##
**Magnetohydrodynamic and slip effects on the flow and mass transfer over a microcantilever-based sensor.**
*(English)*
Zbl 1308.76314

Summary: Hydromagnetic flow and mass transfer of a viscous incompressible fluid over a microcantilever sensor surface are studied in the presence of slip flow. In addition, chemical reaction at the sensor surface is taken into account. The governing equations for the flow are reduced to a local nonsimilarity form. Resulting equations are solved numerically for various values of flow parameters. Effects of physical quantities on the velocity and concentration profiles are discussed in detail.

### MSC:

76W05 | Magnetohydrodynamics and electrohydrodynamics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

### Software:

bvp4c
PDF
BibTeX
XML
Cite

\textit{M. B. Akgül} and \textit{M. Pakdemirli}, J. Appl. Math. 2012, Article ID 289459, 11 p. (2012; Zbl 1308.76314)

Full Text:
DOI

### References:

[1] | E. A. Wachter and T. Thundat, “Micromechanical sensors for chemical and physical measurements,” Review of Scientific Instruments, vol. 66, pp. 3662-3667, 1995. |

[2] | R. Raiteri, M. Grattarola, H.-J. Butt, and P. Skladal, “Micromechanical cantilever-based biosensors,” Sensors and Actuators, vol. 79, pp. 115-126, 2001. |

[3] | J. K. Gimzewski, C. Gerber, E. Meyer, and R. R. Schlittler, “Observation of a chemical reaction using a micromechanical sensor,” Chemical Physics Letters, vol. 217, no. 5-6, pp. 589-594, 1994. |

[4] | J. Lai, T. Perazzo, Z. Shi, and A. Majumdar, “Infrared photodetection in the picowatt range using micromechanical sensors,” in Proceedings of ASME Conference on Micro-electro-mechanical Systems (MEMS ’96), pp. 55-60, 1996. |

[5] | P. I. Oden, P. G. Datskos, T. Thundat, and R. J. Warmack, “Uncooled thermal imaging using a piezoresistive microcantilever,” Applied Physics Letters, vol. 69, pp. 3277-3279, 1996. |

[6] | P. G. Datskos, P. I. Oden, T. Thundat, E. A. Wachter, R. J. Warmack, and S. R. Hunter, “Remote infrared radiation detection using piezoresistive microcantilevers,” Applied Physics Letters, vol. 69, no. 20, pp. 2986-2988, 1996. |

[7] | E. A. Wachter, T. Thundat, P. I. Oden, R. J. Warmack, P. G. Datskos, and S. L. Sharp, “Remote optical detection using microcantilevers,” Review of Scientific Instruments, vol. 67, no. 10, pp. 3434-3439, 1996. |

[8] | R. Berger, C. Gerber, J. K. Gimzewski, E. Meyer, and H.-J. Güntherodt, “Thermal analysis using a micromechanical calorimeter,” Applied Physics Letters, vol. 69, pp. 40-42, 1996. |

[9] | T. Thundat, R. J. Warmack, G. Y. Chen, and D. P. Allison, “Thermal and ambient-induced deflections of scanning force microscope cantilevers,” Applied Physics Letters, vol. 64, no. 21, pp. 2894-2896, 1994. |

[10] | T. Thundat, G. Y. Chen, R. J. Warmack, D. P. Allison, and E. A. Wachter, “Vapor detection using resonating microcantilevers,” Analytical Chemistry, vol. 67, no. 3, pp. 519-521, 1995. |

[11] | M. E. Wright, D. K. Han, and R. Aebersold, “Mass spectrometry-based expression profiling of clinical prostate cancer,” Molecular and Cellular Proteomics, vol. 4, no. 4, pp. 545-554, 2005. |

[12] | L. A. Liotta, V. Espina, A. I. Mehta et al., “Protein microarrays: meeting analytical challenges for clinical applications,” Cancer Cell, vol. 3, no. 4, pp. 317-325, 2003. |

[13] | H. F. Ji, X. Yon, J. Zhang, and T. Thundat, “Molecular recognition of biowarfare agents using micromechanical sensors,” Expert Review of Molecular Diagnostics, vol. 4, no. 6, pp. 859-866, 2004. |

[14] | W. Shu, E. D. Laue, and A. A. Seshia, “Investigation of biotin-streptavidin binding interactions using microcantilever sensors,” Biosensors and Bioelectronics, vol. 22, no. 9-10, pp. 2003-2009, 2007. |

[15] | L. A. Pinnaduwage, T. Thundat, J. E. Hawk et al., “Detection of 2,4-dinitrotoluene using microcantilever sensors,” Sensors and Actuators, B, vol. 99, no. 2-3, pp. 223-229, 2004. |

[16] | H. P. Lang, M. K. Baller, R. Berger et al., “An artificial nose based on a micromechanical cantilever array,” Analytica Chimica Acta, vol. 393, pp. 59-65, 1999. |

[17] | A. R. A. Khaled and K. Vafai, “Hydromagnetic squeezed flow and heat transfer over a sensor surface,” International Journal of Engineering Science, vol. 42, no. 5-6, pp. 509-519, 2004. · Zbl 1211.76148 |

[18] | M. Mahmood, S. Asghar, and M. A. Hossain, “Squeezed flow and heat transfer over a porous surface for viscous fluid,” Heat and Mass Transfer, vol. 44, no. 2, pp. 165-173, 2007. |

[19] | A. R. A. Khaled, K. Vafai, M. Yang, X. Zhang, and C. S. Ozkan, “Analysis, control and augmentation of microcantilever deflections in bio-sensing systems,” Sensors and Actuators, B, vol. 94, no. 1, pp. 103-115, 2003. |

[20] | K. Khanafer and K. Vafai, “Geometrical and flow configurations for enhanced microcantilever detection within a fluidic cell,” International Journal of Heat and Mass Transfer, vol. 48, no. 14, pp. 2886-2895, 2005. · Zbl 1189.76121 |

[21] | N. Islam, M. Lian, and J. Wu, “Enhancing microcantilever capability with integrated AC electroosmotic trapping,” Microfluidics and Nanofluidics, vol. 3, no. 3, pp. 369-375, 2007. |

[22] | K. Khanafer, A. Alamiri, and I. Pop, “Fluid-structure interaction analysis of flow and heat transfer characteristics around a flexible microcantilever in a fluidic cell,” International Journal of Heat and Mass Transfer, vol. 53, no. 9-10, pp. 1646-1653, 2010. · Zbl 1191.80018 |

[23] | S. Kiwan and M. A. Al-Nimr, “Investigation into the similarity solution for boundary layer flows in microsystems,” Journal of Heat Transfer, vol. 132, no. 4, Article ID 041011, 9 pages, 2010. |

[24] | F. M. White, Viscous Fluid Flow, McGraw-Hill, New York, NY, USA, 1991. |

[25] | T. David, S. Thomas, and P. G. Walker, “Platelet deposition in stagnation point flow: an analytical and computational simulation,” Medical Engineering and Physics, vol. 23, pp. 299-312, 2001. |

[26] | E. M. Sparrow, H. Quack, and C. J. Boerner, “Local non-similarity boundary layer solutions,” AIAA Journal, vol. 8, no. 11, pp. 1936-1942, 1970. · Zbl 0219.76032 |

[27] | E. M. Sparrow and H. S. Yu, “Local non-similarity thermal boundary-layer solutions,” Journal of Heat Transfer. ASME, pp. 328-334, 1971. |

[28] | L. F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with MATLAB, chapter 3, Cambridge University Press, Cambridge, UK, 2003. · Zbl 1079.65144 |

[29] | J. Kierzenka and L. F. Shampine, “A BVP solver based on residual control and the MATLAB PSE,” ACM Transactions on Mathematical Software, vol. 27, no. 3, pp. 299-316, 2001. · Zbl 1070.65555 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.