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Journal of Electrostatics 72 (2014) 82e90

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Journal of Electrostatics

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Empirical correlation for performance evaluation of electric/coronawind on natural convection

Shahin Nasiri Vatan a,*, Ehsan Shabahang Nia b, Arshia Merdasi c

aDepartment of Mechanical Engineering, Sharif University of Technology, Tehran, IranbDepartment of Mechanical Engineering, University of Tabriz, Tabriz, IrancDepartment of Energy Systems Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

a r t i c l e i n f o

Article history:Received 9 June 2013Received in revised form9 November 2013Accepted 6 December 2013Available online 17 December 2013

Keywords:Natural convectionHeat transferElectrohydrodynamic fieldEmpirical correlationEfficiency

* Corresponding author. Tel.: þ98 912 541 3094.E-mail address: Nasirivatan@mech.sharif.ir (S. Nas

0304-3886/$ e see front matter � 2013 Elsevier B.V.http://dx.doi.org/10.1016/j.elstat.2013.12.004

a b s t r a c t

The effect of the corona wind on the natural convection at a rectangular channel was investigatedexperimentally. The results indicate that the natural convection in the absence of electric/corona wind atobtuse angles outperforms than acute angles and keeps improving by increasing the angle. However, theefficiency of the electric/corona wind at acute angles is higher than obtuse angles. Generally, in thepresence of electric/corona wind, heat transfer coefficient was increased. The effect of the electric/coronawind was decreased by raising heat flux. This mainly stems from the fact that the temperature gradientraises the thermal boundary layer and reduces the secondary flow power. Eventually, empirical corre-lation for the estimation of Nusselt number was achieved.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

As far as energy issue concerns, the human beings have lookedfor generating energies and transforming them to their benefits,one of which is heat energy. It plays a significant role in human-kind’s life cycle. Perhaps, in some cases, heat was a harmful phe-nomenon to them and they have tried to decrease and transmit theheat based on their needs. In accordance with developing hu-mankind’s needs and their progress in different fields especially inindustries, their requests for inhibiting heat in a variety of indus-trial procedures, whether in large scales like power plants andcondensers or small scales such as microchips and electroniccomponents, have been increased. In recent decades, numerousattempts in the field of heat transfer increase and optimize havebeen made. Generally, these attempts could be classified in twocategories: active methods and passive methods. In the inactivemethods, developed surfaces along with creation of vortex thor-ough raised surfaces were more utilized. On the other hand, inactive methods, external powers such as electrical and acousticfields or surface vibration was frequently applied for heat transferenhancement.

iri Vatan).

All rights reserved.

Using electrical fields account for a particular position amongstactive methods. When the electrical current is low enough as toneglect the magnetic effect, electrical powers will have animpact on the hydrodynamic of the fluid, which is calledelectrohydrodynamics powers. The facility, high reliability, andshort response time are among the advantages of this methodol-ogy. Therefore, in recent years these kinds of powers attractedscientists’ attention.

Windischmann [1], investigated the temperature profiles of aflat plate in the presence of the coronawind and concluded that theeffect of corona wind is more in Helium than in the air, Nitrogen,and Argon. Then Yabe et al. [2] presented the analytical andexperimental model for corona wind. Moreover, it was demon-strated that the Coulomb force acting on the ions and treating be-tween ions and neutral gas molecules forms corona wind.Furthermore, Velkoff and Godfrey [3] conducted a research on heattransfer from air fluid flow of flat plate with presence of coronadischarge. Hutson and Franke [4] also investigated the effect of theelectrical field, as one of natural convection approaches, on the fluidin the hollow vertical cylinder at constant temperature. Theyproved that the heat transfer ratio has approximately twiceincreased chiefly due to the presence of the corona wind.

Ohadi et al. [5] surveyed the effect of electrical discharge inforced convection with air fluid in the tube at Reynolds numberranged between 1000 < Re < 1500, And zero Electrical potential

Nomenclature

Ra Rayleigh NumberQ 00 heat flux (W/m2)b thermal expansion coefficient (1/k)a thermal diffusivityCp Specific heat at constant pressure (J/Kg K)y kinematic viscosity (m2/s)H length of plate (m)K thermal conductivity (W/m K)Tsx wall temperature (k)Tin bulk temperature (k)V voltage (V)I current (A)D degree of plateX distance (m)g standard gravity (m/s2)R resistance of wire (U)A area of plate (m2)

Fig. 1. Schematic of laboratory setup.

S. Nasiri Vatan et al. / Journal of Electrostatics 72 (2014) 82e90 83

near the discharge was obtained practically when the arrangementof electrodes is single or double. The conclusions showed signifi-cant heat transfer in laminar and transient flow in single electrodecase whereas in double electrodes arrangement, heat transferprevails in turbulent flow. Tada et al. [6] investigated the heattransfer increase in the flow in terms of forced relocation by theelectrical field and they detected the fluid behavior under the filedby using the smoke. They also experienced a pair reverse vortex dueto fluid flow and the ionic wind interactions. In another study, Ngoand Lai [7] surveyed the effect of electrical fluid on natural con-vection at the bottom of the channel, which was heated in 2-dimensional and concluded that corona wind is effective at lowRayleigh numbers. Bhattacharyya and Peterson [8,9] worked onnovel flow visualization as well as extensive and controlled heattransfer enhancement. The study was conducted in order to char-acterize the corona wind augmentation via natural convectionprocess from a vertical copper plate subjected to a reversible po-larity DC high-voltage electric field at various constant heatingfluxes.

Legar et al. [10] investigated the fluid flow with low velocityalong a flat surface in presence of DC discharge field. Accordingto the characteristics of the electrical discharge, they indicatedthat the features are depended on the moisture and electricalgeometry. Molki and Bhamidipati [11] examined the amount ofheat transfer obtained from corona wind at developed zone inthe tube experimentally. Based on the results, the maximum andaverage amount of local heat transfer coefficient are 8%, 23%,respectively.

Yan et al. [12] accomplished the mathematical and numericalmodel for natural convection in chambers with electro-hydrodynamic. They observed that in the same electrical field, heattransfer due to EHD has been changed by altering the electricaldensity injection. Using a non-uniform electrical field has given abetter feedback in comparison with that of uniform electrical field.Heat transfer is dependent on Rayleigh number while the effect ofEHD is mainly at low Rayleigh number. Kasayapanand and Kiat-siriroat [13] worked on the convection at wavy channels throughEHD technique. They also surveyed various arrangements of elec-trodes. Their conclusions represented that the heat transfer in-crease is dependent on the quantity of electrodes and waves alongthe length of the channel. Molki and Harirchian [14] conducted aresearch on the effect of corona discharge on the natural convectionheat transfer inside a rectangular channel. The results showed that

increasing heat transfer for different Rayleigh numbers is within 1e4%. This increase occurred at Ra ¼ 3737 and applied voltage wasbetween 7 and 9 (kV). Kasayapanand [15] developed a study con-cerning the effect of EHD on the natural convection inside thechamber with different electrodes arrangement. He worked on thereciprocal effects of electrical field, fluid flow, and thermal field.More recently, Kasayapanand [16] investigated heat transfer in-crease by EHD technique inside a channel with numerous electrodearrangements in a numerical manner and it was seen that heattransfer coefficient in presence of electrical field increased by risingthe applied voltage and decreased by increasing Reynolds number.They also found that the electrode arrangement in a row createdmore heat transfer in comparisonwith the checkered arrangement.Then, Kasayapanand and Kiatsiriroat [17] presented a numericalsolution in surveying natural convective heat transfer in a verticalchannel. Kasayapanand [18] investigated heat transfer increase in asolar chimney in a natural convection form in presence of EHD inthe recent research. GO et al. [19] studied heat transfer increase inthe forced convection through unique wind. They realized that thevalue of heat transfer is dependent on the distance between elec-trodes whereas the heat transfer coefficient is proportional to thefourth root of corona flow. Recently, Lakeh and Molki [20] con-ducted a numerical research on the impact of corona jet on heattransfer in rectangular channels with longitudinal and flatelectrodes.

In this project, heat transfer from flat surface of rectangularchannel, wherein there is active zone, was investigated experi-mentally through EHD technique. We studied how heat transfermechanism operates in various fluxes and at different angles inpresence and absence of the distinct electro-hydrodynamic fields.According to the obtained data, an equation is presented in order tocalculate Nusselt number in terms of different parameters such asangle, flux, field, and Rayleigh number.

S. Nasiri Vatan et al. / Journal of Electrostatics 72 (2014) 82e9084

2. Experimental set-up

As illustrated in Fig. 1, laboratory setup consists of an airchannel with length of 50 cm. Channel walls are made of Plexi-glas with a thickness of 5 mm. The dimensions of the cross-section for inlet air channel are 5 � 15 cm2. The copper platewith dimensions of 50 � 15 cm2 has been attached to one of thechannel funds. The copper plate is heated by nickel e chromicresistance wires whereby attached behind it. The amount ofapplied voltage to resistance wires could be tuned by using an ACpower supply with the variable voltage. Correspondingly, ther-mal flux applied to the copper plate could be adjusted. Twothermal sensors were installed at each inlet and outlet section ofchannel, respectively. Four thermal sensors have been setuplengthwise behind the copper plate with the equispaced distanceof 10 cm along channel. These sensors are classified as SMT-160;thereby have the potential to measure the temperature in alimitation of 0e130� with an appropriate accuracy (approxi-mately 0.7�). The information relevant to these kinds of sensorshas been saved by measurement device and data entry andcorresponding software programs. Nine holes with equal dis-tance of 2 cm along each other and 2.5 cm from plate have beencreated on the lateral funds of the channel lengthwise. Positiveelectrodes have been located inside these holes and connected tothe high voltage source. On the other hand, copper heater platehas been used as the ground for discharging the load of voltagesources. Setup has been such designed that air channel has thepotential to change the angle from zero to 180�. Airflow isentered the channel from the bottom segment of channel.Airflow was heated after passing the copper plate and subse-quently was exited from the top of the setup.

3. Data analysis and measurement errors

3.1. Data analysis

Used non-dimensional numbers are calculated from belowequations:

Rax ¼ gbQ 00x4

yak(1)

Nux ¼ hxkf

¼ xkf

�Q 00

DT

�¼ Q 00x

kf ðTsx � TNÞ (2)

In the above equations, x is the length of the plate from the inletchannel section. Ts is the temperature of the plate at the point x andTN is the ambient temperature. In Equation (2), Q 00 is the enteredflux into the copper plate, which calculated as follows:

Q ¼ VI ¼ V2

R(3)

Q 00 ¼ V2

RA� Q 00

loss (4)

where V, I, R, and A denote heater voltage, heater current, heaterresistance of ohm wire, and the cross-section area of the plate,respectively.

It is noticeable that in spite of using two-layer thermal insu-lation, some of the thermal flux permeates out of the channelfrom the plate. The effect of pervaded heat was offset as wasteflux. This waste flux has been shown as Q 00

loss in the Equation (4).The amount of waste flux is around 5 to 7 percent of the appliedflux.

3.2. Uncertainty analysis

Uncertainty analysis for the instruments used in the experi-ments was implemented according to Beckwith et al. [21]. The re-sults are shown in Table 1. The uncertainty errors for the involvedparameters were also calculated as well.

Rax ¼ gbQ 00x4

yak;URa

Ra

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�UTsTs

�2

þ�UTNTN

�2

þ�Ub

b

�2

þ�Ux

x

�2

þ�Uy

y

�2

þ�Ua

a

�2s

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2:1Þ2þð1:8Þ2þð0:1Þ2þð0:625Þ2þð0:1Þ2þð0:1Þ2

q¼ 2:84%

Q 00 ¼ V2

RA;UQ 00

Q 00 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�2*UV

V

�2

þ�UR

R

�2

þ 2*�Ux

x

�2s

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2*0:2Þ2 þ ð0:125Þ2 þ 2*ð0:625Þ2

q¼ 0:98%

Nux ¼ Q 00xkf ðTsx � TNÞ;

UNux

Nux

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�UTsTs

�2

þ�UTNTN

�2

þ Ukfkf

!2

þ�Ux

x

�2

þ�UQ 00

Q 00

�2vuut

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2:1Þ2 þ ð1:8Þ2 þ ð0:1Þ2 þ ð0:625Þ2 þ ð0:98Þ2

q¼ 3:00%

4. Results and discussion

The diagrams with regard to Nusselt number were primarilyinvestigated in terms of Rayleigh number for the power of115 W per square meter in presence of different fields. Fig. 2indicates the diagram of Nusselt number with respect to Ray-leigh number for 45� channel angle. As expected and can berecognized from the figure, Nusselt number is lower at thebeginning of the surface and Nusselt number increases byincreasing Rayleigh number. It is also seen that Nusselt numberrises by increasing the field. Thus, it can be deduced thatNusselt number increases twice as much in presence of 15 (kV)field than those of in the absence of electro-hydrodynamic fieldat the end of the plate.

It is also seen that Nusselt number rises by increasing the field,thereby it can be reported that in presence of 15 (kV) field, Nusseltnumber increases at the end of the plate more than twice whilstwithout any electrohydrodynamics fields.

Now, after surveying the effect of the field at definite angle andconstant flux, the effect of the field at different angles would beinvestigated. To this effect, three angles have been chosen. Fig. 3illustrates the diagram of Nusselt number versus Rayleigh num-ber for the 60� angle of inclined channel in the same flux of 115 Wper square meters.

As depicted in Fig. 3, the trend of increasing Nusselt number hasthe previous pattern by rising Rayleigh number in all states. It canbe seen clearly in Figs. 2 and 3 that the effect of the field on Nusseltnumber in all states would become weaker by increasing the angle.

Having surveyed acute angles, obtuse angles are taken intoconsideration. The Diagram of Nusselt number in terms of Rayleighnumber for angle of 120 in flux of 115 W per square meters ispresented in Fig. 4. It is seen that those states that exist at acute

Table 1Uncertainty analysis of the instruments.

No Name Variable measured Range Accuracy Minimum and maximum measured %Uncertainty

1 Temperature sensor Wall temperatures (Tsx) �45 to þ130 0.01 �C 38.58e86.58 2.12 Temperature sensor Bulk temperatures (Tin) �45 to þ130 0.01 �C 19.54e26.93 1.83 Voltage Voltage (V) 0e220 V 0.1 V 0-25 0.24 Current Current (I) 0e10 A 0.001 A 0e0.500 0.15 Heater resistance Resistance (R) 0e40 U 0.1 0e40 0.1256 Length Length (x) 0e0.4 m 0.005 m 0e0.4 0.6257 Properties Density, specific heat, thermal conductivity, viscosity 0.1

S. Nasiri Vatan et al. / Journal of Electrostatics 72 (2014) 82e90 85

angles, can be observed at the aforementioned angles, too. It meansthat by increasing Rayleigh number, Nusselt number increases aswell. In addition, by increasing the value of the electrostatic field,Nusselt number rises, irrespective of Rayleigh numbers. Never-theless, there is an interesting point; the ratio of increasing Nusseltnumber with respect to different fields at acute angles is more thanobtuse angles.

In Fig. 5, changes of Nusselt number versus Rayleigh number atangle of 150 and power of 115Wwas considered for different fields.Point by point comparing Fig. 5 with Fig. 2 reveals that Nusselt

Fig. 2. Diagram of Nusselt number in terms of Rayleigh number at

Fig. 3. Diagram of Nusselt number in terms of Rayleigh number at

number increases in both cases, but the raising ratio is different.The peak efficiency was attributed to the angle of 45� and this highefficiency (High Voltage) tends to decline when the angle rose atthe field of 15 (kV). Fig. 6 elucidates the reasoning in transparentway.

The cold fluid entered the channel, after contacting with heatedcopper plate; it is driven outside the channel due to the reduction ofdensity and buoyancy force. However, the crucial point is that theapplied flux was employed from the top at acute angles and thefluid is driven towards the heater.

angle of 45 and power of 115 W in presence of different fields.

angle of 60 and power of 115 W in presence of different fields.

Fig. 4. Diagram of Nusselt number in terms of Rayleigh number at angle of 120 and power of 115 W in presence of different fields.

Fig. 5. Diagram of Nusselt number in terms of Rayleigh number at angle of 150 and power of 115 W in presence of different fields.

Fig. 6. Schematic of applying forces and fluid flows at acute and obtuse angles.

S. Nasiri Vatan et al. / Journal of Electrostatics 72 (2014) 82e9086

It is necessary to notice that the thermal boundary layer tends tohave more contact with the heater and prevents heat transfer fromheater to the air through convection approach. It is owing to theapplied flux from the top and a large component of the Buoyancyforce that makes fluid direction toward the heater. Yet, at obtuseangles, because the applied flux from bottom the fluid in contactwith the heater left the heater plate with increased temperature,moved towards heat plate. Hence, the thermal boundary layer couldgrow upwards and its thickness was incremented easily. On theother hand, athwart the acute angles at obtuse angles the buoyancydirection and applying the flux from bottom helps to increasing theNusselt number of plate Through this analysis, it should be expectedthat the Nusselt number in acute angles in absence of the field is lessthan obtuse angles. The mentioned trend can be appreciated byconcentration on Figs. 2e5. Thus, the heat transfer value in the stateof nofields growsby increasing the angle. Taking45,150� angles intoaccount, it could be seen that the heat transfer increase ismore than25% at 150� in comparison with 45� when Rayleigh number is 108.

When the field acts in the issue, the heat transfer operatesdifferently. By applying the field inside the channel as illustrated inFig. 1, a secondary flow was formed due to the air ionization and

Fig. 7. Diagram of Nusselt number in terms of Rayleigh number without the presence of the field in a constant flux of 115 W per square meters.

Fig. 8. Diagram of Nusselt number in terms of Rayleigh number in the presence the field of 15 (kV) in a constant flux of 115 W per square meters.

Fig. 9. Diagram of Nusselt number in terms of Rayleigh number without the presence of the field in a constant flux of 75 W per square meters.

S. Nasiri Vatan et al. / Journal of Electrostatics 72 (2014) 82e90 87

Fig. 10. Diagram of Nusselt number in terms of Rayleigh number in the presence the field of 15 (kV) in a constant flux of 75 W per square meters.

Fig. 11. Diagram of Nusselt number in terms of Rayleigh number without the presence of the field in a constant flux of 60 W per square meters.

Fig. 12. Diagram of Nusselt number in terms of Rayleigh number in the presence the field of 15 (kV) in a constant flux of 60 W per square meters.

S. Nasiri Vatan et al. / Journal of Electrostatics 72 (2014) 82e9088

Fig. 13. Diagram of the experimental Nusselt number versus equation Nusselt number.

S. Nasiri Vatan et al. / Journal of Electrostatics 72 (2014) 82e90 89

creating corona wind from the electrode with high voltage (wire)toward the electrodewith low voltage (plate). The direction of thisflow is shown in Fig. 6. The secondary flow causes creation ofvortex in the thermal boundary layer and yields the heat transferincreases. The direction of major component relevant to this sec-ondary fluid flow is the same as buoyancy force at acute angles;therefore, the created corona wind is stronger. Hence, it could beseen at the field of 15 (kV) that heat transfer increase is the mostefficient at the angle of 45�. It is noteworthy that corona wind di-rection at obtuse angles is opposite to the direction of buoyancyforce therefore reducing corona wind power. Meanwhile, byincreasing the angle, the heat transfer has been decreased ac-cording to Figs. 2e4. But as previously mentioned at state ofwithout any field or have low field the strength of “B” vector(secondary flow) is poor at all angles. As a result, it has not anyvortex at boundary layer or have poor disturbances, therefore aswe expected at the acute angles with thin boundary layer Nusseltnumber decreases. By increasing the angle the direction of buoy-ancy cased the thick boundary layer and the Nusselt numberincreased. Figs. 3e5 represent aforesaid phenomenon.

After surveying the effects of angle and field, the influence of theamount of flux in two states, namely in presence of the field andwithout any fields, at different angles were examined. Figs. 7 and 8indicate the diagramofNusselt number in termsof Rayleighnumberin two modes, without any fields and in the field of 15 (kV),respectively. As it was already observed, in accordance with previ-ous figures, Nusselt number in the state of no fields at obtuse anglesis more than acute angles when the flux is constant at 115 W persquare meters. However, heat transfer operates better at acute an-gles in comparisonwith that of obtuse angles by applying the fields.

In Figs. 9 and 10, the effect of the field at different angles inabsence and presence of the filed-15 (kV) was presented in aconstant flux of 75W per squaremeters. As it was described before,heat transfer operated better at obtuse angles in comparison withacute angles without the presence of the field. The pattern isreverse when the field is applied.

Figs. 11 and 12 represent the diagram of Nusselt number withrespect to Rayleigh number in constant heat flux of 60W per squaremeters for different channel positions. The results for this flux aresimilar to twopreviousfluxes. Although, there is anunderlyingpoint;heat transfer experienced an increasing trendbygrowing the value offlux from60 to70; conversely, this increasing trendhasbeendeclinedwhen the flux reached 115 W per square meters. As it was earlierpointed out, the power of vortex has been increased by growing the

field such that itwill bemore effective at acute angles. Thementionedeffect operatesmore efficiently by increasing thermal flux from 60 to75 since the more temperature difference between the fluid outsideand inside boundary layer, the higher fluxes causes more heattransfer improvement. This flux increase continues to make heattransfer increase more that corona wind, as the secondary flow hasthe potential to make proper vortex inside the boundary layer.

It was seen that the thermal boundary layer is thicker byincreasing thermal flux and temperature of the fluid in the vicinityof the wall. Increasing the Buoyancy force is not allowed the sec-ondary flow to create the vortex inside the channel as well asbefore. Hence the amount of heat transfer increase in case of the115 W is less than the 75 W.

By using attained data in various fluxes and angles in presenceof the different fileds a formulas was developed through nonlinearregression. The equation for Nusselt number in terms of Rayleighnumber at the angles between 45 and 150� and fluxes between 60and 115 W per square meters in presence of the fields varied be-tween 0 and 150 (kV) has been obtained as follows:

Nu ¼ aRab Q*� �c

D*� �d

X*� �e

f V*

� �a ¼ 17:043; b ¼ 0:007; c ¼ 0:083; d ¼ 0:016;

e ¼ 0:815; f ¼ 1:032

Q* ¼ QQ0

; D* ¼ DD0

; X* ¼ XL; V* ¼ V

V0

(6)

where in this relation, Ra is Rayleigh number, Q*,D*, X* and V*are nondimensional thermal flux, angle, position and voltagewith constant values of Q0 ¼ 1ðW=m2Þ;D0 ¼ 1

�; L ¼ 50 cm;

V0 ¼ 1 kV, respectively.Fig. 13 shows the diagram of Nusselt number obtained through

correlated equation versus experimental Nusselt number. It is seenthat over 90 percent of data is located at the error limitation of �20percent. So, the above equation is acceptable with a proper spec-trum at the corresponding working limit.

5. Conclusion

In the current project, the effect of electrohydrodynamic andthermal flux on natural convection inside a channel has been sur-veyed experimentally. In this investigation, four different angles fora channel in three various states of thermal flux, in presence of fourdifferent kinds of electrohydrodynamic fields have been studied. In

S. Nasiri Vatan et al. / Journal of Electrostatics 72 (2014) 82e9090

accordance with the obtained results, it can be summarizedregarding different states as follows:

U Heat transfer at obtuse angles is better than acute angles inthe state of no field.

U heat transfer on the plate rises by increasing the field in allstates.

U The heat transfer increase of the plate in presence of the fieldat acte angles is better than obtuse ones.

U Creating vortex on the thermal boundary layer at acute an-gles requires a more powerful field in terms of obtuse angles.vortex at acute angles has a greater efficiency in comparisonwith obtuse angles.

U The value of heat transferring increments by rising thethermal flux. Although, it keeps increasing up to a certainpoint.

U An equation was developed in order to calculate the averageNusselt number in terms of all parameters such as appliedvoltage, thermal flux of the plate, operational angle, andRayleigh number through using multivariate nonlinearregression from obtained data.

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