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This study looks into the steady heat transfer issue of a flow of an incompressible Carreau fluid. Carreau fluid exhibits the shear thinning and thickening characteristics at low, moderate, and high shear rates. At the tubule wall, the fluid absorption is used as a function of pressure gradient and wall permeability through the tubule wall. Supposing the tubule radius considerably small in comparison to its length, the governing equations are considerably simplified. Significant quantities of interest are computed analytically by using perturbation, and the influence of emergent parameters is discussed through graphical results. The comparisons of results with existing data are set up to be good agreement.