Studying the Transient Thermal Contact Conductance Between the Exhaust Valve and Its Seat Using the Inverse Method

  • Mohsen Motahari Nezhad
  • Mohammad Hassan Shojaeefard
  • Saeid Shahraki


In this study, the experiments aimed at analyzing thermally the exhaust valve in an air-cooled internal combustion engine and estimating the thermal contact conductance in fixed and periodic contacts. Due to the nature of internal combustion engines, the duration of contact between the valve and its seat is too short, and much time is needed to reach the quasi-steady state in the periodic contact between the exhaust valve and its seat. Using the methods of linear extrapolation and the inverse solution, the surface contact temperatures and the fixed and periodic thermal contact conductance were calculated. The results of linear extrapolation and inverse methods have similar trends, and based on the error analysis, they are accurate enough to estimate the thermal contact conductance. Moreover, due to the error analysis, a linear extrapolation method using inverse ratio is preferred. The effects of pressure, contact frequency, heat flux, and cooling air speed on thermal contact conductance have been investigated. The results show that by increasing the contact pressure the thermal contact conductance increases substantially. In addition, by increasing the engine speed the thermal contact conductance decreases. On the other hand, by boosting the air speed the thermal contact conductance increases, and by raising the heat flux the thermal contact conductance reduces. The average calculated error equals to 12.9 %.


Air-cooled engine Exhaust valve Inverse method Thermal contact conductance (TCC) Transient heat transfer 



Conjugate gradient method

\(h_c \)

Thermal contact conductance (W\({\cdot }\)m\(^{-2}\) \({\cdot }\)K\(^{-1}\))


Thermal conductivity (W\({\cdot }\)m\(^{-1}\) \({\cdot }\)K\(^{-1}\))


Heat flux (W\({\cdot }\)m\(^{-2}\))


Temperature (K)


Result function


Cartesian spatial coordinate



\(e_{rms} \)

Root mean square error


Length (m)


Time (s)


Measured temperatures (K)


Constant temperature at x = 0 (K)

\(T_i \)

Initial temperature (K)

Greek symbols

\(\upalpha \)

Thermal diffusivity (m\({\cdot }\)s\(^{-1}\))

\(\upbeta \)

Search step size

\(\upgamma \)

Conjugation coefficient

\(\Delta \)


\(\updelta \)

Distance from interface (m)

\(\Delta \)T

Temperature drop (K)


Density (\(\hbox {kg}{\cdot }\hbox {m}^{-3}\))

\(\uplambda \)

Lagrange multiplier satisfying the Adjoint problem





i-th parameter


j-th sensor


k-th sensor


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Mohsen Motahari Nezhad
    • 1
  • Mohammad Hassan Shojaeefard
    • 2
  • Saeid Shahraki
    • 3
  1. 1.Department of Automotive EngineeringIran University of Science and Technology (IUST)TehranIran
  2. 2.Department of Mechanical EngineeringIran University of Science and Technology (IUST)TehranIran
  3. 3.Department of Mechanical EngineeringUniversity of ZabolZabolIran

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