Double diffusive convection is the phenomena that describes the convection driven by two differ-ent densities which have different rates of diffusion. A comparison of two temperature boundaries when i) both the surfaces are set at adiabatic temperature, and ii)upper free surface is adiabatic and lower rigid surface is isothermal cases, on surface tension driven double diffusive convection in a horizontal composite layer is studied analytically using exact method. For both cases i) and ii), the thermal Marangoni number (Tmn) is determined, which is the eigen value, for upper free and lower rigid velocity boundary conditions. The results indicate that the given system is a fluid dominant composite system and adiabatic-isothermal thermal boundary is more stable compare to adiabatic-adiabatic boundary condition.
In a composite layer that comprises of a porous layer which is sparsely packed and saturated with two component incompressible fluid and above this porous layer lays a layer of the same fluid, with variable heat sources or sinks in both the layers double diffusive non-Darcian Benard Marangoni (DDNBM) convection is investigated. The upper surface of the composite layer has Marangoni effects which depend on temperature and concentration, whereas the lower surface is rigid. The inverted parabolic, parabolic and linear temperature profile is applied to this composite layer, which is surrounded by adiabatic boundaries. The appropriate thermal Marangoni numbers (TMANs) which are the eigen values (EVs) are calculated for all the three temperature gradients. The impact of different parameters on the EVs with respect to depth ratio is examined, thoroughly. The parameters that effect DDNBM convection are found.
An investigation is carried out to determine the effect of uniform and non-uniform temperature profiles on single component Darcy-Benard Marangoni (DBM) convection in a composite layer system consisting of an incompressible fluid saturated porous layer on top of which is a layer of the same fluid with variable heat sources in both layers. The upper surface of the fluid layer is free with surface tension effects depending on temperature and the lower surface of the porous layer is rigid. The eigen value, thermal Marangoni number (TMN) is solved exactly for linear, parabolic and inverted parabolic temperature profiles for the adiabatic thermal boundary conditions at the horizontal boundaries of the composite layer. The influence of various dimensionless parameters on the eigen value against depth ratio is discussed in detail.
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