=O .664R~ill?_····-·--7 ~~.~~ . ~ ~~~g turbulentC,x=0.0592Re;1f5 ' ~: mtJ ~ ~gg
.......... _- .... ........ .. .. -.
2DOOO 30000 40000 50000 60000
Rex 70000
Fig. 6- Skin friction coeffic ient as a function of Reynolds number for a flat surface
00 14
0012
C.OI
ooos
0 0.006
0004
0002
q=336.0 t 5.0 % W/m2
·laminar;C,,=0,664Rex' !!.?
turbulent:C'x=0.0592Rex·1f5
laminar -lurbulenl - - • -
Rc (O~ = 12801)
-.. ~: .~.~ ~ ~gg
°0~--~'~DOO~0~-~~00~0--~30~00~0~-4~D~DD-O~-5~D~00-D---6-0LOO-D---7-0LOO~0--~A-OOLD~D--·-g~DOOD
Re,
Fig. 7- Skin fri ction coefficient as a function of Rey nolds number for a flat surface with a rib
, f-;-
DC
R 0 6
q=336.0 ! 5.0 % W/m2 I
/ ~ ;:;:-X 0-4 ! ~ ,I f-' J
D.l
y/8T
IIc. , &.1Ol He, 8448
l le. , 10161
lle. ' 11'601 a He, " H~l n.. , ' l lJJIl
II<I. " I$IJI 1l" , , ?O, n .v. , ~II!1l
' '''. ' <'S1!>11 Hex ' 111f81 He, - J0896 R.. . ' 169tO Re. - J99ll ~. ' J"94 He. - 481.10 Ilc , ' 401G6
He. ' !.!r'..;(.J U" . + .G4~J
He, 61111 4 Om,,,,, -
' "turbOlCnt "-_ ·
Fig. 8- - 1\;mperature profiles in fl ow over a flat surface
'8 f-;-X .. ~ f-;-x .. t:.
X
~
0.8
0.6
q=336.0 ' 5 .0 % W/m2
•• , •.••• ,-#
:// / _ 0
.:' 0
i .. iiJ ....... i··-·····~ i
0.'
( 0 . 2~~~J
Re,. =' 21 083 He. ::; 34861 Re. :: 494 10 Re~ :: 77715 Re. = 31496 Re. :: 4634 2 Re~ = 65683 Re. == 6 1996 RC}I ::; 87497
laminar -turbulent _ •••• -.
D.'
O.OS
0.06
0 04
0.02
D.2 0 .• D.6 0.8
y/8
Fig. 9- Temperature profiles in flow over a flat surface with a rib
.. ... ;
q=336.0 I 5.0 % W/m2
laminar:o,./x =5.496Re;'t2
turbutent&j1x =0.40671Re; "5
..... .. ...... .. .... -
x n
laminar -turbulent · ...
Re(D~ :: 12800 He (D. :: 15950 Re (0 :: 20900 Re (0 = 23900 Re (0 :: 29400
..... ... ..... ... . .... ...
O ~~~~-h~~----~--~--~--~----~--~--~ o 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
Rex
Fig. 10--Variation of thermal boundary layer thickness for flow over a flat surface
0.1 r-~.....,c---~....,.~~....,..~~..,..,~~,.....~~,.....~.....,.~~....,..~~-,
laminar -turbulent - - --
o.os
D.06
D.04
0.02
q=336.0 15.0 % W /rn 2
laminar:/),-/x =5.496~e;'t2
turbIJlent&rlx =0.40671Re;"S
Re (0 :: 20900 Re (O~ :: t2800
Rc (0 :: 29400
.... --.-... -----•.... ---.',
------ .
)( .. -~.-.-.. ---.~.~.--===:::
D~~~--~~~~--~~~~~~~h-~~--~ 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
Re,
Fig . II - Variation of thermal boundary layer thickness for flow over a fl at surface with a rib
470 INDI AN .I . ENG. MATER. SCI., DECEMBER 2002
10000
q=336 0 ' S O% W1m'l
l;:Imlnar ux ; O;J32Rc~ 1,'2Pr 11.1
turbulent Nux::() 0296Pr lI.lRtlA 0 /1
200!)) 30000 40000
Re, 50000 60000 70000
Fi g. 12- Loca l Nusse ll nUlll ber va rialion w ilh Reyno lds nUlllber for !l01V over a !lat surface
1;0 ~ ICoO ~
q=336 0 : 50 % Wlrr?
lam nat Nu, =OJ37 f.:e. 17p r II)
turbulent Nu;=O 0296Pr 1 3RexO"
------
50 1- .:--~
lamlnar turbulent .--~---
Re (0,,):;. 12800 • Rt;! (0,,) = 20900 Re (0,,) :;. 29400
oL .. , L........ ............... ~~~............,c..........-..........J 100:)0 ?OOOO 3eOOO 40000 ~OOOO 60000 70000 80000 90000
Re,
Fi g . I :1- Loca l Nu sse lt number va ri a lion with Reyno lds number for fl ow over a !lat surface w ilh a rib
and ribbed surfaces , respectively. For smooth surfaces there ex ists a good agree ment between the measured data and turbulent correlation. This is understandabl e because the Nusselt number follows closely the local temperature profil e. The figures show that at low Reynolds number, the local Nusselt number of the ribbed chan nel is signi ficantl y hi gher than that of smooth channel; but at a higher Rey nolds number, thi s difference is less. Also the loca l Nusselt number of the ribbed channel increases monotonica ll y with an increase in the loca l Rey nolds number.
Tra nsient heat transfer experi ment
The transient liquid crys tal thermography (LCT) technique offers significant advantage of yielding loca l heat transfer coefficients over co mplete test surfaces in a single ex periment. In this case, the surface is heated to a constant temperature and suddenly cooled by an ambient mainstream. The
Flow direction
Tempenllurc "C
(a)
(b)
(c)
(d)
Fig . 14-lmages show ing the co lo ur changes during cooling o f pl ate in the upslream and down Slream of rib dur ing the lrans ient ex pe rimclll : a (0.00 min). b (4.00 min ). c (6.00 min). cI (8.00 min)
images are captured at regular intervals and then temperature contours are drawn. The colour images of the transient tes t experiment conducted at Re(Dl,)=20900 for a ribbed surface are shown in Figs 14a-d . In the coloured images, black indicates the coldest regions, followed by red, green, ye ll ow and blue respectively for increase in the temperatures.
Initially , the pl ate is heated up to 41 °C and correspondingly the LC sheets appears to be pure blue, then on forced cooling the gradua l changes in temperature with time occurs which is clearly depicted in the images. Fig. 14a shows the constant
TARIQ el al .: CONVECTIVE HEAT TRANSFER FROM FLAT AND RIBBED SURFACES 471
plate temperature at the start of the ex peri ment by uniform colour distribution. Figs 14b, 14c and 14d show the colour/temperature di stributi on at later time, i .e. after 240, 480 and 720 s respectively . The green/red region in Fi gs 14b, 14c and 14d indicate lower temperature. The ex istence o f low temperature at a di stance from the downstream edge of the rib indicates that the heat transfer is maximum near the reattachment region. Comparatively, high temperature near th e rib points to the low heat tran sfer zone due to the stagnant fl ow in the rec irculation zone. Overall , the v isuali zation image shows that the flow is twodimensional as was expected from th e 2-D nature of the rib-channel geometry. The ex istence of definite two-dimensionality in the downstream region of the fl ow behind rib is supported by the uniform colour di stribution in the span wise direc tion. Further, after ten minutes of cooling, the plate cools to a
temperature less than 35°C, and the thermal fi eld is outside the range of liquid crystal and it appears black.
Conclusions Fluid fl ow and heat transfer characteristics in the
ReC Dil ) range of 12,800 to 29,400 have been carried out ex peri mentally. The present inves ti gati on shows that the ve loc i ty profi Ie for the smooth surface case is very similar to the Blasius profil e indicating the flow to be laminar in nature. The skin friction coefficient ve rsus Reynolds number plot supports the observation regard ing the laminar nature o f the tlow. Contrary to the above finding, the temperature profile for the smooth wall case is observed to be similar to the law of the wall profile indicating the flow to be turbul ent in nature. The Nusselt number versus Reynolds number plots support the observat ion about the turbulent nature of the flow. The local Nusselt number, average Nusselt number and sk in fri cti on coeffi cient for the ribbed surface are higher than that of the smoot h sur face . Both the Nusselt number and the sk in friction coefficient are funclions of the Reynolds number, the former being a stronger function of the Reynolds number than the later one. The above observati on supports the square rib to be an effec ti ve lurbulator for heat transfer enhancement point o f view.
The transient liquid crystal thermography shows the !low behind the rib to be two dimensional in nature. The ineffec tiveness o f the recirculation region and thc effect i veness o f the reattach ment region for
heat tran sfer enhancement are clearly vi sible f ro m the liquid crystal images.
Nomenclature
Rex
T(x.v) T,,(x)
T'.,
, /I
1I. V
= Ski n friction coefficient = Spec ific heat = Hydraulic diameter of the duct = Local usse lt number = Prandtl number = Turbulent Prandtl number = Heat nux supplied by the heating foil
= Wall heat flu x = Rey nolds number based on hyd rauli c diameter
= Local Reynolds number (U ~X /y ) = Temperature o f the air = Loca l temperature of the plate = Free stream temperature
= Temperature in wa ll coordinate
= Ve loci ty in wa ll coordinate = Velocities componcnts in cartesian coord inates (x .y) = Free stream veloci ty
X . ." =Streamwi se (ax ial ) and transverse coordinates respectively (Fig. I )
1'+ = Transverse wall coord inates
8 8r
8 y
J..l
P
= Velocity boundary layer thi ckness
= Thermal boundary layer thick ness
= Non-dimensional tcmperature = Kinematic viscosit y
= Dynamic viscosity
= Density of the air
= Wall shear stress
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