A computational study is carried out to investigate the flow in a hybrid nanofluid near a slender needle. It is further examined that the flow is subjected to a slip effect at the needle surface. The appropriate similarity transformations lead to nonlinear coupled differential equations. The solutions that expressing the temperature, velocity, rate of heat transfer as well as coefficient of skin friction is determined via bvp4c solver in MATLAB program. The impacts of the emerging variables embedded in the flow model are investigated and presented in various graphs. The numerical outcomes show that there exists more than one solution in the system. Finally, an analysis of stability has been executed to examine the realizable solution (or physically stable).