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Show with which the values of the variables are associated. point. Then the transport equation of a variable 4? is integrated over each individual control volume. This process is called the discretization process which results in the conversion of each partial differential equation into a set of linear algebraic equations. Therefore, the problem of solving the partial differential equation has been reduced to the problem of solving a set of linear algebraic equations. The integration of Eq. (18) over the control volume ~ V = ~x~y~z gives J~ ,e - J~ .w + J~ , n - J~,!J + J~ ,t - J~.b = S~~ v. (22) The final form of Eq. (22) is where q>p is the value of the solution variable at the grid point and 4?w, 4?E, q>s, 4?N, q>B, and q>T are the values of the solution variables at the neighboring grid points. The coefficient a's of the discretization equation were here evaluated by a Hybrid Differential Scheme (HDS). The detailed procedure of solving Eq. (23) is found in Patankar [11]. The SIMPLE pressure correction is currently employed. The inlet conditions are specified by fixing the values of all solution variables. At exit boundaries, the constant pressure drop through the checker wall is assumed and the checker wall acts like a porous wall. The mean velocity and turbulence profiles adjacent to a solid wall are defined by semi-empirical relationships derived from the wall function (13]. 4.2. Discrete Ordinates Method (DOM) The radiant energy transfer equation Eq. (11) is solved through the Discrete Ordinates Method [14] using a TN quadrature set [12]. This equation can be integrated within the same control volume used in the finite volume method and the intensity gradients are estimated through the area averaged intensities of the faces at the control volume Iw , Ie, I., In, Ib, and It. The volume averaged density for the control volume Ip is located at the grid point. The temperature and the absorption coefficient are assumed to be uniform within the control volume. The integration yields (24) For positive direction cosines, Iw , 1$ and Ib are known. However the surface intensities on the east Ie, north In and top faces Iw are unknown. The common approach to solve this 7 |