ORIGINAL

Convective heat transfer in engine coolers influencedby electromagnetic fields

C. Karcher1 & J. Kühndel1,2

Received: 30 March 2017 /Accepted: 31 July 2017 /Published online: 22 August 2017

Abstract In engine coolers of off-highway vehicles, convec-tive heat transfer at the coolant side limits both efficiency andperformance density of the apparatus. Here, due to restrictionsin construction and design, backwater areas and stagnationregions cannot be avoided. Those unwanted changes in flowcharacteristics are mainly triggered by flow deflections andsudden cross-sectional expansions. In application, mixturesof water and glysantine are used as appropriate coolants.Such coolants typically show an electrical conductivity of afew S/m. Coolant flow and convective heat transfer can thenbe controlled using Lorentz forces. These body forces aregenerated within the conducting fluid by the interactions ofan electrical current density and a localized magnetic field,both of which are externally superimposed. In future applica-tion, this could be achieved by inserting electrodes in thecooler wall and a corresponding arrangement of permanentmagnets. In this paper we perform numerical simulations ofsuch magnetohydrodynamic flow in three model geometriesthat frequently appear in engine cooling applications: Carnot-Borda diffusor, 90° bend, and 180° bend. The simulations arecarried out using the software package ANSYS Fluent. Thepresent study demonstrates that, depending on the electromag-netic interaction parameter and the specific geometric arrange-ment of electrodes and magnetic field, Lorentz forces are suit-able to break up eddy waters and separation zones and thus

significantly increase convective heat transfer in these areas.Furthermore, the results show that hydraulic pressure lossescan be reduced due to the pumping action of the Lorentzforces.

1 Introduction

MAHLE Industrial Thermal Systems specializes in efficientand sophisticated thermal management (https://www.mahle-industry.com). The portfolio ranges from coolers to entirecooling and air conditioning modules. Areas of applicationinclude railway vehicles, busses, agricultural andconstruction machinery, and special vehicles. Basicrequirements in the development of engine coolers arecompactness, easy manufacturing, low material costs, andhigh performance density. These requirements are generallymet by coolers designed in package-type blocks, cf. Fig. 1.Such coolers preferentially operate in the so-called indirectcross-flow mode: air flow (the fluid to be cooled down) andcoolant flow are in orthogonal directions and are separated bythin aluminum panels. To increase heat transfer from the air tothe coolant, air channels are equippedwith corrugated ribs andturbulence-enhancing entry sheets, all of which are made ofaluminum [1]. In such complex heat exchange systems, lim-iting factors for both efficiency and performance density in-clude the appearance of stagnant flow, eddy waters, wakes,and separation zones at the coolant side, all of which are trig-gered by sudden expansions and/or deflections of the flow [2].In such zones, convective heat transfer is drastically reduceddue to a significant drop of wall shear stress [3]. In the presentpaper we investigate the option of an electromagnetic control[4–7] of heat transfer in such zones. Control is based on thefact that the coolant is electrically conductive. Hence, in thepresence of an electrical current and an applied magnetic field,

* C. Karcherchristian.karcher@tu-ilmenau.de

1 Institute for Thermodynamics and Fluid Mechanics, TechnischeUniversität Ilmenau, P.O. Box 10 05 65, D-98684 Ilmenau, Germany

2 MAHLE Industrial Thermal Systems GmbH& Co. KG, HeilbronnerStr. 380, D-70469 Stuttgart, Germany

Heat Mass Transfer (2018) 54:2599–2605DOI 10.1007/s00231-017-2130-4

# Springer-Verlag GmbH Germany 2017

Lorentz forces can be generated within the coolant. TheseLorentz forces may contribute to an increased heat transferdue to a favorable modification of the flow topology in thecritical areas. In the present study electromagnetic control isachieved by superimposing electrical currents, which areinserted via wall electrodes, and localized magnetic fields ofconstant magnitude and prescribed direction.

The present feasibility study aims to demonstrate thatconvective heat transfer on the coolant side can be in-creased electromagnetically. Three canonical model ge-ometries were chosen, within which coolant flow underthe influence of Lorentz forces are numerically investi-gated. These are a Carnot-Borda diffusor and both a 90and 180° bend, all of which are characterized by suddenexpansions. The paper is organized as follows: InSection 2 we describe the governing equations and di-mensionless parameters of the problem as well as thenumerical methods used. In Section 3 we define themodel geometries mentioned above and show the mainsimulation results. Finally, Section 4 provides a summa-ry and an outlook towards a possible application inengine coolers.

2 Governing equations and numerical methods

2.1 Governing equations

The forced coolant flow is described by the incompressibleNavier Stokes equations. For electromagnetic control, we addthe Lorentz force density fL as a source term on the right handside of this momentum balance. Moreover, convective heattransfer is governed by the heat transport equation. Underthese assumptions, the governing equations read as [4–6]

∇⋅u ¼ 0; ∂=∂tuþ u⋅∇ð Þu ¼ −1=ρ∇pþ ν∇2u

þ 1=ρ fL;; ∂=∂tTþ u⋅∇ð ÞT ¼ κ∇2T:

ð1Þ

Here, u, p, and T denote the velocity vector, pressure andtemperature, respectively. Coolant properties are density ρ,dynamic viscosity υ, and thermal diffusivity κ, all of whichare taken to be constant. The Lorentz force density is definedas

fL ¼ j� B; ð2Þwhere j is the electric current density and B is the magneticfield. In order to calculate the Lorentz force density, we needfurther equations defining the solenoidal vector fields j and Baccording to Eq. (2). In general, these further equations areOhm’s law for a moving conductor and the magnetic induc-tion equation. However, in the present case of superimposedelectrical currents and magnetic fields and a weaklyconducting coolant, we can neglect the secondary magneticfield induced by the current density itself. Hence, B is fixed inboth magnitude and direction by the applied field definedwithin regions of electromagnetic control. Secondly, we canneglect any eddy current induced by the interaction of the flowwithin a magnetic field. Under this assumption, j is given bythe gradient of the electric scalar potential ϕ, governed itselfby Laplacian [8]. Thus we have

∇2ϕ ¼ 0; j ¼ −σ∇ϕ;B ¼ B0⋅eB: ð3Þ

Here, σ is the electrical conductivity of the coolant, and B0

and eB are the flux density and the unit vector of the appliedfield, respectively. In our simulations we shall apply a constantcurrent density at the wall electrodes and electrically insulat-ing walls elsewhere. The hydrodynamic boundary conditionsare the mass flux at the inlet and the pressure at the outlet.

coolant

channels

separation

panel

air

channels

corrugated

ribs

turbulence sheet

air

coolant

side part Fig. 1 Sketch of an indirectpackage-type cross-flow enginecooler. Air flow and coolant floware orthogonal and separated bythin panels. Air channels areequipped with corrugated ribs toenhance heat transfer.Additionally, turbulenceenhancing entry sheets are used

2600 Heat Mass Transfer (2018) 54:2599–2605

Moreover, we apply no-slip conditions at rigid walls. Thethermal boundary conditions are a fixed inlet temperatureand isothermal walls.

2.2 Dimensionless parameters

The present problem is governed by two dimensionlessgroups, the Reynolds number Re and the electromagnetic in-teraction parameter N. These groups are defined according tothe relations.

Re ¼ UL1=ν;N ¼ j0B0L2= ρU2� �

: ð4Þ

Here, U is fluid inlet velocity based on mass flux and L1

and L2 are characteristic length scales for fluid dynamics (hy-draulic diameter) and electromagnetics (dimension of elec-trode). Throughout this study we shall use Re = 3.000, whichis a typical value in application. The interaction parameterrepresents the ratio of electromagnetic forces to inertia. Weexpect that for N < < 1 Lorentz forces will have little effecton the flow since inertia dominates. In turn, for N > > 1 therewill be strong modifications of the flow structure due to thepresence of Lorentz forces. In application, N may be varied bychanging the values of both j0 and B0. Important output quan-tities are the mean Nusselt number Nu and the pressure coef-ficient cp. These parameters are defined as

Nu ¼ αL1=λ; cp ¼ Δp= §ρU2� �

: ð5Þ

Here, α denotes the convective heat transfer coefficient, λis heat conductivity of the coolant and Δp is pressure dropacross the geometry. The Nusselt number can be interpreted asthe ratio of convective to conductive heat transfer. The param-eter cp relates the pressure drop to the dynamic pressure of theflow. The present study aims to find the relations Nu = Nu (N)and cp = cp (N).

2.3 Numerical approach

The equations above are numerically solved in three dimensionsusing the commercial program ANSYS Fluent 16.2 and itsMHD (magnetohydrodynamic) module [9]. This module allowsus to define volumes within which a constant magnetic field ispresent. In this study, the imposed magnetic fields point either inthe x- or y-direction, cf. Fig. 2. Moreover, the module allows usto define wall areas where electrical currents are injected. In thepresent study, the injected currents point in the z-direction, cf.Fig. 2. According to Eq. (2) the main component of the Lorentzforces then acts either in the y- or x-direction. TheMHDmodulesolves for the electrical potential and calculates the Lorentz forcedensity, cf. Eq. (2). The data are then read into the CFD solverANSYS Fluent, cf. Eq. (1). In the present study, we fix theReynolds number at Re = 3.000. Some pre-studies [10] show

that in the present geometries the transition Reynolds number isabout 1.000. Hence, we are in the regime of turbulent flow. Weuse the standard k-ω SST turbulence model. Moreover, the pre-studies show that equidistant meshing with a grid size of Δ =0.3 mm is appropriate. Coolant properties are fixed at σ = 0.4 S/m, ρ = 1028 kg/m3, υ = 8.8 e−7 m2/s, κ = 1.2 e−7 m2/s, and λ =0.435 W/(m⋅K). Temperatures were fixed at 30 and 200 °C atinlet and isothermal walls, respectively. Validation of the numer-ical scheme was performed for the case when Lorentz forces areabsent. We found nearly perfect agreement of our calculatedresults for cp with respective literature data [11, 12].

3 Results

3.1 Model geometries

We select three canonical model geometries to investigate theeffect of Lorentz forces on heat transfer: Carnot-Bordadiffusor, cf. Fig. 2 (i), 90° bend, cf. Fig. 2 (ii), and 180° bend,cf. Fig. 2 (iii). Areas within which stagnant flow with reducedconvective heat transfer is expected are indicated by red dots.In these areas, we insert pairs of electrodes at the front andback side walls on which an electric current density of mag-nitude j0 is applied in the z-direction. The specific arrange-ments of the applied magnetic field are chosen in such a waythat the resulting Lorentz forces point either in the x-directionand/or the y-direction.

3.2 MHD flow in a Carnot-Borda diffusor

We start with the electromagnetic control of flow in a Carnot-Borda diffusor. Figure 3 shows a color plot of the magnitudesof velocity in the x-y mid-plane. Colors correspond to 0 (deepblue) and 1.27 m/s (deep red). Figure 3 (i) refers to the caseN = 0, i.e. when Lorentz forces are absent. Here, we observethat due to the Coanda effect [13] the jet entering the diffusoris deflected to the bottom wall. The jet separates from the wallat a position downstream. At the outlet the velocities are con-siderably reduced. As is obvious from Fig. 3 (i), there areextended regions of stagnant flow at inlet and outlet withinwhich convective heat transfer from the walls is diminished.

In contrast, Fig. 3 (ii) refers to the case N = 3, i.e. whenelectromagnetic control is active. Here, rectangles representthe electrodes that are inserted in the walls. In detail, 6 pairsof electrodes are arranged in such a way that the three pairs atthe bottom and the top generate an electrical current in thenegative and positive z-direction, i.e. into and out of the plane,respectively. Furthermore, within the electrode regions we ap-ply localized magnetic fields pointing into the positive y-di-rection. This arrangement results in Lorentz forces acting inthe negative and positive x-direction at top and bottom, re-spectively. As a result a large-scale forced circulation is

Heat Mass Transfer (2018) 54:2599–2605 2601

generated. As is obvious from Fig. 3 (ii) the wall jet is accel-erated and its separation from the bottom wall is prevented.Moreover, due to the electromagnetically forced circulation,almost all regions of stagnant flow disappear. We concludethat this special arrangement of applied electrical current andmagnetic field contributes to an increase of convective heattransfer. However, due to the formation of an extended recir-culation zone, we may expect a slight increase of pressuredrop, cf. Subsection 3.5.

3.3 MHD flow in a 90° bend

Next, we investigate electromagnetic control of flow inthe 90° bend. Figure 4 again shows a color plot of themagnitudes of the velocity in the x-y mid plane. Colorsare from 0 (deep blue) to 1.26 m/s (deep red). Figure 4(i) again refers to the case N = 0. Here, we observe thatthe jet entering the bend remains at the bottom wall and

widens up. At the right end the jet is bent into theupward direction. Again, this hydrodynamic flow patterngives rise to extended regions of stagnant flow withreduced convective heat transfer at the top part andthe lower right corner of the bend. Figure 4 (ii) showsthe velocity field modified by the action of Lorentzforces for the case N = 3. In order to break up the eddywaters observed in Fig. 4 (i), a total of 4 pairs of wallelectrodes and corresponding localized magnetic fieldsare implemented. At all electrodes we inject an electri-cal current density pointing out of the plane, i. e. in thepositive z-direction. In the region of the electrodes atthe inlet and the right end of the bend, the magneticfield direction is in the positive x-direction. Hence, thegenerated Lorentz forces act in the positive y-direction,i.e. in the direction of the outlet flow. On the otherhand, in the regions of the two pairs of electrodes ar-ranged in the middle of the bend, the corresponding

Fig. 2 Model geometries: (i)Carnot-Borda diffusor;d1 = 2.6 mm, d2 = 17.6 mm,d3 = 7.5 mm, l1 = 193 mm,l2 = 113 mm, b = 10 mm; (ii) 90°bend; d1 = 2.6 mm, d2 = 17.6 mm,l1 = 193 mm, l2 = 113 mm,b = 10 mm; (iii) 180° bend;d1 = 2.6 mm, d2 = 20 mm,d3 = 55.2 mm, l1 = 80 mm,b = 10 mm. Red dots indicatezones of stagnant flow. Wallelectrodes are inserted at which anelectrical current density in the z-direction is applied. Directions ofthe applied magnetic fields areeither in the x- and/or y-direction,generating Lorentz forcespointing in the y- and/or x-direction, respectively

(i)

(ii)

Fig. 3 Color plot of the magnitudes of velocity in the x-y plane ofsymmetry in a Carnot-Borda diffusor at Re = 3.000 and (i) N = 0 and(ii) N = 3. The magnitudes range from 0 (deep blue) to 1.27 m/s (deepred). Mean flow is in the positive x-direction. Rectangles indicate the wallelectrodes driving an electrical current in the negative (bottom electrodes)

and in the positive (top electrodes) z-direction. The applied localizedmagnetic fields act in the positive y-direction. The generated Lorentzforces are pointing in the positive (bottom) and negative (top) x-direction, respectively

2602 Heat Mass Transfer (2018) 54:2599–2605

magnetic fields point in the negative y-direction. Thisarrangement results in Lorentz forces acting in the pos-itive x-direction. As a result of this specific set-up ofelectromagnetic control, the inlet jet is deflected towardsthe bulk region. As a consequence, stagnant flow at theinlet area is broken up. Moreover, in the center part ofthe bend, coolant is pushed to the right end. Here, theLorentz forces support the bending of the fluid into thepositive y-direction of the outlet flow. Again, the areaof stagnant flow at the right end is broken up. As be-fore, we conclude that the imposed electromagnetic con-trol leads to an increase of convective heat transfer.Moreover, in contrast to the previous case of a diffusor,we may expect that since the generated Lorentz forcessupport the flow bend, the pressure drop shall signifi-cantly decrease, cf. Subsection 3.5.

3.4 MHD flow in a 180° bend

Finally, we investigate electromagnetic control of flow inthe 180° bend. Figure 5 shows as before the color plot ofthe magnitudes of the velocity in the x-y mid plane.Colors are from 0 (deep blue) to 1.63 m/s (deep red).The case when Lorentz forces are absent, i.e. N = 0, isillustrated in Fig. 5 (i). Here, we observe that the inlet jethits the right wall and keeps attached to the curved con-tour in the downstream direction. At the end of the bend,the coolant is deflected towards the direction of the out-let flow, i.e. the negative x-direction. This flow structureagain results in the formation of extended regions ofstagnant flow within the bend. As obvious from fig. 5(i), especially the areas above and below the inlet ductand the entire left part of the bend are considered to be

(i)

(ii)

Fig. 4 Color plot of the magnitudes of velocity in the x-y plane ofsymmetry in a 90° bend at Re = 3.000 and (i) N = 0 and (ii) N = 3. Themagnitudes range from 0 (deep blue) to 1.26 m/s (deep red). Inlet flow atthe left is in the positive x-direction, outlet flow is at the top in the y-direction. Rectangles indicate the wall electrodes driving an electricalcurrent in the positive z-direction out the plane. The applied localized

magnetic fields act either in the positive x-direction (left and rightelectrode) or in the positive y-direction (middle electrodes),respectively. The generated Lorentz forces are pointing in the positivey-direction (left and right electrode) and in the positive x-direction(middle electrodes), respectively

(i) (ii)

Fig. 5 Color plot of themagnitudes of velocity in the x-yplane of symmetry in the 180°bend at Re = 3.000 and (i) N = 0and (ii) N = 3. The magnitudesrange from 0 (deep blue) to1.63 m/s (deep red). Rectanglesindicate the wall electrodesdriving an electrical current in thenegative z-direction into theplane. The applied localizedmagnetic fields act in the positivex-direction of inlet flow. Thegenerated Lorentz forces arepointing in the negative y-direction

Heat Mass Transfer (2018) 54:2599–2605 2603

regions of reduced convective heat transfer. In order tobreak up these regions, we implement a total of 5 pairsof wall electrodes and corresponding magnetic fields insuch a way that all generated Lorentz forces are pointingin the negative y-direction. According to Eq. (2) this isachieved by inserting an electrical current density intothe negative z-direction (into the plane) and fixing themagnetic fields in the positive x-direction of the inletflow. As a result of this arrangement, similar to the caseof the diffusor, a large-scale circulation is established inthe bulk of the bend. Coolant flowing up the outer wallrecirculates downwards along the inner wall of the bend.This flow pattern is shown in Fig. 5 (ii) for an interac-tion parameter of N = 3. Also in this case we may con-clude that this specific set-up of electromagnetic controlresults in an increase of convective heat transfer.However, similar to the case of the diffusor, due to thecirculation this benefit will be accompanied by an in-creased pressure drop, cf. Subsections 3.2 and 3.5.

3.5 Pressure drop and heat transfer

The main results of our simulations are summarized inFig. 6. Here, Fig. 6 (i) shows the reduced pressurecoefficient ĉp = cp/cp0 as a function of the interactionparameter N, where cp0 denotes the pressure coefficientfor the case N = 0. For the 90° bend we find a remark-able decrease in pressure drop when the electromagneticcontrol is present. As discussed before, in this case thegenerated Lorentz forces support the bending of thecoolant flow. Contrary, for the diffusor and the 180°bend we find an increase in pressure drop. In orderdissolve areas of stagnant flow the coolant has to recir-culate. Hence, the Lorentz forces act as an additionalelectromagnetic brake. Figure 6 (ii) shows the corre-sponding Nusselt number as a function of N. Here, forall geometries we find a significant increase of convec-tive heat transfer when electromagnetic flow control isactive. For instance, for N = 3.2 the increases in Nu areabout 60% for the diffusor and about 20% for the 90and 180° bend.

4 Conclusions and outlook

We have studied electromagnetic control of coolant flow andconvective heat transfer in three canonical model geometries:a diffusor, a 90° bend and a 180° bend. Under the action ofsuperimposed electrical currents and magnetic fields in theelectrically weakly conducting coolant, Lorentz forces aregenerated that tend to dissolve areas of stagnant flow withreduced heat transfer. As a result, we find an increase in theNusselt number when the electromagnetic control is active.Moreover, when the Lorentz forces do not create recirculatingflow, enhanced heat transfer is accompanied by a reduction inpressure loss. To evaluate the efficiency of the electromagneticcontrol we define the ratio of the increase in heat transfer andthe electric power consumption of the electrodes [9]. A roughestimate shows that in the case of the diffusor, this ratio isgreater than unity when the electrical conductivity may begreater than 70 S/m. Thus, to transfer these findings into ap-plication it is necessary to significantly increase the electricalconductivity of the coolant, either by additives or by develop-ing new mixtures. Thus, the magnitude of the injected currentdensity and therefore costs for control can be drastically re-duced. With increased conductivity, it is possible to avoidJoule losses when the coolant heats up and hydrogen genera-tion via electrolysis, which are added benefits [10].

Acknowledgements The authors acknowledge support from DeutscheForschungsgemeinschaft (DFG) within the frame of the ResearchTraining Group BLorentz force velocity and Lorentz force eddy currenttesting^ under grant GRK-1567. We thank M.Sc. Thomas Mischer forcarrying out the simulations.

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2604 Heat Mass Transfer (2018) 54:2599–2605

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