[1] Ghanem RG, Spanos PD (1991) Stochastic finite element method: Response statistics, in Stochastic finite elements: a spectral approach. Springer, New York.
[2] Wiener N (1938) The homogeneous chaos. Am J Math 60(4): 897-936.
[3] Raisee M, Kumar D, Lacor C (2015) A non‐intrusive model reduction approach for polynomial chaos expansion using proper orthogonal decomposition. Int J Numer Methods Eng 103(4): 293-312.
[4] Salehi S, et al. (2018) On the flow field and performance of a centrifugal pump under operational and geometrical uncertainties. Appl Math Model 61: 540-560.
[5] Carnevale M, et al. (2013) Uncertainty quantification: A stochastic method for heat transfer prediction using LES. J Turbomach 135(5).
[6] Mohammadi A, Raisee M (2017) Effects of operational and geometrical uncertainties on heat transfer and pressure drop of ribbed passages. Appl Therm Eng 125: p. 686-701.
[7] Maitre OPL, et al. (2001) A stochastic projection method for fluid flow. I: Basic formulation. J Comput Phys 173(2): 481-511.
[8] Lacor C, Smirnov S (2008) Non-deterministic compressible navier-stokes simulations using polynomial chaos. in Proc. ECCOMAS Conf..
[9] Dinescu C, et al. (2010) Assessment of intrusive and non-intrusive non-deterministic CFD methodologies based on polynomial chaos expansions. Int J Eng Syst Model Simul 2(1-2): 87-98.
[10] Xiu D, Tartakovsky DM (2006) Numerical methods for differential equations in random domains. SIAM J Sci Comput 28(3): 1167-1185.
[11] Xiu D, Karniadakis GE (2003) Modeling uncertainty in flow simulations via generalized polynomial chaos. J Comput Phys 187(1): 137-167.
[12] Salehi S, Raisee Dehkordi M (2016) Application of Gram-Schmidt orthogonalization method in uncertainty quantification of computational fluid dynamics problems with arbitrary probability distribution functions. Modares Mechanical Engineering 15(12): 1-8.
[13] Esfahanian V, Rahbari I, Mortazavi MH (2015) Uncertainty quantification of RANS turbulence models for power-law non-newtonian fluid flows. Modares Mechanical Engineering 15(5): 287-294.
[14] Nouri R, Raisee M (2017) Uncertainty quantification of electroosmotic flow in a microchannel. Modares Mechanical Engineering 17(8): 291-300.
[15] Bogard DG, Thole KA (2006) Gas turbine film cooling. J Propul Power 22(2): 249-270.
[16] Han JC, Dutta S, Ekkad S (2012) Gas turbine heat transfer and cooling technology. CRC press.
[17] Montomoli F, et al. (2012) Geometrical uncertainty and film cooling: Fillet radii. J Turbomach 134(1).
[18] D’Ammaro A, Montomoli F (2013) Uncertainty quantification and film cooling. Comput Fluids 71: 320-326.
[19] Babaee H, Wan X, Acharya S (2014) Effect of uncertainty in blowing ratio on film cooling effectiveness. J Heat Trans-T ASME 136(3).
[20] Papell SS (1960) Effect on gaseous film cooling of coolant injection through angled slots and normal holes. Technical Report, National Aeronautics and Space Administration.
[21] Singh K, Premachandran B, Ravi M (2015) A numerical study on the 2D film cooling of a flat surface. Numer Heat Tr A-Appl 67(6): 673-695.
[22] Ghorab MG (2014) Film cooling effectiveness and heat transfer analysis of a hybrid scheme with different outlet configurations. Appl Therm Eng 63(1): 200-217.
[23] Naghashnejad M, Amanifard N, Deylami H (2014) A predictive model based on a 3-D computational approach for film cooling effectiveness over a flat plate using GMDH-type neural networks. Heat Mass Transfer 50(1): 139-149.
[24] Carnevale M, et al. (2013) Uncertainty quantification: A stochastic method for heat transfer prediction using LES. J Turbomach 135(5): 051021.
[25] Greenshields CJ (2017) OpenFoam user guide. Version 6. OpenFOAM Foundation Ltd July.
[26] Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: The finite volume method. Pearson Education.
[27] Xiu D, Karniadakis GE (2002) The Wiener--Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2): 619-644.
[28] Eldred M, Webster C, Constantine P (2008) Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos. in 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 16th AIAA/ASME/AHS Adaptive Structures Conference, 10th AIAA Non-Deterministic Approaches Conference, 9th AIAA Gossamer Spacecraft Forum, 4th AIAA Multidisciplinary Design Optimization Specialists Conference.
[29] Karimi MS, et al. (2019) Probabilistic CFD computations of gas turbine vane under uncertain operational conditions. Appl Therm Eng 148: 754-767.
[30] Soize C, Ghanem R (2004) Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM J Sci Comput 26(2):395-410.
[31] Hosder S, Walters R, Perez R (2006) A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations. in 44th AIAA aerospace sciences meeting and exhibit.
[32] Sobol' IyM (1967) On the distribution of points in a cube and the approximate evaluation of integrals. Zh Vychisl Mat Mat Fiz 7(4): 784-802.
[33] Sobol' IyM (1990) On sensitivity estimation for nonlinear mathematical models. Mat Model 2(1): 112-118.
[34] Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Safe 93(7): 964-979.
[35] Sobol IM (2003) Theorems and examples on high dimensional model representation. Reliab Eng Syst Safe 79(2): 187-193.
)