A Stability Analysis for Radiation Effects on Marangoni Convection Boundary Layer Over a Permeable Surface
Keywords:permeable surface, dual solution, stability analysis
The objectives are to derive the stability analysis theoretically and to set up the stability analysis numerically for radiation effects on Marangoni convection boundary layer over a permeable surface. The stability analysis is used to determine which branch solutions are stable and physically realisable. The stability can be tested via the smallest eigenvalue. Negative smallest eigenvalue produces an initial growth of disturbance and the flow becomes unstable. In contrast, the positive smallest eigenvalue results in an initial decay of the disturbance, thus the flow is stable. The research has an implication in order to identify which solution is stable, whether the first or the second solution.
Al-Mudhaf A, Chamkha AJ. (2005). Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects. Heat and Mass Transfer, 42, 112-121.
Arifin NM, Nazar R, Pop I. (2011). Non-isobaric Marangoni boundary layer flow for Cu, Al2O3 and TiO2 nanoparticles in a water based fluid. Meccanica, 46(4), 833-843.
Awaludin IS, Weidman PD, Ishak A. (2016). Stability analysis of stagnation-point flow over a stretching/shrinking sheet. AIP Advances, 6, 045308.
Bakar SA. (2018). Stability analysis on boundary layer flow and heat transfer over a permeable surface in presence of thermal radiation. PhD Thesis, Universiti Putra Malaysia.
Bataller RC. (2008). Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition. Applied Mathematics and Computation, 206, 832-840.
Golia C, Viviani A. (1986). Non isobaric boundary layers related to Marangoni flows. Meccanica, 21, 200-204.
Hamid RA, Arifin NM, Nazar R, Ali FM, Pop I. (2011a). Dual solutions on thermosolutal Marangoni forced convection boundary layer with suction and injection. Mathematical Problems in Engineering, 1-19.
Hamid RA, Arifin NM, Nazar R, Ali FM. (2011b). Radiation effects on Marangoni convection over a flat surface with suction and injection. Malaysian Journal of Mathematical Sciences, 5(1), 13-25.
Ishak A. (2010). Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect. Meccanica, 45, 367-373.
Magyari E, Chamkha AJ. (2008). Exact analytical results for the thermosolutal MHD Marangoni boundary layers. International Journal of Thermal Sciences, 47(7), 848-857.
Mat NA, Arifin NM, Nazar R, Ismail F, Pop I. (2013). Radiation effects on Marangoni convection boundary layer over a permeable surface. Meccanica, 48(1), 83-89
Merkin JH, Pop I, Lok YY, Grosan T. (2022). Similarity solutions for the boundary layer flow and heat transfer of viscous fluids, nanofluids, porous media, and micropolar fluids. United Kingdom: Elsevier Inc.
Pop I, Postelnicu A, Gros T. (2001). Thermosolutal Marangoni forced convection boundary layers. Meccanica, 36, 555-571.
Tadmor R. (2009). Marangoni flow revisited. Journal of Colloid and Interface Science, 332, 451-454.
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Copyright (c) 2023 Nor Azian Aini Mat, Annie Gorgey, Muzirah Musa, Nurul Akmal Mohamed
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