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Thermodynamic and heat transfer analysis of heat recovery from engine test cell by Organic Rankine Cycle


During manufacture of engines, evaluation of engine performance is essential. This is accomplished in test cells. During the test, a significant portion of heat energy released by the fuel is wasted. In this study, in order to recover these heat losses, Organic Rankine Cycle (ORC) is recommended. The study has been conducted assuming the diesel oil to be composed of a single hydrocarbon such as C12H26. The composition of exhaust gases (products of combustion) have been computed (and not determined experimentally) from the stoichiometric equation representing the combustion reaction. The test cell heat losses are recovered in three separate heat exchangers (preheater, evaporator and superheater). These heat exchangers are separately designed, and the whole system is analyzed from energy and exergy viewpoints. Finally, a parametric study is performed to investigate the effect of different variables on the system performance characteristics such as the ORC net power, heat exchangers effectiveness, the first law efficiency, exergy destruction and heat transfer surfaces. The results of the study show that by utilizing ORC, heat recovery equivalent to 8.85 % of the engine power is possible. The evaporator has the highest exergy destruction rate, while the pump has the lowest among the system components. Heat transfer surfaces are calculated to be 173.6, 58.7, and 11.87 m2 for the preheater, evaporator and superheater, respectively.

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Fig. 9


Afr :

Frontal surface (m2) (Eq. 7)

Ai :

Inner surface (m2)

Ao :

Outer surface (m2)

Aop :

Heat transfer surface for each pass (m2) (Eq. 16)

Aph :

Preheater heat transfer surface (m2)

Atp :

Evaporator heat transfer surface (m2)

Ash :

Superheater heat transfer surface (m2)

Aw :

Wall surface (m2) (Eq. 20)


Heat capacity ratio (Eq. 32)

Cmin :

The smaller value of heat capacity rate for hot and cold fluids (kW/K)

Cmax :

The larger value of heat capacity rate for hot and cold fluids (kW/K)

cp :

Specific heat at constant pressure (kJ/kg K)

Dh :

Flow passage hydraulic diameter (m) (Eq. 9)

Di :

Inner diameter of tubes (m)


Exergy performance coefficient

E, S, F:

Correction factor (Eqs. 17, 29)

\( {\mathop {Ex}\limits^{ \cdot }}_{D} \) :

Exergy destruction rate (kW)

\( {\mathop {Ex}\limits^{ \cdot }}_{D,tot} \) :

Total exergy destruction rate (kW)

\( {\mathop {Ex}\limits^{ \cdot} }_{in} \) :

Rate of exergy transfer into a control volume (kW)

\( {\mathop {Ex}\limits^{ \cdot }}_{out} \) :

Rate of exergy transfer out of control volume (kW)

\( {\mathop {Ex}\limits^{ \cdot} }_{ch} \) :

Chemical exergy rate (kW)

\( {\mathop {Ex}\limits^{ \cdot }}_{ph} \) :

Physical exergy rate (kW)


Mass flux (kg/m2 s) (Eq. 9)


Enthalpy (kJ/kg)

h0 :

Enthalpy at dead (environmental) state (kJ/kg)


Convective heat transfer coefficient (W/m2 K)

Hi :

Convective heat transfer coefficient at the inner surface (W/m2 K)

Ho :

Convective heat transfer coefficient at the outer surface (W/m2 K)

He :

Height of heat exchanger (m)

Hf0 :

Convective heat transfer coefficient for film boiling (W/m2 K)

Hnb :

Convective heat transfer coefficient the nuclear boiling (W/m2 K)

kf :

Fin thermal conductivity (W/m K)

\( \dot{m} \) :

Mass flow rate (kg/s)

\( \dot{m}_{exh} \) :

Exhaust gasses mass flow rate (kg/s) (Eq. 2)

\( \dot{m}_{ref} \) :

ORC fluid mass flow rate (kg/s) (Eq. 2)

Ncol :

Number of tubes in a column

Nrow :

Number of tubes in a row

Ntp :

Number of tubes in a pass


Number of transfer units

NTUc.f. :

Number of transfer units for counter flow heat exchanger

Nui :

Nusselt number at the inner surface


Prandtl number

\( \dot{Q} \) :

Heat transfer rate (kW)

\( \dot{q}_{act} \) :

Actual heat transfer rate (kW)

\( \dot{q}_{max} \) :

Maximum heat transfer rate (kW)

Rdi :

Dirty resistance at the inner surface (m2 K/W) (Eq. 20)

Rdo :

Dirty resistance at the outer surface (m2 K/W) (Eq. 20)

Rw :

Thermal resistance of wall (K/W)


Reynolds number


Entropy (kJ/kg K)

s0 :

Entropy at dead (environmental) state (kJ/kg K)


Stanton number


Temperature (K)

T0 :

Environmental temperature (K)

Tc :

Condenser temperature (K)

Te :

Evaporator temperature (K)

Tpp :

Pinch point temperature (K)

Tsup :

Superheat temperature (K)


Overall heat transfer coefficient (W/m2 K)


Volume of heat exchanger (m3)


Width (m)

\( \dot{W}_{net} \) :

Net output power (kW)

\( \dot{W}_{t} \) :

Power of ORC turbine (kW)

\( \dot{W}_{p} \) :

Power of ORC pump (kW)

xi :

Molar fraction

xl :

Longitudinal tube pitch (m)

xt :

Transverse tube pitch (m)

YD :

Exergy destruction ratio


Correction factor

β :

Fin area to total heat transfer area of heat exchanger


Minimum free flow area to frontal area


Viscosity (kg/m s)


Density (kg/m3)


Efficiency (%)

ηf :

Efficiency of a single fin (%)

ηo :

Overall surface efficiency (%)

δf :

Fin thickness (m)

\( \Delta T_{LMTD} \) :

Log mean temperature difference (K)


Effectiveness (%)

1, 2, 3, 4, 5, 6:

State points for the R11

a, x, y, b:

State points for the exhaust gas


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Correspondence to Naser Shokati.

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Shokati, N., Mohammadkhani, F., Farrokhi, N. et al. Thermodynamic and heat transfer analysis of heat recovery from engine test cell by Organic Rankine Cycle. Heat Mass Transfer 50, 1661–1671 (2014).

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  • Heat Exchanger
  • Convective Heat Transfer Coefficient
  • Heat Transfer Surface
  • Organic Rankine Cycle
  • Exergy Destruction