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.