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CFD Analysis of Combined Thermal Radiation and Conjugate Heat Transfer in a 3D FFS

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Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Mathematical investigation of conjugate heat transfer in a 3-d rectangular duct having a vertical forward-facing step with a participating medium is carried out using OpenFOAM. The stepped interface splits the rectangular domain into two regions (viz., solid and fluid). The fluid considered is carbon-dioxide, which is a participating medium. The ability of the code has been verified by validating conjugate heat transfer and radiative heat transfer. The fluid flows at a Reynolds number 250 through a rectangular domain with a contraction ratio of 0.5. The case study mainly focused on the effect of optical thickness and linear scattering albedo on thermal characteristics of the flow. The changes in average Nusselt number with optical thickness and linear scattering albedo are analyzed. Also, the sense of including radiation effects into a thermal analysis are discussed.


  • Radiation heat transfer
  • Participating media
  • Conjugate heat transfer
  • Forward-facing step
  • fvDOM
  • OpenFOAM

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Backward-Facing Step


Discrete Ordinate Method


Forward-Facing Step


Finite Volume Method


Radiative Transfer Equation


Contraction ratio (h/H)

H :

Height of the inlet section (m)

h :

Height of the outlet section (m)

I :

Radiation intensity (Wsr−1)

L :

Characteristics length (m)

n :

Refractive index


Nusselt number


Prandtl number

q :

Heat Flux (Wm−2)


Reynolds number

S :

Step Height (m)

T :

Temperature (K)

θ :

Dimensionless temperature


Bulk temperature






Hot wall

i, j :

1, 2, 3 corresponds to x, y, z directions respectively








Interface wall

α :

Thermal diffusivity (α = κ/ρcp m2s−1)

β :

Extinction coefficient (m−1)

κ :

Thermal conductivity (Wm−1K−1)

µ :

Dynamic viscosity (Pas)

ω :

Linear scattering albedo


Scattering phase function

ρ :

Density (kg m−3)

σ :

Stefan–Boltzmann-Constant 5.67 × 10−8 Wm−2K−4

σ a :

Absorption coefficient (m−1)

σ s :

Scattering coefficient (m−1)

τ :

Optical thickness


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Correspondence to J. S. Jayakumar .

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Krishnendu, G.S., Jayakumar, J.S. (2021). CFD Analysis of Combined Thermal Radiation and Conjugate Heat Transfer in a 3D FFS. In: Mohan, S., Shankar, S., Rajeshkumar, G. (eds) Materials, Design, and Manufacturing for Sustainable Environment. Lecture Notes in Mechanical Engineering. Springer, Singapore.

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-9808-1

  • Online ISBN: 978-981-15-9809-8

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