The laminar combined free and forced convection is studied in pseudoplastic or shear-thinning fluids flowing past a confined horizontal cylinder. The forced flow is directed normal to the direction of thermal buoyancy in a confined channel with adiabatic walls. The study expands the results over the range of pseudoplastic fluids varying in the power-law index, n from 0.3 to 1, including Newtonian fluid as a limiting case. The effect of non-dimensional parameters on the cross-buoyancy flow, Prandtl number, 1 ≤ Pr ≤ 100, Reynolds number, 1 ≤ Re ≤ 20, Richardson number, 0 ≤ Ri ≤ 3, and Grashof number, 10 ≤ Gr ≤ 105 have been explored for two values of cylinder confinement B, defined as the diameter of cylinder to height of the channel, D/H = 1/10, 1/5. The governing equations have been solved for the steady-state flow over the range of parameters by employing finite-element numerical scheme. The flow and thermal field distorted by cross-buoyancy past a hot cylinder is analysed by plotting the streamlines and isotherms in the channel. The total drag, lift coefficients, and average Nusselt number increase as the confinement ratio, B increases from 1/10 to 1/5. At Ri = 3 for B = 1/5, the flow reversal adjacent to the wall in the downstream section of the cylinder has been observed at Re = 20 for Pr = 1 which is abolished as the shear-thinning effect of fluid decreases. Finally, a correlation to predict the average Nusselt number as Nuavg = f(Re, Pr, Ri, n) for both the confinements has been proposed over the range of parameters.