The current study focuses on the natural-convection flow of nanofluids with boundary layer over a circular cylinder of uniform thermal wall with varying magnetic force from 0 to 1.5, radiative effects from 0 to 1, heat generation effects from 0 to 1, and Joule heating effects from 0 to 1. The problem is represented in the form of partial differential equations. The dimensional form of the equations is converted into a dimensionless form with the help of suitable stream functions. Then, the resultant equations are further reduced into the system of first-ordered differential equations, and the Keller box scheme is applied to obtain a solution numerically with the help of MATLAB code. The numerical solutions for Nusselt number, skin friction coefficient, Sherwood number, velocity profile, temperature profile, and concentration profile are represented with the help of graphs. The most interesting fact of the analysis is the flow of the fluid; the heat-mass and energy transfer rates could be managed in a controlled way through slight variations in the Brownian motion parameter from 0.1 to 0.7, in the Lewis number from 1 to 40, in the Eckert number from 0.1 to 0.4, in the thermophoresis parameter from 0.1 to 0.7, in the Prandtl number from 0.1 to 0.7, and in the buoyancy ratio from 0.1 to 0.7, as it is here analyzed and discussed.