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In the present paper, nondeterministic CFD has been performed using polynomial chaos expansion and Gram-Schmidt orthogonalization method. The Gram-Schmidt method has been used in the literature for constructing orthogonal basis of polynomial chaos expansion in the projection method. In the present study, for the first time the Gram-Schmidt method is used in regression method. For the purpose of code verification, the output numerical basis of code for uniform and Gaussian probability distribution functions is compared to their corresponding analytical basis. The numerical method is further validated using a classical challenging function. Comparison of numerical and analytical statistics shows that developed numerical method is able to return reliable results for statistical quantities of interest. Subsequently, the problem of stochastic heat transfer in a grooved channel was investigated. The inlet velocity, hot wall temperature and fluid conductivity were considered uncertain with arbitrary probability distribution functions. The UQ analysis was performed by coupling the UQ code with a CFD code. The validity of numerical results was evaluated using a Monte-Carlo simulation with 2000 LHS samples. Comparison of polynomial chaos expansion and Monte-Carlo simulation results reveals an acceptable agreement. In addition a sensitivity analysis was carried out using Sobol indices and sensitivity of results on each input uncertain parameter was studied.

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In this paper, the performance of three turbulence models, zonal k-ε, linear low-Reynolds k-ε and nonlinear low-Reynolds k-ε in the prediction of flow and heat transfer through a dimpled channel is investigated. Furthermore, the effect of YAP term replacement with NYP length scale correction term is studied. Dimples are heat transfer devices which are employed in gas turbine blades to increase the heat transfer levels. These devices do not act as an obstacle for flow, and thus they produce low pressure losses. In this study, the governing equations on flow and energy are solved using the finite volume method together with the SIMPLE algorithm. The results obtained with YAP term indicate that the nonlinear model predicts larger recirculation flow inside the dimple than zonal and linear models. Also, the intensity of impingement and upwash flow in this model is greater than other models. Heat transfer results show that the zonal model predicts the heat transfer levels lower than experimental measurement. Using the linear model leads to a better prediction of heat transfer inside the dimples and their back rim. Compared to these models, the nonlinear model yields a better prediction not only for the smooth area between the dimples, but in the back rim of the dimple. The replacement of the YAP term with the NYP term in linear and nonlinear models leads to more accurate results for heat transfer in dimple span-wise direction and back rim.