Influence of Variable Viscosity on Hydrodynamic and Thermal Characteristics of Casson Fluid Flow over a Stretching Surface

Abstract

This research examines the steady two-dimensional boundary-layer flow and thermal behavior of a Casson fluid over a stretching surface, taking into account viscosity variations with temperature. Using suitable similarity transformations, the governing momentum and energy equations are transformed into ordinary differential equations. These equations are then solved numerically using the successive linearisation method. Special attention is given to the effects of the Casson parameter, variable viscosity, and the Prandtl number on the velocity and temperature distributions. The results reveal that stronger non-Newtonian effects tend to slow down the fluid motion and thicken the momentum boundary layer, while higher Prandtl numbers lead to a reduction in the thermal boundary-layer thickness. Viscosity variation is also found to significantly influence both the hydrodynamic and thermal behavior of the fluid. These findings contribute to a better understanding of transport phenomena in non-Newtonian fluid flows over stretching surfaces and are relevant to various engineering and industrial processes.

Introduction

This study focuses on the flow and heat transfer characteristics of a Casson non-Newtonian fluid over a stretching surface, a topic of significant importance in engineering applications such as polymer processing, paper manufacturing, molten metal treatment, glass fiber production, and biomedical systems. Numerous previous studies have investigated the effects of magnetic fields, thermal radiation, chemical reactions, slip conditions, nanofluids, and non-Newtonian fluid models on heat and mass transfer over stretching surfaces.

Literature Review

The reviewed research highlights several key findings:

• Radially stretching surfaces strongly influence velocity, temperature, concentration distributions, and boundary-layer development.
• Various non-Newtonian fluid models, including Cross, Sisko, Jeffrey, Powell-Eyring, Maxwell, and Casson fluids, have been extensively studied.
• Effects such as magnetohydrodynamics (MHD), thermal radiation, chemical reactions, viscous dissipation, Joule heating, Soret and Dufour diffusion, slip conditions, and nanofluid behavior significantly impact transport processes.
• Many studies have emphasized unsteady flow conditions, which better represent real industrial processes than steady-state assumptions.
• Despite extensive research on stretching surfaces, comparatively fewer studies have focused specifically on Casson fluid flow over radially stretching sheets, motivating the present investigation.

Model Formulation

The study considers:

• A steady, two-dimensional, incompressible laminar Casson fluid flow over a stretching sheet.

• The sheet stretches linearly with velocity:

  Uw(x)=axU_w(x)=axUw?(x)=ax

  where aaa is the stretching rate.

• The flow is generated solely by the stretching motion of the sheet.
• Fluid viscosity varies with temperature, making the problem more realistic for industrial applications.
• Boundary-layer assumptions are applied, where velocity gradients normal to the sheet dominate those along the sheet.

Governing Mathematical Framework

The model is based on:

1. Continuity equation (mass conservation)
2. Momentum equation incorporating:
   • Casson fluid characteristics
   • Variable viscosity effects
3. Energy equation governing heat transfer

The viscosity is assumed to depend on temperature through a viscosity variation parameter. Appropriate boundary conditions are specified at the stretching sheet and in the free stream.

Similarity Transformation

To simplify the governing partial differential equations, similarity variables are introduced. This transformation converts the flow and heat transfer equations into a set of ordinary differential equations that can be solved numerically to obtain:

• Velocity profiles
• Temperature distributions
• Boundary-layer characteristics
• Effects of viscosity variation and Casson fluid parameters

Conclusion

In conclusion, the Prandtl number Pr plays a crucial role in shaping both the temperature ? and velocity profile f^\' within the flow field. As Pr increases, a consistent reduction is observed in the temperature distribution due to the weakening of thermal diffusion. This results in a thinner thermal boundary layer, limiting the spread of heat across the fluid. The decline in temperature directly influences the flow behavior, since reduced thermal energy leads to weaker buoyancy forces. Consequently, the velocity profile f^\' also exhibits a decreasing tendency with higher values of Pr This indicates that fluids with larger Prandtl numbers tend to resist both heat transfer and fluid motion more strongly. In contrast, lower Pr values promote greater thermal diffusion, resulting in higher temperature levels and enhanced flow velocity. Overall, the interaction between thermal and momentum transport becomes more restricted as Pr rises, significantly affecting the overall dynamics of the system. Therefore, the Prandtl number serves as an important controlling parameter in determining the combined thermal and hydrodynamic behavior of the fluid.The results indicate that increasing ? leads to a rise in dimensionless skin friction, reflecting stronger surface shear effects. This trend highlights the sensitivity of flow behavior to changes in ?, suggesting that the parameter plays a significant role in controlling boundary layer characteristics and overall fluid resistance.The findings show that increasing ? leads to a decline in the Nusselt number, indicating reduced heat transfer performance. This behavior reflects the impact of ? on thermal boundary layer development, demonstrating its important role in governing temperature distribution and overall heat transfer characteristics of the system. Conflicts of interests/Competing interests: The author declares that there are no competing interests.

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Copyright

Copyright © 2026 Bhanoth Rajender. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.