LAUSR

This study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid moving over an isothermal stretching sheet are solved using a novel numerical approach. A comparison of flow and heat transfer characteristics between an actively controlled (AC) and a passively controlled (PC) nanoparticle concentration boundary is considered. The boundary value partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The system of ODEs is solved using a new block method without having to reduce the equivalent system to first‐order equations. The solutions are verified using the spectral local linearization method and further validation of the results is confirmed by comparing the current results, for some limiting cases, with those in existing literature. The solutions obtained using the block method are in good agreement with the solution obtained using the spectral local linearization method. The results are in good agreement with existing findings in previous studies. The solutions obtained using the AC and PC nanoparticle concentration boundary conditions are analyzed.