Exact analytical solutions for thermosolutal Marangoni convection in the presence of heat and mass generation or consumption

Abstract

The steady laminar thermosolutal Marangoni convection in the presence of temperature-dependent volumetric heat sources/sinks as well as of a firstorder chemical reaction is considered in this paper. Assuming that the surface tension varies linearly with temperature and concentration and that the interface temperature and concentration are quadratic functions of the interface arc length x, exact analytical similarity solutions are obtained for the velocity, temperature and concentration fields. The features of these exact solutions as functions of the physical parameters of the problem are discussed in detail. Greek symbols a thermal diffusivity, Eq. 3 D discriminant, Eq. 25 c coefficients, Eq. 5 g similarity independent variable, Eq. 8 / dimensionless heat generation/absorption coefficient, Eq. 13 l dynamic viscosity t kinematic viscosity, m = l/q h temperature similarity variable, Eq. 8 q density r surface tension, Eq. 5 w stream function, Eq. 8 Subscripts T thermal quantity c solutal quantity 0 at g = 0 ¥ for g fi ¥ List of symbols

Marangoni boundary layer flow and heat transfer of copper-water nanofluid over a porous medium disk

“…14,15,20 Further, the surface also was assumed to vary linearly with the concentration and the thermosolutal surface tension radio parameter was introduced to describe the mass transfer. [21][22][23][24][25] Zheng et al 20 established the Marangoni convection over a liquid-vapor surface due to an imposed temperature gradient by the Adomian analytical decomposition technique and the Páde approximant technique. Chamkha and coworkers [21][22][23] considered the steady laminar MHD thermosolutal Marangoni convection in the presence of a uniform applied magnetic field in the boundary layer approximation.…”

“…[21][22][23][24][25] Zheng et al 20 established the Marangoni convection over a liquid-vapor surface due to an imposed temperature gradient by the Adomian analytical decomposition technique and the Páde approximant technique. Chamkha and coworkers [21][22][23] considered the steady laminar MHD thermosolutal Marangoni convection in the presence of a uniform applied magnetic field in the boundary layer approximation. And exact analytical solutions for the velocity, temperature and concentration boundary layers were reported.…”

“…Motivated by the above mentioned works, [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] in this paper we have a study on Marangoni boundary layer flow and heat transfer of copper-water nanofluid over a porous medium disk. The temperature of the disk (the surface temperature of Cu-water nanofluid) is a quadratic function of the radius.…”

“…Unlike the Boussinesq effect on the body force term in buoyancy-induced flow, the Marangoni surface tension effect acts as a boundary condition on the governing equations of the flow field. [21][22][23][29][30][31] The governing equations for this study are based on the balance laws of mass, momentum and energy species. Taking the above assumptions into consideration, the boundary layer governing equations can be written in dimensional form as: 35,36 ∂u ∂r…”

Marangoni abnormal convection heat transfer of power-law fluid driven by temperature gradient in porous medium with heat generation

“…It has received much attention in recent years [2]. In the mid 1860s, Marangoni found the phenomenon that the natural convection dominated by liquid gravity gradually disappeared in a microgravity environment, whereas, at the interface of liquid, the surface tension plays a leading role and causes a surface tension gradient [3]. In 1978, Napolitano observed that there may be a dissipative layer in liquid-liquid or liquid-gas system, which is called Marangoni boundary layer [4].…”