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We determine the effects of micro‐inertia density and the vortex viscosity on laminar free convection boundary layer flow of a thermomicropolar fluid past a vertical plate with exponentially varying surface temperature as well as surface heat flux. The governing nonsimilarity boundary layer equations are analyzed using: first, a series solution for small ξ (a scaled streamwise distribution of micro‐inertia density), second, an asymptotic solution for large ξ and, third, a full numerical solution implicit finite difference method together with Keller‐box scheme. Results are expressed in terms of local skin friction and local Nusselt number. The effects of varying the vortex viscosity parameter, Δ, surface temperature and the surface heat flux gradient n and m respectively against ξ for fluids having Prandtl number equals 0.72 and 7.0 are determined.

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