article · Modern Physics Letters B
A theoretical study examines how heat transfer and magnetic forces influence the wave-like pumping movement of non-Newtonian couple stress fluids. The mathematical model analyses fluid travelling through an inclined space between two nested cylinders, where the inner boundary is rigid and the outer boundary ripples with a wave pattern. By applying perturbation techniques under low-speed and long-wavelength assumptions, the analysis determines how physical conditions change fluid behaviour. Higher slipping parameters reduce fluid velocity because of reverse slipping. Imposing a magnetic field increases the pressure gradient required to move the fluid, while porous surroundings enhance the overall pressure difference. In addition, raising the wave amplitude alongside heat input triggers vortex development inside the flow stream. These mathematical insights detail the physics of complex fluids operating in confined, heated, and magnetically influenced passages.
Understanding how non-Newtonian fluids move under magnetic fields and thermal effects is important for interpreting natural biological flows, such as blood circulation. Mathematical models of this nature provide foundational benchmarks for predicting fluid behaviour in specialised industrial or medical environments where external magnetic fields and temperature variations alter normal pumping actions.
The abstract points to future relevance in biomedical and industrial contexts, particularly applications involving magnetic resonance imaging and radiosurgery. However, this is early-stage theoretical and mathematical research based on simplified equations and perturbation techniques. Developers of medical instrumentation or specialised fluid-handling systems may find the mathematical relationships informative, but significant applied experimental work is needed before these principles can directly support commercial devices or protocols.
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In this study, we explore the analysis of peristaltic flow with heat transfer occurring within the gap between coaxial inclined tubes. The inner tube’s wall is rigid, while the outer tube’s wall features a sinusoidal wave propagating through it. The cylindrical system is employed to formulate the problem. The flow is characterized using continuity, momentum, and energy equations. We apply the assumption of long wavelength and the low Reynolds number approximation to simplify the nonlinear governing equation, subsequently solving it through perturbation techniques. We investigate the impact of crucial parameters, such as the magnetic field, porous media, slipping conditions, and others, on the peristaltic flow of a couple stress fluid. Our focus lies on assessing their influence on axial velocity, pressure gradient, and flow streamlines. The outcomes are visually presented through graphical representations. Notably, an increase in the slipping parameter results in a reduction of fluid velocity, attributed to the reverse slipping of the flow. The introduction of a magnetic field leads to an augmentation of the pressure gradient. Moreover, elevating the peristaltic amplitude and heat source induces the formation of a vortex within the flow. The presence of porous media leads to an increase in the pressure difference of the fluid flow. The primary objective of this research is to enhance our understanding of the peristaltic motion of non-Newtonian fluid dynamics, specifically incorporating a couple stress fluid. This contributes to a deeper understanding of crucial fluids, such as blood, within the human circulatory system. The implications extend to biological and industrial applications like magnetic resonance imaging (MRI) and radiosurgery, advancing our scholarly understanding of fluid behavior, especially in non-Newtonian scenarios.
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DOI: 10.1142/s0217984924502336
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