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This study explores thermal convection in suspensions of neutrally buoyant, non-colloidal suspensions confined between horizontal plates. A constitutive diffusion equation is used to model the dynamics of the particles suspended in a viscous fluid and it is coupled with the flow equations. We employ a simple model that was proposed by Metzger, Rahli & Yin ( J. Fluid Mech. , vol. 724, 2013, pp. 527–552) for the effective thermal diffusivity of suspensions. This model considers the effect of shear-induced diffusion and gives the thermal diffusivity increasing linearly with the thermal Péclet number ( Pe ) and the particle volume fraction ( ϕ ). Both linear stability analysis and numerical simulation based on the mathematical models are performed for various bulk particle volume fractions $$({\phi _b})$$ ranging from 0 to 0.3. The critical Rayleigh number $$(R{a_c})$$ grows gradually by increasing $${\phi _b}$$ from the critical value $$(R{a_c} = 1708)$$ for a pure Newtonian fluid, while the critical wavenumber $$({k_c})$$ remains constant at 3.12. The transition from the conduction state of suspensions is subcritical, whereas it is supercritical for the convection in a pure Newtonian fluid $$({\phi _b} = 0)$$ . The heat transfer in moderately dense suspensions $$({\phi _b} = 0.2\text{--}0.3)$$ is significantly enhanced by convection rolls for small Rayleigh number ( Ra ) close to $$R{a_c}$$ . We also found a power-law increase of the Nusselt number ( Nu ) with Ra , namely, $$Nu\sim R{a^b}$$ for relatively large values of Ra where the scaling exponent b decreases with $${\phi _b}$$ . Finally, it turns out that the shear-induced migration of particles can modify the heat transfer.