Using blood as a carrier fluid in a rectangular domain between two permeable channels, the current work examines the laminar flow of a copper and copper oxide (Cu/blood and Cu + CuO/blood) hybrid nanoliquid. The drug delivery method and the microcirculatory system's flow dynamic mechanism are two examples of the things this study may modify. The impact of MHD and heat sources/sinks on the flow pattern were examined in the suggested model. Moreover, each channel's sides are permeable, enabling the nanoliquid to filter, exit, squeeze, and dilate at a set speed. The governing partial differential equations and the boundary conditions are transformed appropriately so that they may be computed. The resulting system of nonlinear differential equations is analytically approximated using the elegant homotopy perturbation method (HPM). The physical explanation for the simulated and evaluated features of flow characteristics, such as temperature profiles and velocity in response to variations in the emergent parameters, is provided. Since the magnetic field is essential to blood flow, more and more information on it has been added to the body of current literature. One of the study's many findings is that, in the flow regime's center, the pressure distribution decreases as the magnetic parameter's cumulative values rise. The electric conductivity and pH values are estimated via the increase in the temperature distribution. For pharmaceutical reasons, the Cu and CuO hybrid nanofluids are employed in this investigation. Since blood flow is significantly influenced by the magnetic field, the magnetic field was used in the extended investigation. To keep the blood flow's temperature uniform, the heat emission/absorption factor was included in the energy equation. We anticipate that the effort will produce effective results for medicinal applications like medication administration.