Enhancement of heat transfer from a #at surface in a channel #ow by attachment of rectangular blocks

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1 INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. 2001; 25:563}576 (DOI: /er.703) Enhancement of heat transfer from a #at surface in a channel #ow by attachment of rectangular blocks O. N. S, ara*, T. Pekdemir, S. Yapmcm and M. Ymlmaz Faculty of Engineering, Atatu( rk University, Erzurum, Turkey SUMMARY Enhancement of the heat transfer from a #at surface in a channel #ow by attachment of rectangular crosssectional blocks has been investigated as a function of Reynolds number (Re), arrangement of the blocks with respect to the main #ow direction as well as each other, and the numbers (spacing)of the blocks. The channel had a cross-sectional area of mm (i.e. an aspect (width-to-height)ratio of 2). Re, based on the hydraulic diameter of the channel (D )and bulk mean velocity (u), changed in the range of 6670} The blocks were positioned both transverse and parallel with respect to the main #ow direction. The parallel blocks were arranged in both in-line and staggered orientation with respect to each other. The e!ect of the blocks on the #ow pressure drop was also measured. The results indicated that the heat transfer could be enhanced or reduced depending on the spacing between the blocks and their positioning and arrangement. For a given pressure drop, the best heat transfer enhancement by the blocks over that from a smooth surface (without blocks)was obtained when the blocks were positioned parallel to the #ow and arranged in a staggered manner with respect to each other. Copyright 2001 John Wiley & Sons, Ltd. KEY WORDS: heat transfer enhancement; heat transfer augmentation; channel #ow; heat transfer; rectangular blocks; forced convection; heat exchangers 1. INTRODUCTION The increasing necessity for conserving and saving energy as well as material imposed by the diminishing world resources has prompted development of more e!ective heat transfer equipment for better heat transfer rates. In many industrial systems, heat must be transferred to either input energy into the system or remove the energy generated in the system. Considering the world-wide rapid increase in energy demand, reducing energy loss due to ine!ective use and also enhancement of the energy transfer (in the form of heat)has become an increasingly important task for the design and operation engineers for such systems. In recent years, many techniques have been proposed for the enhancement of the heat transfer rate. These can be classi"ed into two main groups: (i)passive techniques not requiring additional power sources and (ii)active techniques requiring additional external power inputs (Bergles and Webb, 1985; Reay, 1991). In the case of the passive techniques, convection heat transfer * Correspondence to: O. N. S ara, Faculty of Engineering, AtatuK rk University, Erzurum, Turkey. onuri@rocketmail.com ' Contract/grant sponsor: AtatuK rk University; contract/grant number: 1996/61. Received 28 January 2000 Copyright 2001 John Wiley & Sons, Ltd. Accepted 19 April 2000

2 564 O. N. ȘARA E¹ A. from surfaces with attachments of di!erent shapes with di!erent geometry, such as "ns, ribs, blocks, have been widely exploited (Ledezma et al., 1996; Goldstein et al., 1994; Tahat et al., 1994; Jurban et al., 1993; Babus'Haq et al., 1993; Naik et al., 1987; Liou and Hwang, 1992a, b; Hong and Hsieh, 1993; Hwang and Liou, 1994; Hwang and Liou, 1995; Liou et al., 1995; Han, 1988; Zhang et al., 1994; Molki and Mostou"zadeh, 1989; Molki et al., 1995). Heat transfer enhancement with such arrangements is achieved by the increase in the surface area and also by the turbulence (or the mixing)generated due to the attachments. This type of forced convection heat transfer is encountered in many process equipment such as heat exchangers, nuclear reactor fuel elements, turbine blades, electronic boards and components. Improved heat transfer rates are normally accompanied by increases in the pressure drop in the #ow over such surfaces. Thus the main target is to design the attachments in such a way and geometry that they will yield maximum enhancement in the heat transfer rate with minimum increase in the pressure drop or minimum decrease in the #ow rate. It has been reported by Hwang and Liou (1994, 1995)that when solid blocks are positioned with an angle of attack of 903 (transverse positioning)to the main (bulk)#ow direction, hot spots develop in the wake of the blocks because of the low-speed recirculating #ow in the region. This results in lower heat transfer rates from the surface. The intensity of this adverse e!ect may change signi"cantly depending on the #ow and geometrical conditions. However, Lau et al. (1991)showed that as the angle of attack decreases, that is if the blocks are positioned more aligned with the bulk #ow direction, the adverse e!ects diminish and beyond a certain point, depending again on the #ow and the geometrical conditions, the heat transfer rate is enhanced. In the present work, it is intended to investigate the e!ects of attachment of rectangular crosssectional blocks on the convective heat transfer as well as on the pressure drop from a #at surface in an air #ow in a rectangular channel. Two extreme positions of the blocks with respect to the main #ow direction have been studied, namely transverse and parallel. The parallel blocks were arranged in both in-line and staggered manner with respect to each other. In the present study, the blocks used to extend the surface area and to promote #ow turbulence had a di!erent size, (H/D (height of the block-to-hydraulic diameter of the channel ratio)"0.234). H/D ratios used in previous experimental studies were generally between and for ribs (Hwang and Liou 1994, 1995) and approximately 0.6 for "ns (Babus'Haq et al., 1993). Furthermore, in the transverse arrangement, there is a spacing between blocks and side wall of the channel to reduce the recirculating regions causing hot spots behind the ribs as reported previously by Liou and Hwang (1992a,b, 1993). The objective of this study was to compare the heat transfer results of transverse and parallel con"gurations and to develop a heat transfer correlation for the transverse arrangement. As mentioned earlier, the heat transfer enhancement is achieved at the expense of the increased pressure drop. For many practical applications it may thus be necessary to determine the economic bene"t due to the heat transfer enhancement. Therefore, it is also intended to determine the e!ect of the blocks and their arrangement on the overall energy performance of the present heat transfer system through a thermal performance analysis. The average Nusselt number was measured by thermocouple technique and resistance heating method, whereas the pressure drops with pressure taps connected to an inclined glass tube kerosene manometer. 2. EXPERIMENTAL DETAILS The channel #ow experimental rig is shown in Figure 1. The rig consisted of a closed rectangular channel with a removable test section and two fans, a data acquisition system, an inclined manometer, an anemometer/thermometer, and a number of thermocouples.

3 HEAT TRANSFER ENHANCEMENT 565 Figure 1. (a)a schematic display of the experimental set-up and (b)a detailed view of the test section and its structure for the transverse arrangement of seven blocks. The channel, constructed of wood of 20 mm thickness, had an internal cross-section of 160 mm width and 80 mm height (channel aspect ratio"2). The total length of the channel was 2000 mm and it was operated in suction mode. A #ow straightener was "tted immediately after the inlet of the channel.

4 566 O. N. ȘARA E¹ A. The test section, of which only the bottom surface was heated (see Figure 1(b)), was located 900 mm downstream of the #ow straightener. The upper wall of the test section was "tted with a glass window which enabled the visual observation of the test surface and also to make alteration on the surface for di!erent arrangements of the blocks when necessary. A #ow mixer was "tted to 100 mm downstream of the heated surface for homogenising the heated air prior to the mean outlet temperature measurement. The base plate of the test surface was made of a smooth aluminium plate of 2 mm thickness, 140 mm width, and 320 mm length. An electrical heater (or thermofoil)with the same dimensions of the base plate was "tted immediately underneath the plate. A thin layer of thermal glue with negligible heat resistance was applied between the heater and the plate to provide a complete contact. In order to minimize the heat loss the other surfaces of the heater were insulated by combination of a 12 mm thick asbestos layer and a 20 mm thick wood layer. Blocks with a rectangular cross-section of 25 mm height and 10 mm width, and a length of 140 mm were attached only on the upper surface of the base plate. The thermal glue was also applied between the plate and the blocks for a better contact. The blocks were made of the same aluminium material as the base plate because of the considerations of conductivity, machinability and cost. The number of the blocks varied depending on the predetermined experimental conditions and they were positioned either transverse or parallel to the bulk #ow as shown in Figure 2. In parallel positioning, two di!erent arrangements of the blocks with respect to each other were used; in-line and staggered. With the present arrangements, it was possible to apply an electrical energy up to 808 W m to the base plate. Current and voltage measurements were performed with an ADM multimeter. Eight thermocouples of K-type were "tted on the central axis line of the base plate #ash with its outer surface for the measurement of the local surface temperatures (see Figures 1 and 2). The thermocouples were equally spaced and in all cases positioned in the spaces between the blocks. There was no thermocouple attached on the blocks. The temperature readings from these eight thermocouples and from those at the inlet and outlet were all recorded after reaching steady state conditions by using a PC equipped with an Advantech PCLD-8115 terminal card and an Advantech 818HG data acquisition card. Another thermocouple of the same type was used to measure the temperature of the outer surface of the bottom wall of the test section. Reading from this thermocouple was also recorded in steady state conditions by using the same data acquisition system and used in the evaluation of the heat loss. The pressure drop across the test section under heated conditions was determined using pressure taps and an inclined glass tube kerosene manometer (see Figure 1). The air velocity over the test surface (bulk mean velocity) was determined by averaging the local measurements across the channel cross section using an electronic anemometer. The #ow conditions were characterized in terms of Reynolds number (Re), which was based on the hydraulic diameter of the channel over the test section (D )and the bulk mean velocity (u). Re changed in the range of 6670} The experimental heat transfer system had a Prandtl number (Pr)of & DATA REDUCTION The steady-state energy balance for the electrically heated test surface may be given as Q "Q #Q (1)

5 HEAT TRANSFER ENHANCEMENT 567 Figure 2. A detailed schematic display of the arrangements and positioning of the blocks: (a)transverse to the #ow; (b)parallel to #ow with in-line arrangement; (c)parallel to #ow with staggered arrangement. The geometrical parameters investigated and their range are listed in the tables above the "gures. where Q indicates the heat transfer rate and subscripts elect, conv, and loss denote electric, convection, and loss, respectively. The electrical heat input is calculated from the measured thermofoil resistance and the electrical current. The heat loss from the system may be by (i)radiation from the surface and (ii)conduction through the walls of the channel towards cooler surrounding atmosphere. In similar studies Naik et al. (1987)and Hwang and Liou (1995)reported that total radiative heat loss from a similar test surface would be about 0.5 per cent of the total electrical heat input. Therefore, the radiative heat loss can be neglected. The conductive heat loss from the side walls can be neglected in comparison to that from the bottom surface of the test section since the total side areas of the heated plate ( )is only 2.8 per cent of that of the bottom surface ( ). Moreover, as mentioned above those surfaces of the test plate which are not exposed to the #ow have been insulated by combination of a 12 mm thick asbestos layer and a 20 mm thick wood layer. Thus, it is thought

6 568 O. N. ȘARA E¹ A. that the heat loss from the heated plate will be mainly from its back surface into the environment through the bottom wall of the channel. This was evaluated at the steady-state conditions by using experimentally measured mean temperature of the outer surface of the bottom wall of the test section and a well-tried correlation equation suggested for natural convection for geometrically similar systems (Incropera and Dewitt, 1996). The results indicated that, for the extreme conditions, the maximum loss was 7 per cent of the total electrical heat supplied to the surface. In spite of its low quantity, the loss from the bottom surface was taken into account in the calculations of the heat transfer coe$cient. The steady-state rate of the convection heat transfer from the test surface can be given by (Naik et al. (1987)) Q "h A ¹! ¹ #¹ 2 (2) where h is the average convective heat transfer coe$cient, ¹ the average surface temperature ¹ and ¹ the mean temperature of the #ow at the outlet and inlet, respectively, and A the surface area. Either the projected or the total area of the test surface can be taken as the surface area in the calculations. These two areas can be related to each other by Total area"projected area#total surface area contribution from the blocks A" = # N[2(H=)#2(Ht)] (3) where = is the width of the base plate, its length, N the number, H the height and t the thickness of the blocks, respectively (see Figure 2). = is also the length of the blocks. The average convective heat transfer coe$cient can thus be calculated by h " Q!Q A [¹!(¹ #¹ /2)] (4) The average Nusselt number (Nu)can be evaluated by Nu" h D k (5) where D is the hydraulic diameter of the channel over the test section, and k the thermal conductivity of air. Nu was calculated on the basis of both the total area and the projected area. Nu that is based on the projected area will re#ect the e!ect of the variation in the surface area as well as that of the disturbances in the #ow due to the blocks on the heat transfer. But Nu that is based on the total area will re#ect the e!ect of the #ow disturbances only. The later is therefore used in determining the e!ects of the disturbances in the #ow on the heat transfer. Once the #ow disturbance e!ect is determined, the former is used in the evaluation of the e!ect of surface area increase. Error analysis carried out for Nu (Holman, 1989)indicated that experimental measurements could be in error by up to 9.5%.

7 HEAT TRANSFER ENHANCEMENT 569 Pressure drops over the test section in the channel can be represented in terms of the friction factor, which may be expressed as f" P ( /D )(ρu /2) (6) where ρ is the density of the air, u the bulk mean velocity, the length of test section, and P the pressure drop. Error analysis indicated that f measurements could be in error by up to 18.8 per cent. The physical properties of the air were evaluated at (1/2)(¹ #¹ ). 4. RESULTS AND DISCUSSION In order to have a basis for the evaluation of the e!ects of the blocks on the heat transfer as well as on the pressure drop, some experiments were carried out without any blocks attached to the plate, which will be called &smooth surface' hereafter. Using data obtained from these tests, the average Nusselt number (Nu s )was correlated as a function of Re and Pr. The resultant equation was Nu " Re Pr (7) where the subscript &s' indicates the smooth surface. The least-squares error for this equation was 0.63 per cent. The e!ect of the transverse blocks was investigated for three di!erent spacings between the blocks: 33, 76, and 119 mm. As the spacing is determined by the number of blocks, the e!ect of the spacing can be considered as the e!ect of the number of blocks. Figure 3 shows the variation of Figure 3. Variation of Nu normalized with Nu (Nu/Nu )with Re for various spacings between the blocks when they are positioned transverse to the main #ow direction. Nu/Nu based on (a)the projected area (b)the total area.

8 570 O. N. ȘARA E¹ A. Nu/Nu (Nu calculated by Equation (7)) with Re for various spacings between the blocks. Figure 3(a), showing the variation of Nu/Nu based on the projected area, indicates that it is possible to enhance the heat transfer up to approximately 100 per cent by attachments of the blocks of the present geometry. It is seen from this "gure that Nu/Nu decreases slightly with increasing Re indicating that #ow conditions over the surface become unfavourable as the bulk #ow velocity increases. Figure 3(b), depicting the variation of Nu/Nu based on the total area, shows on the other hand that the blocks may also have an adverse e!ect on the heat transfer as the spacing between them becomes smaller (i.e. larger number of blocks). Here Nu/Nu decreases slightly with increasing Re as well. It is evident from Figures 3(a)and 3(b)that the presence of the blocks has an improving e!ect on the heat transfer due to the increase in the surface area, but they may also have an adverse e!ect due to the disturbances in the #ow depending on whether the spacing between the blocks in#uences the #ow favourably or not. The net e!ect will be determined by the more dominant factor. Our computational #uid dynamics (CFD)analysis of the present experimental arrangement (S ' ara, 1998)as well as some other studies (Hwang and Liou, 1994, 1995) demonstrated that the #ow separates from the surface due to the blocks and reattaches it again as it moves downstream thus creating recirculating #ow zones at the wake regions of the blocks. As the blocks become more densely spaced, the spacing between the blocks becomes smaller than the distance from the back surface of the blocks at which the #ow can reattach the surface again. Thus, the whole surface of the plate is covered by a very weak recirculating #ow in the spaces between the blocks and a major portion of the bulk #ow bypasses the heated surface. This phenomenon is thought to be the reason for the adverse e!ect caused on the heat transfer by the more densely spaced blocks. The extent of the #ow detachment from the surface is intensi"ed as the bulk mean #ow velocity increases and this leads to further reduction in the heat transfer rate at higher Re. The present results indicate that for a better improvement of the heat transfer rate it is important to space the blocks with an optimum distance from each other. Nu based on both the total area and the projected area were correlated as a function of Re and the spacing between the blocks (S /D ). The resulting equations were Nu"0.377Re S D Pr based on the total area (8) Nu"0.568Re S D Pr based on the projected area (9) The least-squares errors for these equations were and per cent, respectively. For the blocks parallel to the #ow direction, the variation of Nu/Nu with Re number as a function of varying spacing between the blocks is shown in Figure 4. As seen from Figures 4(a) and 4(c), both in-line and staggered arrangements of the blocks enhance the heat transfer signi"cantly over that from a smooth surface up to 170 per cent. Nu/Nu increases with decreasing spacing (increasing number of blocks and therefore the total surface area)but slightly decreases with increasing Re, being more pronounced for the staggered arrangement. Figures 4(b) and 4(d)indicate that neither in-line nor staggered arrangement causes signi"cant changes in the heat transfer due to the disturbances in the #ow as they are aligned parallel to the #ow. But what

9 HEAT TRANSFER ENHANCEMENT 571 Figure 4. Variation of Nu normalized with Nu (Nu/Nu )with Re for various spacings between the blocks when they are positioned parallel to the main #ow direction. Nu/Nu based on (a)the projected area (b)the total area, for in-line arrangement of the blocks, (c)the projected area (d)the total area, for staggered arrangement of the blocks. is important here is that with the parallel arrangement the adverse e!ect of smaller spacing, which was signi"cant in the transverse arrangement case, does not occur. A comparison of the heat transfer performances of the blocks positioned transverse to the #ow and parallel to the #ow with in-line and staggered arrangements with that of a smooth surface for a typical spacing of the blocks (four blocks)is shown in Figure 5. It is seen from the "gure that the best improvement in the heat transfer is obtained when the blocks are positioned parallel to the bulk #ow with staggered arrangement with respect to each other. This indicates that with this type of arrangement enhancement in the heat transfer rate due to the disturbances in the #ow is more favourable than those of other arrangements. Enhancement in the heat transfer due to the blocks of "xed geometry is thus determined by mainly two factors; the increase in the surface area

10 572 O. N. ȘARA E¹ A. Figure 5. A comparison between the heat transfer performances of the surfaces with blocks of di!erent positioning and arrangements and that of a smooth surface. Nu based on (a)the projected area (b)the total area. Figure 6. Variation of the friction factor with Re for transverse positioning of the blocks to the main #ow direction. (surface extension)and the disturbances in the #ow over the surface (#ow alteration). Considering the e!ect of the latter, arrangement of the blocks with respect to both the #ow direction and each other plays an important role in the heat transfer enhancement. Typical variations in the friction factor normalised by the smooth surface friction factor ( f/f ) with Re are given in Figure 6 for various numbers of transverse blocks. It is seen from the "gure that blocks cause substantial increases in the friction factor; up to approximately 30 times higher than those over the smooth surface. As expected, ( f/f )increases with increase in the number of

11 HEAT TRANSFER ENHANCEMENT 573 blocks. There seems to be no signi"cant in#uence of Re on ( f/f )indicating that increases in ( f/f ) with increasing number of blocks are mainly due to the increases in the surface area. The friction factor for the surface with transverse blocks was correlated as a function of Re and S /D. The resulting equation was: f"10.846re Sx D (10) The least-squares error for this equation was 0.03 per cent. As indicated by Figure 6, the enhancement in heat transfer is accompanied by a signi"cant increase in the pressure drop, which may eliminate the energy gain due to the heat transfer rate enhancement. For the purpose of practical application, a thermal performance analysis is thus thought to be useful for the determination of the net energy gain due to the blocks. One of the performance evaluation criteria is to compare the heat transfer coe$cient per unit pumping power to overcome the resistance in the test section at constant surface area for the channel with the extended (or roughened)surface with that having the smooth surface. The pumping power is proportional to f Re and the relationship between the surface with blocks and the smooth surface for the same pumping power is expressed by f Re "f Re (Hwang and Liou, 1995). Here f and Re are the values for the surface with blocks whereas f and Re are those for the smooth surface. Some typical ratios of Nu/Nu* are plotted against f Re in Figure 7 for the same surfaces as those in Figure 6. Nu* is the average Nusselt number for the smooth surface at Re. This "gure shows that, for the same pumping power, the blocks may result in a loss in the overall energy performance of the heat transfer system up to approximately 20 per cent. These results demonstrate that, if possible, transverse blocks must be avoided due to the overall economical bene"t considerations. When it is not possible (due to the nature of the equipment and/or the process), means of improving #ow conditions should be explored. One such mean may be the use of #ow permeable blocks, which will be the subject of a subsequent study. Figure 7. Heat transfer performance under a constant pumping power constraint for the surfaces with the blocks positioned transverse to the main #ow direction.

12 574 O. N. ȘARA E¹ A. 5. CONCLUSIONS Enhancement of the heat transfer from a #at surface in a rectangular channel #ow by the attachment of rectangular cross-sectional blocks has been investigated as a function of the #ow and geometrical parameters. The conclusions derived from the results are summarized as follows: The net e!ect of the blocks on the heat transfer is governed by two factors; the increase in the heat transfer surface area and the disturbances in the #ow. The disturbances in the #ow may have either an aiding or an adverse e!ect on the total heat transfer depending on the spacing between the blocks and their arrangements with respect to both the main #ow direction and each other. Arrangements of the blocks transverse to the #ow lead to #ow separation from the surface and thus reduce the heat transfer rate. The intensity of the adverse e!ect increases with decreasing space between the blocks (i.e. increasing number of blocks)and increasing Re. With the parallel arrangement of the blocks the #ow separation is eliminated and therefore a better enhancement in the heat transfer rate is obtained. The transverse blocks may increase the friction factor up to 30 times over that of the smooth surface whereas the parallel blocks do not yield a signi"cant increase. If the e!ect of the pressure drop on the total energy balance is considered through a thermal analysis, it seems that in extreme conditions the presence of the blocks may cause up to 20 per cent loss in the overall energy performance of the heat transfer system. NOMENCLATURE A "heat transfer area (m ) C "the distance between the tip of the blocks and the ceiling of the channel (m) D "hydraulic diameter of the channel (m) f "friction factor (dimensionless) h "heat transfer coe$cient (W m K ) H "height of the blocks (m) k "thermal conductivity of air (W m K) "length of the test surface (m) "length of the test section (m) N "number of blocks (dimensionless) Nu "average Nusselt number for the surface with blocks Nu "average Nusselt number for the smooth surface Pr "Prandtl number Re "Reynolds number Q "rate of heat transfer (W) S "distance between the blocks (m) t "thickness of the blocks (m) ¹ "temperature (K) u "mean bulk #ow velocity (m s ) = "the width of the base plate or the length of the blocks (m)

13 HEAT TRANSFER ENHANCEMENT 575 Greek letters P "pressure drop over the test section (N m ) ρ "density of air (kg m ) Subscripts conv elect in loss out s x z "pertinent to convection heat transfer "pertinent to electrical energy "pertinent to inlet conditions "pertinent to total heat loss "pertinent to outlet conditions "pertinent to the smooth surface "pertinent to x direction of Cartesian co-ordinate system "pertinent to z direction of Cartesian co-ordinate system ACKNOWLEDGEMENT We are grateful for support of this work by the AtatuK rk University under contract 1996/61. REFERENCES Babus'Haq RF, Probert SD, Taylor CR Heat transfer e!ectiveness of shrouded, rectangular-"n arrays. Applied Energy 46:99}112. Bergles AE, Webb RL A guide to the literature on convective heat transfer augmentation. Advances in Enhanced Heat ¹ransfer HTD43:81}89. Goldstein RJ, Jabbari MY, Chen SB Convective mass transfer and pressure loss characteristics of staggered short pin-"n arrays. Journnal of Heat andmass ¹ransfer 37(1):149}160. Han JC Heat transfer and friction in rectangular channels with rib turbulators. Journal of Heat ¹ransfer 110(5):321}328. Holman JP Experimental Methods for Engineers (5th Edn). McGraw-Hill: New York. Hong YJ, Hsieh SS Heat transfer and friction factor measurements in duct with staggered and in-line ribs. Journal of Heat ¹ransfer 115(2):58}65. Hwang JJ, Liou TM Augmented heat transfer in a rectangular channel with permeable ribs mounted on the wall. Journal of Heat ¹ransfer 116(11):912}920. Hwang JJ, Liou TM Heat transfer and friction in a low-aspect-ratio rectangular channels with staggered perforated ribs on two opposite walls. Journal of Heat ¹ransfer 117(11):843}850. Incropera FP, Dewitt DP Fundamentals of Heat and Mass ¹ransfer (4th edn). Wiley: New York. Jurban BA, Hamdan MA, Abdualh RM Enhanced heat transfer, missing pin, and optimization for cylindrical pin "n arrays. Journal of Heat ¹ransfer 115(8):576}583. Lau SC, McMillin RD, Han JC Turbulent heat transfer and friction in a square channel with discrete rib turbulators. ASME Journal of ¹urbomachinery 113:360}366. Ledezma D, Morgan AM, Bejan A Optimal spacing between pin "ns with impinging #ow. Journal of Heat ¹ransfer 118(8):570}577. Liou TM, Hwang JJ. 1992a. Turbulent heat transfer augmentation and friction in periodic fully developed channel #ows. Journal of Heat ¹ransfer 114(2):56}64. Liou TM, Hwang JJ. 1992b. Developing heat transfer and friction in a rectangular ribbed duct with #ow separation at inlet. Journal of Heat ¹ransfer 114(2):565}573. Liou TM, Hwang JJ E!ect of ridge shapes on turbulent heat transfer and friction in a rectangular channel. International Journal of Heat andmass ¹ransfer 36:931}940. Liou TM, Wang WB, Chang YJ Holographic interferometry study of spatially periodic heat transfer in a channel with ribs detached from one wall. Journal of Heat ¹ransfer 117(2):32}39.

14 576 O. N. ȘARA E¹ A. Molki M, Faghri M, Ozbay O A correlation for heat transfer and wake e!ect in the entrance region of an in-line array of rectangular blocks simulating electronic components. Journal of Heat ¹ransfer 117(2):40}46. Molki M, Mostou"zadeh AR Turbulent heat transfer in rectangular ducts with repeated-ba%e blockages. Journal of Heat andmass ¹ransfer 32(8):1491}1499. Naik S, Probert SD, Shilston MJ Forced convective steady-state heat transfer from shrouded vertical "n arrays aligned parallel to an undisturbed air stream. AppliedEnergy 26:137}158. Reay DA Heat transfer enhancement-a review of techniques and their possible impact on energy e$ciency in the U. K. Heat Recovery System & CHP 11(1):1}40. Șara ON Doktora Tezi. AtatuK rk UG niversitesi, Fen Bilimleri EnstituK suk, Erzurum, Turkey. Tahat MA, Babus'Haq RF, Probert SD Forced steady-state convections from pin-"n arrays. AppliedEnergy 48:335}351. Zhang YM, Gu WZ, Han JC Heat transfer and friction in rectangular channels with ribbed or ribbed-grooved walls. Journal of Heat ¹ransfer 116(2):58}65.