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Optimization of fin geometry of an exhaust heat exchanger for automotive thermoelectric generators.


Thermoelectric generators (TEGs) are emerging technologies, promising tomorrow's vehicles with free energy sources for empowering future vehicle systems [1] and [2]. Although the anatomy of such systems seems to be fairly simple, the challenges facing the development of an efficient TEG are numerous and multifarious [3] and [4]. Generally, any exhaust-based TEG contains four elements; thermoelectric modules, hot-side (i.e. exhaust) heat exchanger, cold-side (i.e. coolant) heat exchanger, and assembly components. The authors proposed a TEG design which can utilize the vehicle movement to create turbulence around finned heat sinks, as an alternative of coolant cold-side heat exchanger [5]. However, in relatively medium and high capacity engines, the hot-side operating temperature of the TEG exceeds 250 C, which requires the application of coolant based cold-side heat exchanger [3]. The structure and fluid circuitry of a typical TEG are illustrated in figures 1 and 2. Thermoelectric modules are assembled between the hot box (i.e. exhaust heat exchanger) and the cold plate (i.e. coolant heat exchanger). The temperature difference between the hot and cold surfaces generates electric power form the thermoelectric materials, as explained in [6].

In the last three decades, numerous works attempted to design an effective TEG, perhaps with sufficient generated power to replace the alternator [3] and [7]. Some of these researches focused on exploring new thermoelectric materials, such as the work done by Nissan research center [8] and Porsche [9]. On the other hand, other researches focused on developing efficient thermal systems to ensure effective extraction of exhaust heat, and effective dissipation of extra heat to the engine coolant. The latter researches employed commercial thermoelectric modules, which have known conversion efficiency and performance characteristics, in order to highlight the thermal performance of the enclosing thermal system. These researches were analytically criticized by the authors in [3].

The chief mechanical and thermal requirements of an ideal exhaust heat exchanger used for TEG are to provide sufficient surface area to mount the modules, and to maintain the exhaust gas velocity at a high value. Keeping a high value of the exhaust velocity ensures a corresponding convective heat transfer coefficient. Another important, yet not fundamental, requirement is to decrease the surface temperature difference between the inlet (i.e. first module) and outlet (i.e. last module) sides of the heat exchanger. This difference causes unstable power supply from the thermoelectric modules. A novel TEG design to be installed on a V6 2.0 L engine exhaust line is presented by the authors in [10]. The exhaust heat exchanger performance is analyzed through a numerical simulation of the mass and heat transfer within the exchanger via comprehensive CFD study [11]. The results of such simulation were compared to the work done by Nissan [12]. It is evidently proven that the novel design provide significantly enhanced thermal performance characteristics.

The main features of the new hot-side heat exchanger are the flow cross sectional area, internal longitudinal fins, and module mounting space. The flow cross sectional area is kept circular at a minimum diameter increase over the exhaust pipe diameter. Internal longitudinal fins were added to along the exhaust gas path in order to increase the heat transfer area and disturb the thermal boundary layer. Thermoelectric modules, in the respective design, are mounted on two extended fin-like surfaces. The structure of the new hot-side heat exchanger is described in figure 3. Hot exhaust gases will flow from one side to the other of the central cylinder, transferring the heat through the internal fins. Heat will then flow by means of conduction to the extended surfaces, consequently, to the thermoelectric modules.




The added internal fins represent flow resistance in two forms. First through the friction augmented by the added surface area. And second by the total cross sectional area restricting the free flow area. The engine power is fairly sensitive to the pressure in the exhaust line. If the pressure increases in one point of the exhaust line, a backpressure will be generated in the exhaust manifold. Such an increase in the exhaust manifold pressure will restrict the exhaust flow outside the cylinders, causing the combustion efficiency to decrease. In order to prevent any potential negative effect of the TEG on the exhaust line pressure profile, an accurate optimization of the fin geometry and number is mandatory.

Mathematical Formulation

Fin geometry formulation

For geometry optimization of the hot-side heat exchanger--particularly for optimizing the internal fins geometry--empirical equations are adequate for such purpose since they provide convincing results while decreasing the required time for solution convergence. In fact, circular ducts with internal longitudinal fins (i.e. ribs) have enjoyed a great concern of both mathematical and experimental research in the last four decades [13]. This concern is one result of the realization of the heat transfer enhancement achieved by such ribs and their important applications in compact heat exchangers. While experimental data for numerous different geometries and flow arrangements have been reported in the literature [14] and [15], only one set of predictive correlations for the Nusselt number and friction factor have been formulated [16]. Nevertheless the utilization of longitudinal ribs in circular ducts has proved to dramatically enhance the convective heat transfer, it is quite imperative to emphasize that it increases the pressure drop as well.

For laminar viscous flow, the enhancement in heat transfer is not as effective as in turbulent flow if the pressure drop in both cases is taken into consideration. The empirical correlations presented by Carnavos in 1979 for predicting Nusselt number and convective heat transfer coefficient for ducts with internal fins take into account the effect of fin geometry on the heat transfer area as well as on the friction factor. They were driven through experimental investigation on 21 different duct geometries [17]. However, in these correlations a term namely 'meltdown diameter'--as expressed in [18]--or 'fin envelope internal area'--as expressed in [16]--is never expressed mathematically so far. Such ambiguous term made the use of such correlations almost impossible. In the following section, a mathematical formulation for the 'meltdown diameter' is developed.

The Prandtl number of the exhaust gases is expressed as:

Pr = Cp[mu]/[K.sub.a] (1)

While the Nusselt number for fully developed, turbulent flow in smooth tubes can be expressed as recommended in [18]:

[Nu.sub.DB] = 0.023[Re.sup.0.8.sub.d][Pr.sup.n] (2)

Where n = 0.4 or 0.3 for heating or cooling of the fluid, respectively and Reynolds number is formulated as:

[Re.sub.d] = [rho]v d[[mu].sup.-1] (3)

The experimental tests included both axial and helical internal fins with helix angles up to 30[degrees]. The Carnavos experimental fluid database includes water, air, and an ethylene glycol/water mixture, the developed Nusselt number correlation is:

[Nu.sub.C] = [Nu.sub.DB] [([D.sub.i][] - 2[L.sub.f][]).sup.-0.2] [([D.sub.i][D.sub.h][]).sup.0.5][Sec.sup.3][beta] (4)

The implementation of such set of equation will be based on approximating the properties of exhaust gases to the properties of air. The meltdown diameter term is represented in equation (5) as []. Figure 3 illustrates the geometry of hot-side heat exchanger to emphasize the physical meaning of the meltdown diameter. The helix angle [beta] in the issue case will be considered zero.

The meltdown volume is defined in [18] as "that diameter which would exist if the fins were melted down and added to the internal perimeter of the tube", from such definition, the meltdown diameter can be expressed as:



The overall internal heat transfer coefficient is expressed as a function of the Nusselt number calculated from Carnavos equation:

[[alpha].sub.C] = [Nu.sub.C][K.sub.a]/[D.sub.h] (6)


The friction factor is expressed as a function of the Blasius friction factor and fin geometry:

[f.sub.C] = [f.sub.Blasius] ([]/[D.sub.r])[Sec.sup.0.75] [beta] (8)

[f.sub.Blasius] = 0.046/[Re.sup.0.2] (9)

The friction factor should be used in the flow equation to calculate the pressure drop along the heat exchanger, a simple for of the flow equations is:

[DELTA]P = 2[f.sub.C]mL/[rho][D.sub.h] (10)

Properties of the working fluid

The present study introduces polynomial equations derived from the experimental data reported in [20]. It is strongly advised that exhaust air can be treated as air [20]. Fifth and fourth order polynomials are used to predict specific heat and thermal conductivity based on temperature while a power function is used to predict air density as a function of temperature as well. Derived equations are as below:


[rho] = 359.5 x [T.sup.-1.0027] (11)

Specific heat:

[C.sub.P] = 5 x [10.sup.-20][T.sup.6] -4 x [10.sup.-16][T.sup.5]+[10.sup.-12] [T.sup.4]-2x[10.sup.-9][T.sup.3] + 2 x [10.sup.-6][T.sup.2] -0.0006T + 1.0716 (12)

Thermal conductivity:

[K.sub.a] = 8x[10.sup.-15][T.sup.4]-2 x[10.sup.-12][T.sup.3] -4x[10.sup.-8][T.sup.2]+ [10.sup.-4]T-0.0004 (13)

The viscosity is estimated based on equation described in [20] expressing air viscosity as a function o temperature:

[mu] = 3.3x[10.sup.-7][T.sup.0.7] (14)

Simulation Strategy

The optimization of the internal fin geometry aims to have a flow resistance of the heat exchanger at least equal to, or less, than the exhaust pipe flow resistance of the same length. In order to do that, the pressure drop per unit length of the exhaust pipe should be known. A CFD model has been built and validated for the standard exhaust line of a V6 2.0 L gasoline engine [22]. The main pipe for this exhaust line has a diameter of 50 mm, one catalytic converter, a secondary and primary silencers. The pressure drop per unit length has been derived from the CFD model for three different exhaust flow rate values; which represent the engine cruise condition. These pressure gradients are detailed in figure 4 and table 1.


The flow chart of the optimization code is illustrated in figure 5. The computer code based on this flowchart is appended to this paper in Matlab[R] syntax. Fin thickness is maintained constant at 0.5 mm for this optimization. The boundary conditions are calculated throughout the equations (1) and (11-14). The flow and thermal characteristics of plain pipe are important to calculate to consider them as references to those of the internally finned one. The geometry matrix used for the optimization composed of 77 different geometries. The matrix is expressed in the code as two nested loops; one involve the fin length, the second involve the number of fins. For each geometry (i.e. fin length and number of fins) the Nusselt number, heat transfer coefficient and pressure drop are computed based on equations (4-10). The root diameter values used in the optimization are 60 mm, 65 mm and 66 mm. The tendency to decrease the root diameter is justified by the requirement of reducing the flow cross sectional area; in order to maintain a high gas velocity in the heat exchanger. However, as it is discussed later, the pressure drop in the heat exchanger is very sensitive to the root diameter.


Results and Discussion

The Nusselt number and pressure drop for the geometry matrix are plotted for three different exhaust flow rate values in figure 6. The root diameter and length of the heat exchanger are 60 mm and 500 mm respectively. Fin thickness and inlet temperature are constants at 5 mm and 600 K respectively. Since the TEG length is 50 cm, the same length of the hot-side heat exchanger, it will replace a pipe segment of the length 50 cm of the exhaust line. Hence, it is crucial to ensure that the pressure drop in the hot-side heat exchanger is less than the pressure drop in an exhaust pipe segment of the same length; otherwise, the pressure in the exhaust manifold will increase. Evidently, the exhaust temperature drops along the exhaust line; whereas the average gas temperature in section (A) is higher than that of the sections (B) and (C), as in figure 4. The large drop in exhaust temperature is mainly caused by the vehicle movement and the vibration induced turbulence around the exhaust line.


From table 1, the pressure drop in a 50 cm length pipe segment, is 46 Pa at exhaust flow rate of 0.06 kg/s in section (A) of the exhaust line. This value of pressure drop is less than the least pressure drop in the heat exchanger at the same flow rate, as in figure 6-c. Thus, a heat exchanger of such root diameter as above cannot be installed in section (A) of the exhaust line, while section (A) has the highest exhaust average temperature in the whole line. In order to overcome this constraint, the current analysis considered larger root diameter for the heat exchanger at exhaust flow rate of 0.06 kg/s. Root diameters of 65 mm and 66 mm are considered for analysis and the pressure drop vs. fin length is plotted in figure 7.


It is obvious, from figure 7, that a heat exchanger with a root diameter of 66 mm can be installed in section (A) of the exhaust line without causing backpressure effect.

The second most crucial parameter is to determine the installation site of the TEG is the exhaust temperature. TEG should be installed in a position where it can generates the highest power during different engine operating conditions. Since there is no exact heat transfer model for the exhaust manifold, experimental measurements are only practical method to determine the temperature profile of exhaust gases.

The corresponding heat transfer coefficient for the heat exchanger of 66 mm root diameter is plotted against fin length and number as shown in figure 8. From figures 7 and 8, the fin geometries which have the highest heat transfer coefficient in the safe pressure drop range have fin length and number of 8, 16 mm and 20,10 fins, respectively. These two geometries have the same heat transfer coefficient at 112.33 W/m2.K as well as the same pressure drop at 45.878 Pa.



The purpose, limitations, and functionality of exhaust heat exchangers designed as thermal enclosures of TEGs have been illuminated. The current study presents a methodology to optimize the internal heat transfer enhancing fins of such heat exchangers. The study focuses on longitudinal continuous fins. The major optimization constraint is the exhaust line pressure, whereas any increase in the flow resistance causes backpressure in the exhaust manifold. A geometry matrix contains 77 different geometries has been adopted for the optimization. Empirical correlations for the specified geometries have been used to compute the pressure drop, Nusselt number, and heat transfer coefficient. The study introduced a mathematical formulation of the "meltdown diameter" term which is used for representing the added friction effect of the internal fins. In addition, the study investigated three different values of root diameter, and exhaust flow rate. The optimized geometries were identified to have reciprocal fin length and number; to achieve a common meltdown diameter.

[D.sub.h]     Hydraulic diameter (m)
[D.sub.O]     Outer diameter (m)
[]    Meltdown diameter (m)
[Nu.sub.DB]   Dittus-Boelter Nusselt
[D.sub.i]     Inner diameter (m)
[D.sub.r]     Root diameter (m)
[H.sub.f]     Fin height (m)
[beta]        Helix angle
Re            Reynolds Number
[]    Meltdown area (m2)
[T.sub.f]     Fin thickness (m)
S             Offset distance (m)
[L.sub.P]     Pipe length (m)
P             Pressure (Pa)
f             Friction factor
Pr            Prandtl number
N             Number of fins
k             Thermal conductivity of
              fluid (W/[m.sup.2].K)
Ph            Helix pitch (m)
w             Discontinuity distance (m)
[rho]         Density (kg/[m.sup.3])
[??]          Mass flow rate (kg/s)


Matlab[R] Code

Heat Transfer and Flow Characteristics of Compressible Flow in Tubes With Internal Longitudinal Fins



% This code calculates the pressure drop and heat transfer characteristics

% of tubes with internal longitudinal fins at different fin lengths and

% number as well as plain tube. The fluid used is air.

% Related research supported by ScienceFund under grant number 79060

%=== Code Information ===

% For calculating the Nu number for plain tubes, Dittus-Boelter (1930)equation is used--While for calculating the Nu number for tubes with internal longitudinal fins, the correlation proposed by Carnavos (1979) is used.

% The friction factor for smooth plain tube is caluclated using equation from Blasius (1913)--While for calculating the Nu number for tubes with internal longitudinal fins, a corresponding correlation by Carnavos (1979) is used.

% Viscosity Correlation from J.B Heywood 1988 & Prandtl Number from J.P. Holman1997--Density, Cp, and Conductivity from Natl, Bur, Stand (U.S) Circ. 564 1955 after Holman, J. P 1997--Data tables are fitted with sixth order polynomial for specific heat, fourth order polynomial for conductivity and a power function for density.

%=== ===
   Lp = input (' Tube Length (m), Lp = ');
   Din = input (' Tube inner diameter (m), Din = ');
   e = input (' Tube average roughness (m), e = ');
   Tin = input (' Inlet gas temperature (K), Tin = ');
   mdot = input (' Inlet gas flowrate (Kg/s), mdot = ');
   Ft = input (' Fin Thickness (m), Ft = ');
   Lf = [0.001, 0.002, 0.004, 0.006, 0.008, 0.010, 0.012, 0.014,
   0.016, 0.018, 0.020];
   N = [5, 10, 15, 20, 25, 30, 35];

At = (pi/4)* Din^2;
Mue = 3.3*(10^-7)*(Tin^0.7);
Rou = 359.5 * (Tin^-1.0027);
Cp = (5*10^-20*Tin^6)-(4*10^-16*Tin^5)+(10^-12*Tin^4)-
K = (8*10^-15*Tin^4)-(2*10^-12*Tin^3)- (4*10^-8*Tin^2)+
Pr = (Cp*1000)*Mue/K;
V = mdot/Rou;
Vel = V/At;
Ren = (mdot/At)*Din/Mue;
Nu_P = 0.023*(Ren^0.8)*(Pr^0.3);
Alfa_P = Nu_P*K/Din;
Fric_P = 0.046/(Ren^0.2);
dP_P = 2*Fric_P*((mdot/At)^2)*Lp/(Rou*Din);

for i = 1:length (Lf)
      for j = 1:length (N)
        Afc(i,j) = (N(j)*Ft*Lf(i));
        Anet (i,j) = At - Afc(i,j);
        Peri(i,j) = (pi*Din)+(2*Lf(i)*N(j));
        Dh(i,j) = (4*Anet(i,j))/Peri(i,j);
        D_eqP (i,j) = sqrt ((4/pi)*Anet(i,j));

        Um(i,j) = V/Anet(i,j);
        Re(i,j) = Rou*Um(i,j)*Din/Mue;

        Dmd(i,j) = sqrt ((Din^2)-((4/pi)*N(j)*Ft*Lf(i)));

        Alfa_FP(i,j) =

        Fric (i,j) = Fric_P*(Dmd(i,j)/Din);
        deltaP (i,j) =


        Nu_eqP(i,j) = 0.023*(Re(i,j)^0.8)*(Pr^0.3);
        Alfa_eqP (i,j) = Nu_eqP(i,j)*K/Dh(i,j);
        F_eqP (i,j) = 0.046/(Re(i,j)^0.2);
        D_eqP (i,j) = sqrt ((4/pi)*Anet(i,j));
        dP_eqP (i,j) = 2*F_eqP (i,j)*


The authors acknowledge the financial support given through Science-Fund VOT 79060 from the Malaysian Ministry of Science, Technology and Innovation (MOSTI)


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[8] Ikoma, K., M.Munekiyo, K. Furuya, M. Kobayashi, T. Izumi, and K. Shinohara (1998). Thermoelectric Module and Generator for Gasoline Engine Vehicle. Proc. 17th International Conference on Thermoelectrics. Nagoya, Japan: IEEE pp. 464-467.

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[14] Wolverine Tube Inc. Engineering Data Book III, (2001) Ch. 5 Available at:

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[16] Hilsenrath, J., Beckett, C. W., Benedict, W. S., Fano, L., Hoge, H. J., Masi, J. F., Nuttal, R. L., Touloukian, Y. S., and Woolley, H. W., (1955), Tables of Thermal Properties of Gases, Circ. 564, U.S. National Bureau of Standards.

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[18] Saqr, K. M. (2008) Design and simulation of an exhaust based thermoelectric generator for iste heat recovery in passenger vehicles. Master Thesis. Universiti Teknologi Malaysia

Khalid M. Saqr * and Mohd N. Musa

Department of Thermofluids, Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

Skudai, 81310-Johor Darul'Takzim

* E-mail:
Table 1: Summary of the pressure drop per cm of the free-length
profile of the exhaust pipe.

                       PressureDrop (Pa)
Exhaust flow rate
                                (Pa/cm  length)
(kg/s)      (A)       (B)       (C)
                                       (A)     (B)    (C)
0.04      71.64    773.85   2028.58   0.65    7.34   28.4
0.05      74.91    775.98   2382.76   0.68    7.36   33.3
0.06     102.39   1474.48   2944.81   0.92   13.99   41.2
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Article Details
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Author:Saqi, Khalid M.; Musa, Mohd N.
Publication:International Journal of Applied Engineering Research
Article Type:Report
Geographic Code:1USA
Date:Apr 1, 2009
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