Analytical solutions of a set of equations that couples the Ekman and the Prandtl boundary layer (BL) equations were obtained; closure on the subgrid scale was via the eddy exchange (K) approach, where K was made to depend on both the internal stability (μ) and height raised to an arbitrary power. The boundary layer height (h) wis also made to depend on μs. As byproducts of these solutions, generalized expressions for the universal functions of μ, A, B and C and for the resistance and heat-transfer laws (i. e. a, u*/G ind T*/0, respectively) for a given set of external parameters (X, Ro and S) for the general case of the slope angle 0~~~10 rad were presented. From this, an interesting and novel result is the finding that there are three different regimes of solutions depending on whether S (or ~) is less than, equal to or greater than certain critical value S (or ~ ). The solutions for all three regimes were presented in graphical form, from which the appreciable influence of terrain slope on the cross-isobaric inflow angle, the momentum- and heat-transfer is clearly discernible. Also in a preliminary test of the results of this investigation with observations, it is found that the theoretical values of the cross-isobaric angle are in good agreement with the observed values in Antarctica and therefore encouraging for further research.