Influence of variable thermal conductivity and dissipation on magnetic Carreau fluid flow along a micro-cantilever sensor in a squeezing regime

Beg, OA; Muhammed, RKV; Basha, H; Reddy, GJ; Shankar, U

Abstract

Mathematical modelling of squeezing flows finds numerous applications in biological, mechanical and medical engineering. Sensors feature such flows and can be effectively utilized to control vibrations and regulate lubrication. Magnetic fluids are critical to modern sensor systems. Micro-cantilevers are utilized in biomedical
applications as biological, physical or chemical sensors and operate via detection of variations in the vibrational frequency or cantilever bending. In the present article, motivated by the deployment of intelligent electromagnetic rheological liquids in biomedical sensor systems, a theoretical study is conducted to explore the dissipative flow and thermal characteristics in non-Newtonian boundary layer flow along a micro-cantilever sensor surface suspended in a squeezing regime between parallel plates. To accurately simulate the non-Newtonian characteristics of magneto-rheological lubricants, the Carreau viscoelastic fluid model is deployed. Heat transfer is also considered to quantify thermal behaviour of sensor surfaces under squeezing conditions in the presence of Lorentz magnetohydrodynamic (MHD) body forces. Furthermore, to achieve a more refined simulation, the effects of variable thermal conductivity and Joule magnetic dissipation are incorporated. The governing conservation equations for unsteady magnetic Carreau squeezing flow and heat transfer are rendered dimensionless and self-similar via appropriate scaling transformations. The emerging nonlinear coupled boundary
value problem is then solved with an efficient numerical method (Runge-Kutta 4th order shooting technique in MATLAB software). Validation of solutions with earlier simpler models over a range of Prandtl numbers and squeezing parameter values is included. Comprehensive analysis and extensive graphical visualization is included in order to quantify the thermal and hydrodynamic behaviour for the influence of key emerging parameters. It is identified that magnifying Weissenberg (viscoelastic) parameter decays the flow field. Enhancing squeezing flow parameter (plate gap parameter) decelerates the flow and decreases temperatures. Temperatures are boosted with increment in the thermal conductivity parameter and Eckert number. Skin friction is elevated with increasing Carreau power-law index and Weissenberg number. Local Nusselt number is also enhanced with larger values of thermal conductivity parameter and Eckert number (i. e. stronger viscous and Joule heating effects). The novelty of the present study is the inclusion of dissipation and thermal conductivity variation effects which extends previous investigations and provides a more accurate appraisal of thermal characteristics in sensor squeezing flows.

Citation

Beg, O., Muhammed, R., Basha, H., Reddy, G., & Shankar, U. (2022). Influence of variable thermal conductivity and dissipation on magnetic Carreau fluid flow along a micro-cantilever sensor in a squeezing regime. Waves in Random and Complex Media, https://doi.org/10.1080/17455030.2022.2139013

• Journal Article Type: Article
• Acceptance Date: Oct 17, 2022
• Online Publication Date: Nov 8, 2022
• Publication Date: Nov 8, 2022
• Deposit Date: Nov 16, 2022
• Publicly Available Date: Nov 9, 2023
• Journal: Waves in Random and Complex Media
• Print ISSN: 1745-5030
• Electronic ISSN: 1745-5049
• Publisher: Taylor and Francis
• DOI: https://doi.org/10.1080/17455030.2022.2139013
• Publisher URL: https://doi.org/10.1080/17455030.2022.2139013
• Additional Information: Additional Information : This is an Accepted Manuscript of an article published by Taylor & Francis in Waves in Random and Complex Media on 8th November 2022, available at: http://www.tandfonline.com/10.1080/17455030.2022.2139013; Projects : Sensor magneto-rheological fluid dynamics Simulation