This paper presents a theoretical investigation of the influence of fluctuating circulation (flow with magnitude- and direction-dependent amplitudes) upon the transfer of momentum, heat, and mass in two-dimensional laminar boundary-layer fiow past cylinders with or without uniform suction. The boundary-layer equations for flow, temperature, and concentration are linearized by use of a perturbation technique. The solutions of the velocity, temperature, and concentration components are obtained by power-series development so that the universal distribution functions may be applied to any two-dimensional flow. Theoretical results include the frequency response of fluid velocity, temperature, and concentration, the streamline patterns of the steady streaming, the distribution of the steady second-order temperature and concentration, and the net variations in the shear stress, rates of heat, and mass transfer. Numerical results are obtained for flows around a circular cylinder with fluctuating circulations of constant and space-dependent amplitudes. Nomenclature a = coefficient depending on the geometrical configuration of the body, dimensionless b = coefficient depending on the nature of flow oscillation, dimensionless c = dimensionless concentration; = (CV — C*)/(C W* — Co,*) C* = concentration, Ibm-mole; Cw* at the wall; CV of the freestream F = functional coefficient or universal distribution function of temperature (or concentration), dimensionless: Fok for the zeroth-order approximation; Fuk for the first-order approximation; Fzijk for the second-order approximation / = functional coefficient or universal distribution function of velocity, dimensionless; /o* for the zerothorder approximation; fuh for the first-order approximation; fzijk for the second-ordera pproximation i = (~1)1/2 k = integer, dimensionless L = characteristic length, ft; = 2R for a circular cylinder / = integer, dimensionless m = constant, dimensionless Nu = Nusselt number, dimensionless; =(<M/dy)v=Q n = constant, dimensionless Pr = Prandtl number, dimensionless q = rate of heat transfer, Btu/hr-ft2 R = radius of a circular cylinder, ft Re = Reynolds number, dimensionless Sc = Schmidt number, dimensionless Sh = Sherwood number, dimensionless; = (dc/ch/) y=o T = dimensionless temperature; = (Tw* - T*)/(TW* TV) T* = temperature, °F; Tw* of the wall; TV of the freestream t = dimensionless time; = t*Um/L t* = physical time, hr U(x,t) = velocity of potential flow in dimensionless form; = U*(x,t)/Ua UQ(X) = time-average velocity of potential flow in dimensionless form; = UQ*(x)/Um Ui(x) = oscillation amplitude of potential flow in dimensionless form; = Ui*(x)/Um