Radiative heat transfer in a 2D semi-transparent gray medium with a centered inner square cavity

Conductive-radiative heat transfer in a 2D semi-transparent medium with a square centered obstacle

“…In [23], it has been discussed that the present geometry ( = 3ℎ) reveals the existence of sixteen sub-domains, divided into four squares and twelve triangles as illustrated in Fig. 2-(b), where the different expressions of the useful radiative quantities to evaluate have not the same analytical expressions.…”

“…1 a the semi-transparent medium enclosed in a two dimensional square cavity of length , containing a square obstacle of length ℎ at a center position. From Djeumegni et al [23], analytical expressions of the radiative quantities examined in this paper are those derived for the case = 3ℎ. Modelling involving geometries for which < 3, 3ℎ < ≤…”

“…Therefore, following a similar procedure developed in [22,23], all the locations of the calculation points in the medium are characterized by their Cartesian coordinates ( , ). One has − ∆ ≤ ′ ≤ + ∆ and − ∆ ≤ ′ ≤ + ∆ , where = ( − 2)∆ , and = ( − 2)∆ .…”

“…Following a similar procedure proposed in [22,23], a first set of Bickley-Naylor functions [24] is introduced and set by:…”

“…Moreover, the aim of the present paper is to establish an exact semi-analytical solution of the conductive-radiative heat transfer problem, applied to a 2D absorbing and emitting medium with a centered square obstacle. Exact expressions of the incident radiation from the RTE as developed in the case of radiation heat transfer [22,23] are set and coupled with energy equation by using a centered finite scheme in order to derive the temperatures and heat flux distributions. An adequate numerical algorithm to solve the considered conductive-radiative problem is given and performed to obtain the numerical results of temperature and heat flux.…”