MHD mixed convection and entropy generation of a nanofluid in a vertical porous channel

•Entropy generation and MHD mixed convection flow in a porous channel are studied.•The governing equations are solved by the control volume method.•Effects of Da, Ha, Ri and ϕ are considered for both assisting and opposing flows.•The heat transfer is increased with Ha and ϕ, and is decreased with Da and Ec.•The various irreversibilities are increased by rising the value of Hartmann number. A numerical study of entropy generation and MHD mixed convection flow of a nanofluid in a vertical porous channel is made. The left plate is thermally insulated, whereas four discrete heat sources dissipating a uniform heat flux are mounted on the right wall which is adiabatic elsewhere. Both assisting and opposing flows are considered. The Darcy–Brinkman–Forchheimer model with the Boussinesq approximation is adopted and the finite volume method is used to solve the governing equations with the appropriate boundary conditions. The influence of the magnetic field strength (Hartmann number), Joule heating effect (Eckert number), buoyancy force intensity (Richardson number), nanoparticles volume fraction, as well as porous medium permeability (Darcy number) on velocity profiles, isotherms, isentropic lines, global Nusselt number and total entropy generation are analyzed. The results showed an enhancement on heat transfer rate by using a porous medium, a nanofluid, a magnetic field without taking into account the Joule heating and when mixed convection is assisted. Globally, entropy generation increases with the parameters cited above.