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The impact of different arrangement of molecular chains in term of low and high shear rate’s viscosities on heat and mass flow of Non-Newtonian shear thinning fluids


Mohsan Hassan*, Abrar Faisal, Khurram Javid, Salah Ud-Din Khan, Ashfaq Ahmad* and Rawaiz Khan  


Background: Non-Newtonian fluids, especially shear thinning fluids, have several applications in the polymer industry, food industry, and even in everyday life. The viscosity of shear thinning fluids is sometimes decreased by two or three orders of magnitude due to the alignment of the molecules in order when the shear rate is increased, and it cannot be ignored in the case of polymer processing and lubrication problems.

Objective: So, the effects of viscosities at a low and high shear rate on the heat and mass boundary layer flow of shear thinning fluid over moving belts is investigated in this study. For this proposed, the generalized Carreau model of viscosity relates to shear rate and is used in the momentum equation. The Carreau model contains the five parameters: low shear rate viscosity, high shear rate viscosity, viscosity curvature, consistency index, and flow behavior index. For the heat flow, expression of the thermal conductivity model, similar to the viscosity equation due to the non-Newtonian nature of the fluid, is used in the energy equation.

Methods: On the mathematical model of the problem, boundary layer approximations are applied and then simplified by applying the similarity transformations to get the solution. The solution of the simplified equations is obtained by numerical technique RK-Shooting Method. The results are compared with existing results for limited cases and good agreement is found.

Results: The results are obtained in the form of velocity and temperature profiles under the impact of all the viscosity’s parameters and are displayed in graphical form. Moreover, the boundary layer parameters such as the thickness of the regions, momentum thickness, and displacement thickness are calculated to understand the structure of the boundary layer flow of fluid.

Conclusion: The velocity and temperature of the fluid are decreased and increased respectively by all viscosity’s parameters of the model. So, the results of the boundary layer fluid flow under rheological parameters will not only help engineers to design superior chemical equipment, but will also help improve the economy and efficiency of the overall process.


Low and high shear rates viscosities; Shear thinning fluid flow; Five parameter contained Carreau model


Department of mathematics, COMSATS University Islamabad, Lahore Campus 54000, Department of Chemical Engineering, COMSATS University Islamabad, Lahore Campus 54000, Department of Mathematics, Northern University, 24110, Wattar-Nowshera, KPK, Institute of plasma physics, Chinese Academy of Science, Hefei, Anhui, Department of Chemistry, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Engineer Abdullah Bugshan Research Chair for Dental and Oral Rehabilitation, College of Dentistry, King Saud University, Riyadh 11545

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