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<p>This study investigates the heat-transfer and flow characteristics of a Williamson fluid in a converging–diverging channel. The analysis focuses on steady, incompressible, two-dimensional radial flow bounded by two symmetrically inclined vertical walls that may stretch or shrink. The momentum and energy equations, incorporating viscous dissipation, are expressed in polar coordinates and recast into a dimensionless framework to clarify the influence of governing parameters such as the Weissenberg number, viscosity ratio, Eckert number, and channel inclination. Because an exact analytical treatment is impractical, the resulting boundary value problem is solved numerically using Matlab's bvp4c routine, which provides reliable solutions through adaptive mesh refinement. The results show that higher Weissenberg numbers and viscosity ratios cause moderate velocity enhancement under stretching wall conditions, yielding changes of approximately 13% in convergent channels and up to about 115% in divergent configurations, while temperature variations remain below about 3% for most cases and increases noticeably (approximately 20% to 27%) for higher Prandtl and Eckert numbers. Overall, the study enhances understanding of non-Newtonian transport in non-parallel channels and offers useful insights for applications including polymer extrusion, blood flow near arterial bifurcations, microfluidic heat-exchange devices, and lubrication or wedge-bearing systems.</p>

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Heat transfer and flow dynamics of Williamson fluid in a converging/diverging channel under surface stretching and shrinking effects

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月7日

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  • Sharad Sinha,
  • Saumy Mittal

摘要

This study investigates the heat-transfer and flow characteristics of a Williamson fluid in a converging–diverging channel. The analysis focuses on steady, incompressible, two-dimensional radial flow bounded by two symmetrically inclined vertical walls that may stretch or shrink. The momentum and energy equations, incorporating viscous dissipation, are expressed in polar coordinates and recast into a dimensionless framework to clarify the influence of governing parameters such as the Weissenberg number, viscosity ratio, Eckert number, and channel inclination. Because an exact analytical treatment is impractical, the resulting boundary value problem is solved numerically using Matlab's bvp4c routine, which provides reliable solutions through adaptive mesh refinement. The results show that higher Weissenberg numbers and viscosity ratios cause moderate velocity enhancement under stretching wall conditions, yielding changes of approximately 13% in convergent channels and up to about 115% in divergent configurations, while temperature variations remain below about 3% for most cases and increases noticeably (approximately 20% to 27%) for higher Prandtl and Eckert numbers. Overall, the study enhances understanding of non-Newtonian transport in non-parallel channels and offers useful insights for applications including polymer extrusion, blood flow near arterial bifurcations, microfluidic heat-exchange devices, and lubrication or wedge-bearing systems.