An analytical study of linear and non-linear convection in Boussinesq–Stokes suspensions

Abstract

The Rayleigh-Benard situation in Boussinesq-Stokes suspensions is investigated using both linear and non-linear stability analyses. The linear and non-linear analyses are based on a normal mode solution and minimal representation of double Fourier series, respectively. The e ect of suspended particles on convection is delineated against the background of the results of the clean uid. The realm of non-linear convection warrants the quantiÿcation of heat transfer and this has been achieved on the Rayleigh-Nusselt plane. Possibility of aperiodic convection is discussed. ?

An analytical study of linear and non-linear double diffusive convection with Soret effect in couple stress liquids

“…(3.7). These are exactly the values given by Siddheshwar and Pranesh [19] for a single component system. Further when C = 0, i.e., in the absence of couple stresses, we get the classical results α 2 c = 0.5 and R st c = 657.5 for clear viscous fluid (see e.g., Chandrasekhar [25]).…”

“…Rayleigh-Benard convection in fluids with stress non-linearly proportional to velocity gradient is studied by few researchers (see e.g. [19][20][21]). However the study on double diffusive convection in couple stress fluids is not available to the authors' knowledge.…”

Soret-driven double diffusive magneto-convection in couple stress liquid

“…Further when R S = 0 and absence of Soret effect, Eq. (14) reduces to R st = a 6 η π 2 α 2 (15) which is same the result of Siddheshwar and Pranesh [23]. If C = 0 that is when couple stress is absent, we get the classical results of Chandrasekhar [2], that is critical Rayleigh number R st c = 657.5 and wave-number is α 2 c = 0.5.…”

“…In his studied, he suggested simplest theory for the micro fluids, which allows polar effects such as the presence of couple stress, body couples and non-symmetric tensors. Siddeshwar and Pranesh [23], Sharma and Sharma [24] and Malashetty and Basavarja [25] investigated RayleighBenard convection in fluids with stress non-linearly proportional to velocity gradient.…”

The Onset of Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer

“…Sharma and Sharma (2004) studied the onset of convection in a couple stress fluid saturated porous layer in the presence of rotation and a magnetic field. Siddheshwar and Pranesh (2004) have made an analytical study of linear and nonlinear convection in a couple stress fluid layer. Malashetty and Basavaraja (2005) studied the effect of thermal and gravity modulation on the onset of Rayleigh-Benard convection in a couple stress fluid layer.…”