We examine the parameterizations of the turbulent friction velocity u* for the mathematical model of an urban heat island of a low-aspect-ratio in a calm stably stratified environment with a thermophysically inhomogeneous underlying surface (unstable stratification over a localized surface heat source and stable stratification out of it). The results of u* calculation by Louis and Paulson noniterative algorithms for the quasi-steady circulation over an urban heat island are presented.