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• New second-order interpolative-based M2 maximum-entropy closure for constructing approximate solutions of the radiative transport equation in gray-participating media governed Bose-Einstein statistics. • Review of and new insight into the necessary and sufficient conditions for realizability of predicted moments up to second order in multiple space dimensions. • Demonstration of hyperbolicity of proposed interpolative-based M2 closure via numerical experiments. • Development of boundary conditions for M2 moment closure based on partial moment approach. • Illustration of predictive capabilities of interpolative-based M2 closure for several one and twodimensional canonical test problems. A new interpolative-based approximation to the second-order maximum-entropy, M 2 , moment closure for predicting radiative heat transfer in gray participating media is proposed and described. In addition to preserving many of the desirable mathematical properties of the original M 2 closure, the proposed interpolative approximation provides significant reductions in computational costs compared to the costs of the original M 2 closure by avoiding repeated numerical solution of the corresponding optimization problem for entropy maximization. Theoretical details of the proposed interpolative-based closure, along with a description of an efficient Godunov-type finite-volume scheme that has been developed for the numerical solution of the resulting system of hyperbolic moment equations, are presented. The finite-volume method makes use of limited linear solution reconstruction, multi-block body-fitted quadrilateral meshes with anisotropic adaptive mesh refinement (AMR), and an efficient Newton-Krylov-Schwarz (NKS) iterative method for solution of the resulting non-linear algebraic equations arising from the spatial discretization procedure. The predictive capabilities of the proposed interpolative M 2 closure are assessed by considering a number of model problems involving radiative heat transfer within one- and two-dimensional enclosures, the results for which are compared to solutions of the first-order maximum entropy, M 1 , moment closure, as well as those of the more commonly adopted spherical harmonic moment closure techniques (first-order P 1 and third-order P 3) and the popular discrete ordinates method (DOM). The latter is used as a benchmark for comparisons, whenever exact solutions are not available. The numerical results illustrate the promise of the proposed M 2 closure, with the closure outperforming the M 1 , P 1 and P 3 closures for virtually all cases considered. [ABSTRACT FROM AUTHOR]