Effect Of Non-uniform Temperature Gradient Research Articles

Combined effects of nonuniform temperature gradients and heat source on double diffusive Benard-Marangoni convection in a porous-fluid system in the presence of vertical magnetic field

The physical configuration of the problem is a porous-fluid layer which is horizontally unbounded, in the presence of uniform heat source/sink in the layers enclosed by adiabatic and isothermal boundaries. The problem of double diffusive Bènard-Marangoni convection in the presence of vertical magnetic field is investigated on this porous-fluid system for non-Darcian case and is subjected to uniform and nonuniform temperature gradients. The eigenvalue, thermal Marangoni number is obtained in the closed form for lower rigid and upper free with surface tension velocity boundary conditions. The influence of various parameters on the Marangoni number against thermal ratio is discussed. It is observed that the heat absorption in the fluid layer and the applied magnetic field play an important role in controlling Benard-Marangoni convection. The parameters which direct this convection are determined and the effect of porous parameter is relatively interesting.

Effects of Non-uniform Temperature Gradients on Triple Diffusive Surface Tension Driven Magneto Convection in a Composite Layer

The problem of triple diffusive surface tension driven magneto convection in a composite layer is investigated for linear, parabolic and inverted parabolic temperature profiles. The corresponding thermal Marangoni numbers are obtained analytically depending on various physical parameters of interest. The parameters which are effective to enhance convection and to control convection are determined. From the investigation it is found that the linear profile is suitable for fluid layer dominant composite layer whereas parabolic and inverted parabolic profiles are conducive for the porous layer dominant composite layer.

Effects of Non-Uniform Temperature Gradients on Triple Diffusive Marangoni Convection in a Composite Layer

The problem of triple diffusive Marangoni convection is investigated in a composite layer comprising an incompressible three component fluid saturated, sparsely packed porous layer over which lies a layer of the same fluid. The lower rigid surface of the porous layer and the upper free surface are considered to be insulating to temperature, insulating to both salute concentration perturbations. At the upper free surface, the surface tension effects depending on temperature and salinities are considered. At the interface, the normal and tangential components of velocity, heat and heat flux, mass and mass flux are assumed to be continuous. The resulting eigenvalue problem is solved exactly for linear, parabolic and inverted parabolic temperature profiles and analytical expressions of the thermal Marangoni number are obtained. The effects of variation of different physical parameters on the thermal Marangoni numbers for the profiles are compared.

Effects of non-uniform temperature gradients on surface tension driven two component magneto convection in a porous- fluid system

The problem of surface tension driven two component magnetoconvection is investigated in a Porous-Fluid system, consisting of anincompressible two component electrically conducting fluid saturatedporous layer above which lies a layer of the same fluid in the presence of a uniform vertical magnetic field. The lower boundary of the porous layeris rigid and the upper boundary of the fluid layer is free with surfacetension effects depending on both temperature and concentration, boththese boundaries are insulating to heat and mass. At the interface thevelocity, shear and normal stress, heat and heat flux, mass and mass fluxare assumed to be continuous suitable for Darcy-Brinkman model. Theeigenvalue problem is solved in linear, parabolic and inverted parabolictemperature profiles and the corresponding Thermal Marangoni Numberis obtained for different important physical parameters.

Effect of Non-uniform Temperature Gradient on Marangoni Convection in a Relatively Hotter or Cooler Layer of Liquid

The effect of non-uniform temperature gradient on the onset of convection driven by surface tension gradients in a relatively hotter or cooler layer of liquid is studied by means of linear stability analysis. The upper boundary is considered to be free where surface tension gradients arise on account of variation in temperature and the lower boundary is stress free, each subject to constant heat flux. The single-term Galerkin technique is used to obtain the eigenvalue equation. Eigenvalues are obtained and presented. The results are compared with the existing ones and found that even a single-term Galerkin expansion gives quite accurate results. Further, this analysis predicts that the critical eigenvalues for different non-uniform temperature gradients are greater in a relatively hotter layer of liquid than the cooler one under identical conditions otherwise. This qualitative effect is quite significant quantitatively as well.

Gradient on Rayleigh–Bénard – Marangoni – Magnetoconvection in a Micropolar Fluid with Maxwell – Cattaneo Law

The effect of non-uniform temperature gradient on the onset of Rayleigh-Bénard-Marangoni- Magneto-convection in a Micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigen value is obtained for rigid-free velocity boundary combination with isothermal and adiabatic condition on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset is discussed. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (Second Sound) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed.

Effect of Non-uniform Temperature gradient on Marangoni Convection in a Relatively Hotter or Cooler Layer of Liquid

The effect of non-uniform temperature gradient on the onset of convection driven by surface tension gradients in a relatively hotter or cooler layer of liquid is studied by means of linear stability analysis. The upper boundary is considered to be free where surface tension gradients arise on account of variation in temperature and the lower boundary is stress free, each subject to constant heat flux. The single-term Galerkin technique is used to obtain the eigenvalue equation. Eigenvalues are obtained and presented. The results are compared with the existing ones and found that even a single-term Galerkin expansion gives quite accurate results. Further, this analysis predicts that the critical eigenvalues for different non-uniform temperature gradients are greater in a relatively hotter layer of liquid than the cooler one under identical conditions otherwise. This qualitative effect is quite significant quantitatively as well.

Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh–Bénard–Magnetoconvection in Micropolar Fluid with Maxwell–Cattaneo Law

The effect of non-uniform temperature gradient on the onset of Rayleigh-Bénard magnetoconvection in a Micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal condition on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset of convection is discussed. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (Second Sound) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed.

Exact analysis of Effect of Non-uniform Temperature Gradient on Marangoni Convection with Free Slip Condition

The effect of non-uniform basic temperature gradient on the onset of Marangoni convection in a horizontal layer with a free-slip bottom heated from below and cooled from above is considered. A linear stability analysis is performed to undertake a detail investigation. The eigenvalues are obtained for lower rigid isothermal and upper free adiabatic boundaries. The resulting eigenvalue problem is solved exactly and single-term Galerkin expansion procedure. The influence of various parameters on the onset of convection has been analyzed. Three non-uniform basic temperature profiles are considered and the results obtained from both the methods are compared and are found to be in good agreement. Some general conclusions about their destabilizing effects are presented.

Combined Effect of Non-Uniform Temperature Gradient and Magnetic Field on Bénard-Marangoni Convection with a Constant Heat Flux

This paper studied the problem of Benard-Marangoni convection in a horizontal fluid layer heated from below with non-uniform temperature gradient under magnetic field. A linear stability analysis is performed to undertake a detail investigation. The eigenvalues are obtained for both adiabatic boundaries. The influence of various parameters on the onset of convection has been analyzed. Six non-uniform basic temperature profiles are considered and some general conclusions about their destabilizing effects are presented.

Effect of non-uniform temperature gradient and magnetic field on onset of Marangoni convection heated from below by a constant heat flux

This paper investigates the effect of non-uniform temperature gradient and magnetic field on Marangoni convection in a horizontal fluid layer heated from below and cooled from above with a constant heat flux. A linear stability analysis is performed. The influence of various parameters on the convection onset is analyzed. Six non-uniform basic temperature profiles are considered, and some general conclusions about their destabilizing effects are presented.

Onset of convection in a couple-stress fluid-saturated porous medium: effects of non-uniform temperature gradients

Onset of convection in a layer of couple-stress fluid-saturated porous medium is investigated for different types of basic temperature gradients. The boundaries are considered to be adiabatically insulated to temperature perturbations. The eigenvalue equations of the perturbed state obtained from the normal mode analysis are solved analytically using a regular perturbation technique with wave number as a perturbation parameter and also numerically using the Galerkin technique. The critical stability parameters obtained from these two techniques are in excellent agreement and an increase in the value of couple-stress parameter is found to delay the onset of convection. The results also indicate that the piecewise linear temperature profile hastens the onset of convection when compared to linear, parabolic, and inverted parabolic temperature profiles. In addition, the influence of thermal depth on the critical conditions is assessed in the case of piecewise linear temperature profiles, and it is observed that the critical thermal depth decreases marginally with an increase in the couple-stress parameter.

Effects of nonuniform temperature gradients on the onset of oscillatory Marangoni convection in a magnetic field

This article theoretically studies the onset of oscillatory Marangoni convection in a horizontal layer of an electrically conducting fluid, to which a nonuniform thermal gradient and a uniform magnetic field are applied. The top surface of a fluid layer is deformably free and the bottom is rigid. By means of the linear stability theory and a normal mode analysis, the eigenvalue equations of the perturbed state are solved by using the fourth-order Runge-Kutta-Gill's method with the shooting technique. The computational results are compared with those known from the literature, and the agreement is found out to be generally good. The results indicate that the critical Marangoni number −Ma c increases with increasing the Chandrasekhar number Q, the Prandtl number Pr, or the Biot number Bi of the upper free surface, but decreases with increasing the Crispation number Cr. As compared with the linear temperature profile, the inverted parabolic temperature profile shows higher −Ma c values, while the parabolic temperature profile shows lower −Ma c values. In addition, for the piecewise linear temperature profiles, the influences of thermal depth on the critical Marangoni number are also obtained.

Rayleigh‐Benard convection in a viscoelastic fluid‐filled high‐porosity medium with nonuniform basic temperature gradient

The qualitative effect of nonuniform temperature gradient on the linear stability analysis of the Rayleigh‐Benard convection problem in a Boussinesquian, viscoelastic fluid‐filled, high‐porosity medium is studied numerically using the single‐term Galerkin technique. The eigenvalue is obtained for free‐free, free‐rigid, and rigid‐rigid boundary combinations with isothermal temperature conditions. Thermodynamics and also the present stability analysis dictates the strain retardation time to be less than the stress relaxation time for convection to set in as oscillatory motions in a high‐porosity medium. Furthermore, the analysis predicts the critical eigenvalue for the viscoelastic problem to be less than that of the corresponding Newtonian fluid problem.