Modeling heat transfer subject to inhomogeneous Neumann boundary conditions by smoothed particle hydrodynamics and peridynamics

•A new method is introduced for imposing inhomogeneous Neumann and Robin BCs in smoothed particle hydrodynamics (SPH) and peridynamics for modeling heat transfer problems.•The new method can be employed for solving various transient or steady heat transfer problems subject to linear or nonlinear fluxes going through boundaries.•The numerical solutions by the new method converge to the classical solutions with notably improved accuracy.•The new method can be extended in SPH for solving other classical PDEs subject to inhomogeneous Neumann or Robin BCs, e.g., mass transfer in reactive transport, and is transferable to other numerical/modeling frameworks that also rely on nonlocal formulations.