Present numerical simulation is to investigate the Lorentz force and constant axial pressure gradient effects on flow and heat transfer of electrically conducting magneto-hydrodynamic, [Formula: see text] Jeffrey fluid at fully developed region of annular sector duct. The law of conservation of energy is simulated by taking two thermally boundary conditions, known as [Formula: see text]1 thermally boundary condition (i.e. constant axial heat flux with uniform peripherally temperature in the annular sector duct’s cross section) and [Formula: see text] thermally boundary condition (i.e. constant temperature axially and peripherally). The numerical results are simulated in the following range of parameters: the ratio of radii, [Formula: see text], an apex angle of duct [Formula: see text] by using [Formula: see text] number of fins, Hartman number, [Formula: see text] and the ratio of relaxation time to retardation time, [Formula: see text]. During the simulation, it has been concluded that the other parameter corresponding to Jeffrey fluid (i.e. the retardation time, [Formula: see text]), has ignored due to minor attribution on flow and heat transfer by increasing the value from [Formula: see text] to [Formula: see text]. Hartman number, [Formula: see text], upgrades the [Formula: see text] up to 18.76% and 14.60%, while [Formula: see text] / [Formula: see text] up to 1.82% and 1.47%/1.55% and 1.29% for [Formula: see text] and [Formula: see text] respectively at [Formula: see text] and [Formula: see text] by increasing its value from 0 to 2. At higher [Formula: see text], the difference becomes ignored in the case of [Formula: see text] when we change the annular region along radial direction.
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