Development of an experimental set-up for the study of heat

transfer mechanisms in forced convection flows - application to

waste heat recovery systems in vehicles

Filipe A. C. Ferreiraferreira.filipeac@gmail.com

University of Lisbon, Lisbon, Portugal

May 2016

Abstract

Waste heat recovery from exhaust gases is a promising approach to improve internal combustionengines efficiency and, consequently reduce fuel consumption of passenger vehicles. This study addressesthe first step towards the development of a heat exchanger to be included in a waste heat recovery system,based on Rankine cycle. Hence, an experimental set-up was projected, developed and tested, to providethe characterization of heat transfer and fluid flow inside a single channel of the heat exchanger.

Heat exchanger operating conditions were simulated in the experimental set up, with constant heatflux of 31,7 kW/m2 at the wall of an horizontal 5,35 mm I.D. stainless steel channel with heating lengthof 200 mm. Water was used as the working fluid. Reynolds number ranged between 530 < Re < 6050.Atmosphere pressure was considered at this early stage of the work to minimize design complexity.Experimental results were first validated against various correlations available in literature, to evaluatefriction factor and Nusselt number in laminar regime.

Results show that there is a good agreement between experimental values and the correlations,except of larger values of friction factor, associated to entry effects and to flow development. Transitionlaminar-turbulent occurs at the slope changing point of friction factor depicted as a function of Reynoldsnumber.

Experimental Nusselt number values are much higher than those predicted by various correlationsreported in literature for laminar flow regime. In contrast, lower Nu values were obtained in theturbulent regime, which are overpredicted by correlations.

Laminar-turbulent transition occurs at Re = 2700 for adiabatic flow and 3200 for diabatic flow.Friction factor values are higher in diabatic flow than in adiabatic flow for laminar regime, but aresimilar for turbulent regime.

Overall the results show that the correlations found in literature can be used with strong restrictionsfor the particular flow conditions studied here. Hence, this experimental work is also expected to provideuseful information to devise alternative correlations.Keywords: Transitional flow, Diabatic flow, Heat transfer coefficient, Friction factor, Heat exchanger

1. Introduction

ICEs (Internal combustion engines) are nowadaysthe major source of motive power in the world andits use is expected to continue for some decades.With ever increasing price of oil and growing con-cern on energy conservation, a big effort has beendone to develop technologies that promote fuel effi-ciency in passenger vehicles. In ICEs only about 25% of the fuel combustion energy is converted intouseful work to drive the vehicle and its accessoryloads. The remaining energy is wasted in the formof heat in: coolant, engine block and the exhaustline. Furthermore, of the total energy loss, wasteheat of exhaust gas has the larger fraction of about

40 % [1]. As a result, different waste heat recov-ery techniques were recently proposed. Waste heatrecovery systems based on a RC (Rankine cycle)have proved to be one of the most attractive tech-niques, due to smaller pumping losses in the exhaustline and reduced costs in comparison with the otherwaste heat recovery systems [2].

In order to recover the exhaust gas waste heat,the RC is composed by an HEX (heat exchanger)that is placed in the exhaust line. An HEX used inthis type of systems has to be small-sized in a light-weighted arrangement, maintaining high exchangeefficiency. Previous studies demonstrate that ina practical application, the working fluid in the

1

channels of the HEX is in most cases in laminar-turbulent transition regime, for which theoreticaland empirical correlations are still scarce [3]. Inthis context, the present work contributes towardsthe design, test and construction of a modular testsection that will allow to study the fundamentaltransport phenomena, in the laminar and transi-tion regime, that occurs within the channels of theHEX. As a first step, the fundamental fluid flowpressure drop and heat transfer mechanisms are in-vestigated for a single pipe, although covering ex-perimental conditions which are relevant for thecross-flow HEX integrated in the waste heat recov-ery system based on a RC.

Internal flow is usually divided in three regimes:laminar, transitional and turbulent. The main pa-rameter used to define the different regimes is theReynolds number, Re = 4m/(µπDh), which is aratio between inertial and viscous forces. Withincreasing Reynolds number the velocity field ex-hibits random fluctuations (turbulence), whereasthe intermediate region corresponds to the tran-sitional regime. Since the development of Moodydiagram [4] the understanding of transition pro-cess let to conclude that it occurs not at a spe-cific value of Reynolds number but in some intervalof its value between the critical Reynolds number(widely considered equal to 2300 [4]) to a some-what larger value. In this transitional flow regimeinterval, the flow alternately becomes laminar orturbulent [3]. Furthermore, it has been observedin smooth channels that transitional flow regimecan occur for Reynolds number ranging from 400to 10000 [5].

Uniform wall heat flux boundary condition ispresent in every channel of the HEX. This can leadto the occurrence of a secondary flow induced bybuoyancy forces. When heat flux is imposed tochannel’s wall the working fluid near the wall hasa higher temperature and therefore smaller specificmass than the fluid in the centreline of the channel,which leads to fluid circulation in upwards direc-tion (opposite to gravity). However, the fluid inthe centreline of the channel has a smaller temper-ature with higher specific mass so the fluid circu-lates in gravity’s direction. This fluid motion dueto temperature differences originates vortices desig-nated as secondary flow, which leads to a consider-able augmentation of heat transfer coefficient. Fur-thermore, it is possible to distinguish between twodifferent mechanisms: (i) forced convection thatoccurs with higher fluid velocities thus suppress-ing secondary flow effects and (ii) mixed convectionthat occurs when the flow has such conditions thatsecondary flow effects cannot be neglected. Thisheat transfer mechanism is a combination of forcedconvection with natural convection (from secondary

flow). Whenever the flow is laminar or in transi-tional regime, which is typical in many HEXs asthe one studied in the present work, mixed convec-tion dominates and secondary flow effects shouldbe taken in consideration. For turbulent flow, fluidvelocities increase considerably, secondary flow ef-fects are suppressed and forced convection mecha-nism dominates.

Regarding to hydrodynamic phenomena there isan important distinction between entry and fullydeveloped regions. When laminar flow contactswith the channel’s wall, viscous effects contributeto the development of a boundary layer that in-creases along the axial direction and alter the ve-locity profile in each cross-section of the channel -entry length region. Downstream there’s a pointwhere viscous effects no longer alter the velocityprofile and define the beginning of the fully de-veloped region. While studying internal flow it ismandatory to take into account the hydraulic en-try length, zfd,h. These lengths depend whetherthe flow is laminar or turbulent and are given byequations 1 and 2 respectively [4, 6].

zfd,hlam = 0, 05ReDh (1)

10Dh ≤ zfd,hturb ≤ 60Dh (2)

To evaluate the pressure drop along the channelit is convenient to use the friction factor f which iscalculated using equation 3 when assuming constantspecific mass, ρ, in axial direction.

f =Dh

L

2∆p

ρv2(3)

Where Dh is the hydraulic diameter, L is thechannel’s length, v the mean cross-sectional veloc-ity and ∆p the pressure drop along the channel.For fully developed laminar flows, friction factor canbe obtained analytically and is equal to 64/Re [4].However for developing laminar flow, not only fric-tion effects are taken into account, but also entryregion phenomena. Shah [7] developed a correlationto determine the friction factor in both entry andfully developed regions given by equation 4.

fapp = 64Re

(3,44

(z+)1/2+ 0,31/z++16−3,44(z+)−1/2

1+0,00021(z+)−2

)(4)

where:

z+ =z/Dh

Re(5)

Recently, Tam et al. [8] developed a correlationbased on Shah’s given by:

fapp = 4Re

(16 + 0,00314

0,00004836+0,0609(z+)1.28

)(6)

2

which can be applied for: (i) 799 < Re < 2240e (ii) 3 < z/Dh < 200. With a precision between-26,1% and +28,1%.

In turbulent flow, hydraulic phenomena is muchmore complicated in comparison with laminar flow.Even for fully developed flow it is always necessaryto use experimental results to devise empirical cor-relations. There are several correlations in the liter-ature for fully developed turbulent flow. Equations7 and 8 represent the correlations of Blasius [9] andPetukhov [10] respectively which are vastly known.

f = 0, 3164Re−0,25 (7)

f = (0, 79lnRe− 1, 64)−2 (8)

Both correlations were developed for Re > 3000.Regarding transitional flow Tam et al. [8] devel-

oped a correlation given by equation 9 which wasobtained for the following conditions: (i) fully de-veloped flow; (ii) 2026 < Re < 3257 and (iii) 3 <z/Dh < 200.

f =(64Re

) ([1 + (0, 0049Re0,75)0,52

]1/0,52 − 3, 47)

(9)

The authors also devised another correlation (10)for developing flow based on equation 9 which in-cludes a correction factor for taking into accountentry region effects.

f =(64Re

) ([1 + (0, 0049Re0,75)0,52

]1/0,52 − 3, 47) [

1 +(

4,8z/dh

)](10)

The application range for this correlation is:2019 < Re < 3257 and 3 < z/Dh < 200. These cor-relations depicted in equations 9 and 10 have a pre-cision of -8,6% to +7,9% and of -25,9% to +21,9%respectively [8].

Besides hydrodynamic mechanisms it is also nec-essary to evaluate heat transfer in order to char-acterize the internal flow. Whenever a fluid en-ters an heated channel with a uniform temperatureprofile, heat transfer occurs by convection betweenfluid and channel’s wall and the thermal boundarylayer develops in the axial direction while the fluidtemperature is smaller than the channel’s wall tem-perature. If the boundary condition at the wall isfixed, which in the present study corresponds toconstant heat flux, the flow reaches fully developedconditions at a distance from the entrance, corre-sponding to the thermal entry length. As in hy-drodynamic mechanisms, two distinct regions canbe distinguished: thermal entry region and thermalfully developed region. For laminar flow the ther-mal entry length is given by [4]:

zfd,tlam = 0, 05DhRePr (11)

and for turbulent flows the following approxima-tion can be used [4]:

zfd,tturb = 10Dh (12)

While comparing equations 1 and 11 it can benoticed that for Pr > 1 (Pr = µcp/k) the hydraulicboundary layer develops faster than the thermal,whereas zfd,h < zfd,t. Furthermore, it is reasonableto assume a fully developed velocity profile in thethermal entry region for higher Prandtl numbers(> 100) [4]. Kandlikar et al. [6] demonstrated thatfor water, this assumption led to satisfactory resultswhen compared against experimental data.

Heat transfer coefficient varies along a heatedchannel with constant heat flux in the thermal entryregion and remains constant when fully developedthermal conditions are achieved. Figure 1 (a) rep-resents the variation of heat the transfer coefficient,h, against the axial distance from the entrance ofthe channel, z. At the entrance of the channel,z = 0, the heat transfer coefficient is extremelyhigh because the thermal boundary layer is verythin. Although it decreases rapidly with z due tothe thickening of the boundary layer. At z = zfd,tthe heat transfer coefficient assume a specific valuealong axial direction since fully developed thermalconditions are attained. With constant heat fluxat wall boundary condition the mean temperatureof the working fluid at each section of the chan-nel, Tm, varies linearly with the axial direction, z,as seen in figure 1 (b). Furthermore, the tempera-ture difference between the inner wall of the channeland the working fluid, (Ts−Tm), also varies with z,whereas this temperature difference is small at theentrance of the channel due to low heat transfer co-efficient and increases with z, reaching a constantvalue when the flow is fully developed thermally [4].

(a) (b)

Figure 1: Heat transfer inside a channel with con-stant heat flux at the wall (a) h vs z (b) (Ts − Tm)vs z [4].

A majority of studies related with internal flowheat transfer mechanisms make use of the adimen-sional Nusselt number, which is a ratio between

3

heat transfer coefficients due to convection and dueto conduction as defined in equation 13. This num-ber provides a good measure to characterize heattransfer phenomena in both laminar and turbulentregimes.

Nu =h

kDh (13)

For fully developed laminar flow with constantheat flux boundary condition, Nusselt number canbe obtained analytically and assume a constantvalue of approximately 4,364 [4, 11]. However forlaminar flow in the entry region heat transfer mech-anisms present much more complexity since the ax-ial component of velocity is different from zero, incontrast with the fully developed region where thevelocity has no axial component. In literature twomainly different approaches are used to cope withthis problem [4]. The simplified approach consid-ers flow with developing thermal characteristics inthe presence of a fully developed velocity profile,which can be applied when the Prandtl number isconsiderably high, since zfd,h zfd,t. The secondapproach consists in considering both velocity andtemperature developing profiles.

The correlations presented below concern con-stant heat flux at the channel’s wall boundary con-dition. Churchill and Ozoe [12] obtained a correla-tion for both developing and fully developed condi-tions, as in equation 14.

Nuz

4,364[1+(Gz/29,6)2]1/6=

(1 +

[Gz/19,04

[1+(Pr/0,0207)2/3]1/2

[1+(Gz/29,6)2]1/3

]3/2)1/3

(14)

Where local Nusselt number, Nuz, and Graetznumber, Gz, are given by equations 15 and 16, re-spectively.

Nuz =q′′s dh

k[Ts(z)− Tm(z)](15)

Gz =π

4z∗=π

4

RePr

z/Dh(16)

Churchill and Ozoe correlation (equation 14) hasan average deviation of 5%, for Pr=0,7 and Pr=10,when compared against numerical results.

Ghajar and Tam [13] in 1994 developed an-other correlation for the same conditions: lami-nar regime in both entry and fully developed re-gions, as in equation 17. This correlation wasobtained using mixed and forced convection ex-perimental data and has the following applicationrange: (i) 280 ≤ Re ≤ 3800, (ii) 3 < z/Dh < 192,(iii) 40 ≤ Pr ≤ 160, (iv) 1000 ≤ Gr ≤ 2, 8 × 104

and (v) 1, 2 ≤ µ/µs ≤ 3, 8.

Nu = 1, 24[RePrDh

z + 0, 025(GrPr)0,75]1/3 ( µ

µs

)0,14(17)

This correlation represented the experimentaldata to within -16,9% and +15,4%.

Recently and also for laminar regime and bothdeveloping and developed regions, Gnielinski [14]obtained the following correlation:

Nu =

[4, 3543 + 0, 63 +

(1, 953 3

√RePrDh/L− 0, 6

)3+(

0, 924 3√Pr√ReDh/L

)3]1/3 (18)

For fully developed turbulent flow there is a corre-lation widely used which is the Dittus-Boelter equa-tion [4, 11], where:

Nu = 0, 023Re0,8D Pr0,4 (19)

The application range of equation 19 is:(i) 0, 7 < Pr < 120, (ii) 2500 < Re < 1, 24×105 and(iii) L/Dh > 60. All properties needed to calculateReynolds and Prandtl numbers should be evaluatedat fluid mean temperature, Tm. Maximum errorof this correlation in comparison with experimen-tal data is approximatly 40 % [11]. However, it ispossible to find in literature other correlations withbetter accuracy, such as Gnielinski’s [4, 11]:

Nu =(f/8)(Re− 1000)Pr

1 + 12, 7(f/8)1/2(Pr2/3 − 1)(20)

where f is the friction factor and can be calcu-lated using, for example, equation 8. Gnielinski’scorrelation has an accuracy of 10 % for Prandtlnumbers between 0,5 and 106 and Reynolds num-bers between 2300 and 5×106 [11]. Fluid propertiesare evaluated at mean temperature, Tm.

Gnielinski [15] developed another correlation forthe turbulent regime based on equation 20 andadding a correction factor to take into account entryregion effects as expressed in equation 21.

Nu = Nueq20

[1 + (Dh/L)2/3

]( µ

µs

)0,14

(21)

Equation 21 can be applied to Reynolds num-bers larger than 3000 and a wide range of Prandtlnumbers (between 0,5 and 2000). The author rec-comends equation 22 below to calculate the frictionfactor.

feq21 = 4 (1, 58lnRe− 3, 28)−2

(22)

Ghajar and Tam [13] obtained for both develop-ing and fully developed turbulent flow the followingequation:

Nu = 0, 023Re0,8Pr0,385(z/Dh)−0,0054(µ/µs)0,14 (23)

whereas the correlation was compared againstexperimental data where the following parameters

4

were evaluated: (i) 7000 ≤ Re ≤ 49000, (ii) 3 <z/Dh < 192, (iii) 4 ≤ Pr ≤ 34 e (iv) 1, 1 ≤ µ/µs ≤1, 7. This experimental data was correlated within-10,3% and +10,5%.

Ghajar and Tam [13] also developed a correlationspecifically for transitional flow regime as in equa-tion 24.

Nu =(Nulam + exp[(1766−Re)/276] +Nu−0,995turb

)−0,995(24)

Where Nulam = Nueq17 and Nuturb = Nueq23since the three equations (17, 23 and 24) weredeveloped by the same author. This correlationcan be applied for developing and fully developedthermal conditions with an application range of:(i) 1700 ≤ Re ≤ 9100, (ii) 3 ≤ z/Dh ≤ 192,(iii) 5 ≤ Pr ≤ 51, (iv) 4000 ≤ Gr ≤ 2, 1 × 105

and (v) 1, 2 ≤ µ/µs ≤ 2, 2. The results of this cor-relation were within -23% e +25,1% in comparisonwith experimental data obtained by the authors.

2. Experiments2.1. Case study parametrization

In order to characterize the internal flow inside asingle channel of the HEX of the present work it ismandatory to parametrize the main variables. Theshell and tube cross flow HEX used in the WHRSis composed by 210 channels (21 × 10) with 6,35and 5,35 mm of external (De) and internal (Dh) di-ameters, and 200 mm length (L). The conditionsin which the HEX operate are directly related withvehicle’s operation conditions. As a first step in thedevelopment of this experimental apparatus onlyone specific vehicle operation point was selected,in which the exhaust gases have the following char-acteristics: (i) mass flow, mg = 50 g/s; (ii) inlettemperature, Tg,in = 650 oC and (iii) outlet tem-perature, Tg,out = 200 oC Hence, the average heatflux imposed at channel’s wall can be calculated us-ing equation 25:

q′′ =mgcp(Tg,in − Tg,out)

NπDeL(25)

where cp is the specific heat of the exhaust gasesand can be obtained using equation 26 with themean temperature, (Tg,in + Tg,out)/2, in Kelvin.

cp = 956, 0 + 0, 3386Tge − 2, 476× 10−5T 2ge (26)

Using equations 25 and 26 the average heat fluximposed at channel’s wall is 31.7 kW m-2.

The working fluid (water) inside the HEX is at20 bar with inlet and outlet temperatures of 50 and260 oC, respectively. By applying a simple energybalance it possible to estimate that the mass flow is10 g/s. However it is possible to adjust the opera-tion conditions of the HEX by choosing between 1,

2, 5 or 10 channels as inlets. Consequently the massflow of the working fluid varies between 1 g/s (with10 channels as inlets) and 10 g/s (with 1 channel asinlet). The HEX is divided in three sections: pre-heater, evaporator and super-heater; correspond-ing to 65 %, 30 % and 5 % of HEX’s total vol-ume. In the pre-heater the working fluid is heatedfrom compressed liquid to saturated liquid (x = 0).In the evaporator it goes from saturated liquid tosaturated vapour (x = 1) and in the super-heaterfrom saturated vapor to superheated vapor, until itreaches about 260 oC. In the present work an ex-perimental set-up was developed to study the pre-heater and evaporator sections of the HEX. How-ever, as a first step, it is focused in the conditions ofpre-heater section which corresponds to more thanhalf of HEX’s total volume. The working fluid atthe experimental set-up is at atmospheric pressure.In spite of HEX’s pressure being much higher (20bar) there is no significant differences when usingReynolds number to characterize the flow since dy-namic viscosity of working fluid is almost constantfor the same temperature at different pressures.

With this parametrization it was possible tostudy the flow inside HEX, although it is importantto refer that this parameters were calculated for asingle operation point of the vehicle and differentconditions can occur with other operation regimes.

2.2. Experimental apparatus

The experimental set-up was based on previousstudies reported in the literature addressing hori-zontal single- and two-phase flow [16–19]. The ap-paratus consists in three main sections: the pre-heating section, the test section and the visualiza-tion section. The working fluid flows along theset-up in an open loop circuit starting from a con-trolled temperature reservoir (reservoir A) slightlypressurized and ending in a second reservoir (reser-voir B) at atmospheric pressure, which has a pumpto elevate the fluid back to the first reservoir. Tocontrol fluid’s temperature in the reservoir A oneOmega K-type thermocouple was installed at theoutlet. Downstream a volumetric flow sensor (Cyn-ergy UF08B) was placed just before pre-heating,test and visualization sections. Since volumetricflow sensor has a maximum working temperatureof 85 oC a non-return valve was installed betweenthe flow sensor and pre-heating section to avoid thatliquid or vapour back-flows due to instabilities thatcan occur near to saturation temperature.

Pre-heating section consists of a stainless steelchannel AISI 304 with 2000 mm length with inter-nal and external diameters of 6 and 8 mm respec-tively. Heat flux is imposed at the wall by means ofan heating wire with 35, 5Ω coiled around the wholechannel’s length. Electrical power was controlled by

5

adjusting the voltage applied to the heating wire(between 0 and 260 V). Since electrical power is afunction of the voltage applied, Pel = V 2/R, themaximum electrical power of the pre-heating sec-tion was 1900 W. Temperature and pressure weremeasured at the inlet of the pre-heating section us-ing an Omega K-type thermocouple and an abso-lute pressure transducer MPX4250A. Test sectionalso consists of a stainless steel channel AISI 304with 412 mm length whereas internal and externaldiameters are of 5,85 and 6,35 mm respectively. Theheating method is similar to that used in the pre-heating section. However the heating wire has anhigher electrical resistance of 170.4Ω and is coiledaround 200 mm of the channel’s length (to cor-respond with the HEX channels length). Powersupply for the test section provided between 0 and230 V, which corresponds to a maximum electricalpower of 310 W. Temperature was measured at theinlet and outlet of the test section by two OmegaK-type thermocouples. Pressure was measured atthe outlet using a MPX4250A absolute pressuretransducer. Along the channel, pressure drop wasmeasured using a Honeywell 26PC series differentialpressure transducer. To measure the working fluid’stemperature along the test section four Omega K-type contact thermocouples were installed on chan-nel’s outer wall in two distinct cross sections locatedat the inlet and outlet of the heated length. Eachcross-section had a thermocouple at the top and atthe bottom of channel’s outer wall, as in figure 2.

Figure 2: Channel’s cross-section. (a) thermocou-ple; (b) fibreglass; (c) heating wire.

Figure 2 depicts the fibreglass layer that was usedto preclude contact between the heating wire andthe channel’s outer wall. Furthermore, fibreglasswas also used to thermally insulate the pre-heatingand test sections.

The visualization section consists of a glass chan-nel with 100 mm length with internal and externaldiameters of 6 and 9 mm respectively. Thermal in-sulation was achieved using a Kaiflex ST foam witha small window to allow visualization.

In terms of instrumentation, volumetric flow sen-

sor, differential pressure transducer and thermocou-ples were calibrated before any experiment was per-formed. A data acquisition system was used torecord the experimental data and consisted of twodistinct data acquisition boards, NI USB-6008 andDT9828, that were connected to a personal com-puter where Labview software and QuickDAQ soft-ware were used to connect with the boards. Afterrecorded, experimental data was used to calculatethermodynamic properties of the working fluid ac-cording to standard IAPWS-IF97 [20]. A Matlabroutine was developed to perform the calculationsand provided enthalpy i, dynamic viscosity µ, spe-cific mass ρ, thermal conductivity k and specificheat cp at three different locations: pre-heating sec-tion inlet and test section inlet and outlet.

2.3. Data reductionAs aforementioned temperature and pressure

were measured at three different locations: the pre-heating section inlet, the test section inlet and thetest section outlet. It is worth noting that to calcu-late the thermodynamic properties at the test sec-tion inlet it was necessary to add the pressure dropalong the channel with the pressure at the outlet,pin = pout + ∆p.

The effective heat flux in the test section, q′′eff ,was calculated using equation 27.

q′′eff =m(iout − iin)

πDhL, (27)

where i corresponds to fluid’s enthalpy.Temperatures at the outer wall of the test section

channel, Tw(z), were taken in two different crosssections. Unidimensional conduction was assumedto calculate the temperatures at the inner wall ofthe channel, Ts(z), using equation 28:

Ts(z) = Tw(z)−q′′eff ln(De/Dh)

2πkL(28)

where k corresponds to the thermal conductiv-ity of the wall material, which varies with temper-ature, a polynomial correlation was developed todetermine it.

Local heat transfer coefficient, h(z), was calcu-lated by equation 29:

h(z) =q′′eff

Ts(z)− Tm(z)(29)

where Tm is the mean fluid temperature at eachcross section. Equation 30 was used to calculateTm, assuming that it varies linearly along the testsection channel.

Tm(z) =Tout − Tin

Lz + Tin (30)

Global heat transfer coefficient was determinedusing equation 31:

6

h =q′′effTs − T

, (31)

where Ts corresponds to the arithmetic mean ofthe four calculated temperatures at the inner wallof the channel and T is given by equation 32.

T =Tin + Tout

2(32)

Nusselt number, Nu, and j-Colburn factor, j,were used to evaluate the heat transfer mechanismsin the test section. The local and global Nusseltnumbers were calculated using equations 33 and 13respectively.

Nu(z) =h(z)Dh

k(33)

k is the thermal conductivity of the working fluidevaluated at Tm in equation 33 and at T in equation13.

The j-Colburn factor was calculated using equa-tion 34.

j =Nu

RePr1/3(34)

and the friction factor is given by equation 3,where L corresponds to the length of the channelwhere ∆p is measured, i.e. the test section channellength (412 mm). Specific mass, ρ, of the workingfluid was evaluated at T and the velocity, v, wascalculated using the mass flow that was experimen-tally measured (equation 35).

v =4m

πρD2h

(35)

2.4. Experimental validation and uncertaintiesThe absolute error, E, of a measured or calcu-

lated value is given by equation 36:

E =|Mm −Me|

Me(36)

where Mm is the measured or calculated valueand Me is the predicted value. Mean absolute error,E, is then given by equation 37:

E =1

N

N∑k=1

|Mmk −Mek|Mek

(37)

where N is the number of experimental datapoints used.

All uncertainties were calculated within the 95 %confidence level using the method based on Dunn’s[21]. Table 1 lists the instruments used in the studywith their uncertainties. The uncertainty of theReynolds number is almost constant for every testedflow conditions: approximately 7 %. Friction fac-tor’s uncertainty decreases while Reynolds number

is increased, whereas for Re > 4000 the friction fac-tor uncertainty is approximately constant and equalto 12 %. Furthermore in diabatic conditions frictionfactor’s uncertainty is slightly larger than that foradiabatic flow. Nusselt number uncertainty is largerthan that of the Reynolds and of the friction factoressentially due to the developing thermal boundarylayer present along the whole channel. The uncer-tainties of the experimental parameters are summa-rized in table 2.

Instrument Range Uncertainty

ThermocouplesInlet / Outlet a -200 a 1250 oC 0,75 %Channel’s Wall -200 a 1250 oC 0,75 %Flow meter 0,1 - 8 L/min 5 %Absolute pressure transducer (P1 e P3) 0,2 - 2,5 bar 0,0345 barDifferential pressure transducer 0 a 34500 Pa 1,0 %

Table 1: Range and uncertainties of instrumenta-tion. a - test section

Parameter Range Uncertainty

T 23 - 73 oC 0,5 a 6,0 oCTs 23 - 95,7 0,2 a 1,8 oCm 2,9 - 15,2 g/s 5,3 - 9,8 %∆p 66 - 1705 Pa 1,3 - 19,7 %Re 530 - 6050 5,3 - 9,9 %Pr 2,46 - 6,08 1,3 - 1,4 %Nu 2,3 - 29,8 10,3 - 25,8 %j 0,0010 - 0,0056 11,8 - 25,0 %f 0,06 - 0,36 10,8 - 24,9 %

Table 2: Range and uncertainties of the experimen-tal parameters.

Since the present study consisted in the develop-ment, dimensioning and validation of an experimen-tal set-up a significant part of the experiments per-formed were used for validation purposes. In termsof pressure drop this was done by taking measure-ments in the pre-heating section since this proce-dure assumed that the data was obtained in fullydeveloped flow conditions. These experiments weretaken with no heat flux imposed. In figure 3 exper-imental friction factor is compared against litera-ture correlations for adiabatic fully developed flow.For the laminar regime, the mean absolute error offriction factor was 4% in comparison with Poiseuilleequation. For Re > 2800 the deviation from experi-mental values against literature correlations is muchlarger since the flow had not reached fully turbulentconditions and was in the transitional regime.

In terms of the Nusselt number, measurementswere taken for laminar regime in the test section andwith an imposed heat flux of 92 kW m-2 to the wall.Figure 4 shows the experimental values obtained incomparison with different correlations taken fromthe literature for developing flow. Experimentalvalues were better represented by Gnielinski’s corre-

7

Figure 3: Friction factor as a function of theReynolds number - pre-heating section.

lation from equation 18 with a mean absolute errorof 16,3%.

Figure 4: Average Nusselt number in the test sec-tion for laminar regime.

Measurements were taken for the highestReynolds number studied to compare them withturbulent flow correlations taken from the litera-ture. Figure 5 compares the experimental valuesobtained for 5000 < Re < 6500 with correlationstaken from the literature for turbulent flow. Exper-imental values were better represented by Gnielin-ski’s correlation for turbulent flow (equation 21)with a mean absolute error of 8,0 %. In spite offully turbulent conditions were not present in theflow for this range of the Reynolds number, experi-mental data was within the uncertainty of the cor-relations used.

Finally, heat loss analysis was performed for bothpre-heating and test sections. It was concluded thatheat losses were around 30 % for the whole experi-mental studied conditions.

Figure 5: Average Nusselt number in the test sec-tion for 5000 < Re < 6500.

3. Results3.1. Adiabatic friction factor

A series of experiments were performed withoutheating in order to evaluate the adiabatic frictionfactor in the test section. As can be observed infigure 6 the experimental friction factor was con-siderably larger than the values predicted by dif-ferent correlations taken from the literature evenwhen compared with those that include entry re-gion effects. Hence, the laminar regime friction fac-tor is larger than those predicted in the correlationssince developing flow (hidraulically) is present forthe whole experimental data. Using equation 1 atleast 42% of channel’s length corresponds to theentry region. Furthermore 70% of the experimen-tal data points correspond to an entry region thatoccupies at least 80% of the channel’s length. Thisis related with the ratio L/Dh that is small andapproximately equal to 70 for the test section instudy. Barlak et al. [22] studied the effect of thisratio on the friction factor and concluded that forL/Dh < 100 in the laminar regime, the friction fac-tor increases when L/Dh decreases.

Figure 6: Friction factor as function of the Reynoldsnumber.

8

For Re > 2500, friction factor experimentally de-termined was also larger than that predicted by Bla-sius and by Petukhov correlations. This might bedue to the geometry at inlet and outlet of the testsection. Despite of special precautions with sufacecontinuity at these locations there was a small dif-ference between the pre-heating and test sectionsinternal diameters, which were 6 and 5,85 mm re-spectively. This discontinuity could generate an in-crement in pressure drop that increases with flow’smean velocity, becoming more evident in the turbu-lent than in the laminar regime. Also entry regioneffects can influence the results as referred above.However this effect is less pronounced in turbulentregime since fluid’s inertial forces are much largerthan viscous forces.

As it can be seen in figure 6, experimental datafollows the same trend as the values predicted fromthe correlations. Indeed, figure 6 clearly shows thatthe experimental and theoretical curve’s slope arevery similar in both laminar and turbulent regimes.The slope change in the experimental friction fac-tor curve dictates laminar-turbulent transition andoccurs for 1500 < Re < 3000. In the presenttest section transition occurs smoothly instead ofabruptly as usual. This phenomena has also beenobserved by Barlak et al. [22]. Friction factor’s un-certainty has a significant increase from 2 to 7% fora Reynolds number approximately equal to 2700,which has been stated to be a good indicator oftransition [3].

3.2. Diabatic flowThe following results were obtained by a series of

130 experiments with an imposed heat flux of 92kW/m2 and 800 < Re < 6000.

3.2.1. Nusselt numberFigure 7 shows the experimental and predicted

Nusselt number as function of the Reynolds. Thecorrelations used for comparison correspond toequations 18 and 21 for laminar and turbulentregimes, respectively and both include entry regioneffects.

As expected, for laminar flow, the Nusselt num-ber is larger than the analytically obtained valueof 4,364 for fully developed laminar flow. This ismainly due to the fact that the secondary flow ispresent in this regime enhancing heat transfer andalso due to the developing thermal boundary layeralong the whole channel. Thermal entry length in-creases with the Reynolds number leading to largerNusselt number since the axial distance to achievefully developed conditions is larger. It can be seenfrom figure 7 that the Nusselt number increases con-siderably for Re ≈ 3200 which is a good indicator oftransition. Also, uncertainties showed an increaseat this value of Reynolds.

Figure 7: Experimental Nusselt number as a func-tion of the Reynolds number.

In the turbulent regime, the Nusselt number ispredicted to increase with the Reynolds number.As shown in figure 7 this trend can only be ob-served for Re > 4500. This is due to the fact thatfully turbulent conditions are not reached in the testsection and flow is characterized by fluctuations be-tween laminar and turbulent regimes (transitionalregime). Hence, Nusselt numbers are over-predictedin turbulent flow which however is in agreementwith a recent study [3] referring that correlationsfor turbulent regime usually overpredict the Nus-selt number for Reynolds number between the crit-ical value (onset of transition) and about 10000.

3.2.2. Friction factor

Figure 8 depicts the experimental friction factoragainst Reynolds for adiabatic and diabatic flow.The straight line corresponds to the analytical solu-tion for the laminar regime (f = 64/Re) while thedotted line represents the friction factor obtainedwith Blasius equation for turbulent flow (equation7).

Figure 8: Experimental friction factor as a functionof the Reynolds number.

9

Friction factor is larger for diabatic flow, in com-parison with adiabatic flow, when heat flux is im-posed at the channel’s wall for laminar and transi-tional regimes, while for the turbulent regime, fric-tion factor has the same magnitude in both cases.This is in agreement with observations reportedin the literature [3, 23], where authors stated thatthe difference found between diabatic and adiabaticflow in the laminar regime was due to secondaryflow effects that usually occur for small fluid meanvelocities inside the channel. Furthermore when theimposed heat flux increases, shear stress at the wallincreases, augmenting the friction factor [23].

To identify if the heat transfer mechanism ischaracterized by mixed convection, the ratio oflocal heat transfer coefficients at the top and atthe bottom, ht/hb, was used as in previous stud-ies [3, 8, 23, 24]. Accordingly to these studies, ifht/hb < 0, 8 mixed convection is dominant, whilefor ht/hb > 0, 8 forced convection is dominant andsecondary flow effects can be neglected. In thepresent work ht/hb was evaluated for a specificcross-section of the channel where z/Dh = 61, 5and it was observed that for Re > 4600 secondaryflow effects were almost negligible since ht/hb wasslightly higher than 0,8 (approximately 0,9).

Laminar-turbulent transition occurs for Reynoldsaround 3200 as can be observed in figure 8, whichis in agreement with the previous analysis in termsof Nusselt number (figure 7). However an atypi-cal trend is observed for onset of transition, sincethe friction factor decreases abruptly instead of in-creasing as usual. This could be related with theextremely high heat flux imposed at the channel’swall in order to simulate HEX conditions. In previ-ous studies reported in the literature imposed heatflux is always smaller than 20 kW/m2 while in thisstudy it was up to 90 kW/m2. So the friction factorin the laminar regime was even higher than in theturbulent regime, since the extremely high heat fluximposed at the wall lead to severe secondary floweffects that alter the velocity profile and increasethe shear stress at the wall.

For Re > 3300 adiabatic and diabatic friction fac-tors are very similar since no secondary flow effectsare present. Although for Re > 4500 the diabaticfriction factor is slightly smaller than the adiabaticone, which is related to the pressure of very smallair bubbles present inside the channel.

3.2.3. Simultaneous analysis

Figure 9 depicts the j-Colburn factor and the fric-tion factor as a function of the Reynolds number toinfer on a possible relation between the heat trans-fer mechanisms and the pressure drop.

For the laminar regime, the pressure drop is highand heat transfer is reduced, while for Re > 3200

Figure 9: Experimental friction and j-Colburn fac-tors as a function of the Reynolds number.

(start of transition) the pressure drop decreasesand heat transfer is enhanced. Furthermore forRe > 3200 the pressure drop is always smaller thanfor the laminar regime, in contrast with j-Colburnfactor that increases abruptly at the onset of tran-sition and then decreases continuously with largerRe, until it is approximately similar to the valuesobtained for laminar flow.

These results are atypical and specific for theseconditions where imposed heat flux at the chan-nel’s wall is very high. Hence, additional correla-tions should be devised to describe these particulartrends.

4. Conclusions

The present work is the first step towards an ex-perimental study to evaluate the flow characteristicsinside one channel of a specific HEX implementedon a waste heat recovery system in vehicles basedon Rankine cycle. It can be concluded that, dueto the geometric characteristics and imposed condi-tions, heat transfer mechanisms and pressure drophave a very unique behaviour, i.e. high imposedheat fluxes in transitional non-developed flow, andare in some aspects different from those usually re-ported in the literature.

The experimental adiabatic friction factor insidetest-section’s channel is clearly larger than the val-ues predicted by widely used correlations from lit-erature, for instance, the analytical solution f =64/Re for the laminar regime and Blasius correla-tion 0, 316Re−0,25 for the turbulent regime. How-ever the experimental friction factor representedas a function of Reynolds number has the sametrend as the different correlations revised. Laminar-turbulent transition occured for Reynolds around2700.

Average Nusselt number was evaluated in thetest section and mixed convection mechanism was

10

identified due to the developing thermal boundarylayer. Laminar-turbulent transition occurred forRe ≈ 3200. In the laminar regime, Nusselt num-bers were higher than those predicted for fully de-veloped flow. In the turbulent regime experimentalresults were always over-predicted by the variouscorrelations from the literature since fully turbulentconditions were not reached.

When comparing adiabatic with diabatic flow itwas observed that transition occurred earlier for theadiabatic flow. Critical Reynolds number was ap-proximately equal to 2700 for adiabatic flow and3200 for diabatic flow. Experimental friction fac-tors obtained with heat flux imposed on the chan-nel’s wall were larger than those obtained withoutheat flux. However they presented similar valuesin the turbulent regime, i.e. for Re > 4500, sincesecondary flow effects could be neglected.

Diabatic friction factor showed larger values inthe whole laminar regime in comparison with tur-bulent regime.

The results analyzed here show that correlationsreported in the literature agree well with experi-mental data obtained for the friction factor andNusselt number, in fully developed laminar (andturbulent) flow thus being used to validate the ex-perimental set-up in the present study. However,these correlations clearly deviate from the experi-mental data for the specific flow conditions studiedhere, which are representative of the fluid flow inthe HEX channels.

Hence, the experimental set-up devised in thepresent work was validated and shows good poten-tial to study the hydrodynamics and heat transfermechanisms for the specific working conditions ob-served in the HEX channel. The obtained resultsare expected to be useful to devise more appropri-ate conditions to be applied in these flow conditions(high imposed heat fluxes for transitional develop-ing flow).

Acknowledgements

The author gratefully acknowledge the finan-cial support provided by FCT (Science and Tech-nology Foundation) within project RECI/EMS-SIS/0147/2012.

References

[1] Chuang Yu and K.T. Chau. Thermoelectricautomotive waste heat energy recovery usingmaximum power point tracking. Energy Con-version and Management, 50:1506–1512, 2009.

[2] Antonio Domingues, Helder Santos, and MarioCosta. Analysis of vehicle exhaust waste heatrecovery potential using a rankine cycle. En-ergy, 49:71–85, 2013.

[3] Josua P Meyer. Heat transfer in tubes in thetransitional flow regime. In Proceedings of the15th International Heat Transfer Conference,Kyoto, paper KN03, pages 11–15, 2014.

[4] Frank P. Incropera. Fundamentals of Heat andMass Transfer. Wiley, 6th edition, 2006.

[5] AJ Ghajar and LM Tam. Laminar-transition-turbulent forced and mixed convective heattransfer correlations for pipe flows with dif-ferent inlet configurations. American Societyof Mechanical Engineers, Heat Transfer Divi-sion,(Publication) HTD., 181:15–23, 1991.

[6] Satish Kandlikar, Srinivas Garimella,Dongqing Li, Stephane Colin, and Michael RKing. Single-phase liquid flow in minichannelsand microchannels. In Heat transfer andfluid flow in minichannels and microchannels.Elsevier, 2005.

[7] RK Shah. A correlation for laminar hydrody-namic entry length solutions for circular andnoncircular ducts. Journal of Fluids Engineer-ing, 100(2):177–179, 1978.

[8] Hou Kuan Tam, Lap Mou Tam, and Afshin JGhajar. Effect of inlet geometries and heat-ing on the entrance and fully-developed frictionfactors in the laminar and transition regions ofa horizontal tube. Experimental Thermal andFluid science, 44:680–696, 2013.

[9] Heinrich Blasius. Das Ahnlichkeitsgesetz beiReibungsvorgangen in Flussigkeiten. Springer,1913.

[10] BS Petukhov. Heat transfer and friction in tur-bulent pipe flow with variable physical proper-ties. Advances in Heat Transfer, 6(503):i565,1970.

[11] Adrian Bejan and Allan D Kraus. Heat transferHandbook, volume 1, chapter 5. John Wiley &Sons, 2003.

[12] Stuart W Churchill and H Ozoe. Correla-tions for laminar forced convection with uni-form heating in flow over a plate and in de-veloping and fully developed flow in a tube.Journal of Heat Transfer, 95(1):78–84, 1973.

[13] Afshin J Ghajar and Lap-Mou Tam. Heattransfer measurements and correlations in thetransition region for a circular tube with threedifferent inlet configurations. ExperimentalThermal and Fluid Science, 8(1):79–90, 1994.

[14] Volker Gnielinski. G1 heat transfer in pipeflow. In VDI Heat Atlas, pages 691–700.Springer, 2010.

11

[15] Volker Gnielinski. New equations for heatand mass-transfer in turbulent pipe and chan-nel flow. International Chemical Engineering,16(2):359–368, 1976.

[16] W Yu, DM France, MW Wambsganss, andJR Hull. Two-phase pressure drop, boilingheat transfer, and critical heat flux to waterin a small-diameter horizontal tube. Interna-tional Journal of Multiphase Flow, 28(6):927–941, 2002.

[17] Chin L Ong and John R Thome. Flow boilingheat transfer of r134a, r236fa and r245fa in ahorizontal 1.030 mm circular channel. Experi-mental Thermal and Fluid Science, 33(4):651–663, 2009.

[18] Cristiano B Tibirica and Gherhardt Ribatski.Two-phase frictional pressure drop and flowboiling heat transfer for r245fa in a 2.32-mm tube. Heat Transfer Engineering, 32(13-14):1139–1149, 2011.

[19] Romain Charnay, Remi Revellin, and JocelynBonjour. Flow boiling characteristics of r-245fain a minichannel at medium saturation temper-atures. Experimental Thermal and Fluid Sci-ence, 59:184–194, 2014.

[20] Wolfgang Wagner and Alfred Kruse. Proper-ties of water and steam, 1998.

[21] Patrick F Dunn. Measurement and data anal-ysis for engineering and science. CRC press,2014.

[22] S Barlak, S Yapıcı, and ON Sara. Experimen-tal investigation of pressure drop and frictionfactor for water flow in microtubes. Interna-tional Journal of Thermal Sciences, 50(3):361–368, 2011.

[23] Lap-Mou Tam and Afshin J Ghajar. Effect ofinlet geometry and heating on the fully devel-oped friction factor in the transition region ofa horizontal tube. Experimental Thermal andFluid science, 15(1):52–64, 1997.

[24] HK Tam, LM Tam, AJ Ghajar, andCW Cheong. Development of a unified flowregime map for a horizontal pipe with thesupport vector machines. In Proceedings ofthe 2nd International Symposium on Compu-tational Mechanics and the 12th InternationalConference on the enhancement and promo-tion of computational methods in engineeringand science, volume 1233, pages 608–613. AIPPublishing, 2010.

12