Marangoni Convection Flow Along a Wavy Surface with Non-Linear Radiation

Abstract

A boundary-layer analysis is presented for steady, two-dimensional, Marangoni convection along an irregular surface. Thick radiation limit is considered to express the radiative heat flux. A coordinate transformation is adopted to convert the physical domain into computational domain. Implicit finite difference method is then used to obtain the solutions of the problem. The main purpose of this study is to demonstrate the radiation effects on the dissipative layers. Numerical solutions are presented in the form of skin friction coefficient, heat transfer coefficient, velocity and temperature profiles, streamlines and isotherms. It is observed that thermal radiation has a pronounced effect on the flow field and amplitude of the harmonic oscillations also decay with $R_d$. The momentum and thermal boundary-layer thickness increases as $R_d$ gets augmented.

Magnetic and chemical reaction effects on double‐diffusive convection with the effect of heat and salt flux boundary conditions

“…In recent years, the double‐diffusive convection has become increasingly important due to its many applications in several real situations, involving waste disposal, contaminated groundwater, and so on see, for example, Lombardo et al, 1 Franchi and Straughan, 2 and Nie et al 3 It is a subject of growing interest that has attracted many researchers. For example, Jena et al, 4 Liu and Umavathi, 5 Umavathi and Mohite, 6 Agarwal et al, 7 Zhuang et al, 8 Liu et al, 9 Siddiqa et al, 10 Shankar et al, 11 Raghunatha and Shivakumara, 12 Altawallbeh, 13 Mahajan and Tripathi, 14 and counts into the books by Nield et al, 15 Straughan, 16 and Vafai 17 . Moreover, the convection with the chemical reaction and magnetic effects has been much attention by many authors, see, for example, Turkyilmazoglu et al, 18 Turkyilmazoglu, 19,20 Malashetty and Biradar, 21 Ghasemi et al, 22 Teamah et al, 23 Al‐Sulaimi, 24 Yu et al, 25 Israel‐Cookey et al, 26 Gautam and Narayana, 27 Deepika et al, 28 Ebiwareme and Israel‐Cookey, 29 Mishra and Kumar, 30 Mahajan and Tripathi, 31 and Shivakumara et al 32 Recently, Noon and Haddad 33 investigated the impacts of varying gravity and rotation that combined with the reaction effect on the double‐diffusive convection of the Darcy model in a porous material using the linear and nonlinear stability analysis when the layer heated from the bottom and salted from the above or below.…”