Concentration Buoyancy Forces Research Articles

Effect of a Sinusoidal Temperature Profile on Entropy Generation Due to Double-Diffusive Natural Convection in a Square Partly Porous Cavity

Abstract In this paper, entropy generation due to double-diffusive natural convection inside a partly porous enclosure under sinusoidal wall heating is numerically analyzed. The resulting dimensionless coupled partial differential equations are discretized using the finite volume method (FVM), while the pressure–velocity coupling is handled using the SIMPLE algorithm. To ensure the validity of the results obtained from the in-house FORTRAN code, a comparison is made with previous numerical and experimental works. The results of the study indicate that the dimensionless thickness of the porous layer (Δ), the thermal conductivity ratio (Rk), the angle of inclination of the cavity (α), and the buoyancy ratio (N) are critical factors in determining local distribution and global maximum value of entropy generation due to heat transfer and fluid friction. In contrast, their effect on entropy generation induced by concentration is insignificant, except for the buoyancy ratio parameter, where an enhancement of the global maximum of entropy generation is observed by increasing N. Moreover, it is found that Sψ (max) experiences a sharp decline as Δ varies from 0.2 to 0.8, resulting in a reduction of about 67% for the case with N=10 and 83% for the case with N=1. These results highlight the importance of carefully controlling system parameters to minimize energy losses and maximize system efficiency in heat transfer and fluid flow systems.

Hall and Ion Slip Impacts on Unsteady MHD Convective Flow of Ag-TiO2/WEG Hybrid Nanofluid in a Rotating Frame

Background: The radiative magnetohydrodynamic (MHD) flow of an incompressible viscous electrically conducting hybrid nanofluid over an exponentially accelerated vertical surface under the influence of slip velocity in a rotating frame taking Hall and ion slip impacts is discussed. Methods: Water and ethylene glycol mixture have been considered as a base fluid. A steady homogeneous magnetic field is applied under the assumption of a low magnetic Reynolds number. The ramped temperature and time-varying concentration at the surface are taken into consideration. The first-order consistent chemical reaction and heat absorption are also regarded. Silver (Ag) and titania (TiO2) nanoparticles are disseminated in base fluid water and ethylene glycol mixture to be formed a hybrid nanofluid. The Laplace transformation technique is employed on the non-dimensional governing equations for the closed form solutions. Results: The phrases for non-dimensional shear stresses, rates of heat, and mass transfer are also evaluated. The graphical representations are presented to scrutinize the effects of physical parameters on the significantflow characteristics. The computational values of the shear stresses, rates of heat and mass transports near the surface are tabulated by a range of implanted parameters. Conclusion: The resultant velocity grows by an increase in thermal and concentration buoyancy forces, Hall and ion-slip parameters, whereas rotation and slip parameters have overturn outcome on them. The temperature of hybrid Ag-TiO2/WEG nanofluid is relatively superior to that of Ag-WEG nanofluid. Species concentration of hybrid Ag-TiO2/WEG nanofluid decreases due to an increase in Schmidt number and chemical reaction parameter.

Hall Current and Soret Effects on Unsteady MHD Rotating Flow of Second-Grade Fluid through Porous Media under the Influences of Thermal Radiation and Chemical Reactions

The unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible, and electrically conducting fluid passing through a vertical plate embedded in a porous medium in the presence of chemical reactions and thermal radiation is investigated. The effects of the Hall current, rotation and Soret are studied. Using the perturbation approach, one can obtain an accurate analytical solution to the governing equations for the fluid velocity, fluid temperature, and species concentration, provided that the initial and boundary conditions are acceptable. It is possible to obtain expressions for the shear stress, rate of heat transfer, and rate of mass transfer for both plates with the ramping temperature and isothermal conditions. On the one hand, the numerical values of the primary and secondary fluid velocities, fluid temperature, and species concentration are presented graphically. On the other hand, the numerical values of the shear stress and rate of mass transfer for the plate are presented in tabular form for various values of the relevant flow parameters. These values are given for a range of pertinent flow parameters. It was determined that an increase in the Hall and Soret parameters over the whole fluid area leads to a corresponding increase in the resulting velocity. The resultant velocity continually climbs to a high level due to the contributions of the thermal and solute buoyancy forces. Lowering the heat source parameter reduces the temperature distribution, resulting in a lower overall temperature. When there is a rise in the chemical reaction parameter over the whole fluid area, there is a corresponding decrease in the concentration. The concentration buoyancy force, Hall current, and Prandtl number reduce the skin friction. On the other hand, the permeability of the porous medium, rotation, chemical reaction, the Soret number, thermal buoyancy force, and mass diffusion all have the opposite effects on the skin friction.

Hall, Soret, and rotational effects on unsteady MHD rotating flow of a second-grade fluid through a porous medium in the presence of chemical reaction and aligned magnetic field

The effects of Hall current, rotation and Soret effects on an unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible and electrically conducting fluid past an inclined plate embedded in a porous medium in the presence of chemical reaction and an aligned magnetic field are investigated. An exact analytical solution of the governing equations for fluid velocity, fluid temperature, and species concentration subject to appropriate initial and boundary conditions is obtained using the perturbation technique. Expressions for shear stress, rate of heat transfer and rate of mass transfer at the plate are derived for both ramped temperature and isothermal plates. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically, whereas those of shear stress and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. It is concluded that, the resultant velocity is increased with an increasing in Hall and Soret parameters throughout fluid region. The thermal and solutal buoyancy forces contribute to the resultant velocity ever-increasing to high. The temperature distribution is trim downs through an increasing in heat source parameter. The concentration is reduced with an increase in the chemical reaction parameter in the entire fluid region. Concentration buoyancy force, hall current, and Prandtl number have tendency to reduce in skin friction whereas permeability of the porous medium, Rotation, chemical reaction, Soret number, thermal buoyancy force and mass diffusion have reverse effect on it.

A computational study on the MHD Casson fluid flow with thermal radiation and variable physical properties under the influence of Soret and Dufour effects

AbstractThis research study discusses the flow of a magnetohydrodynamic Casson fluid under the influence of Soret, Dufour, and thermal radiation. Nonlinear partial differential equation (PDE) of governing equations is transformed into a dimensionless version of the modified PDEs presented in terms of dimensionless parameters. The solution of coupled PDEs is obtained by the finite difference method with a combination of the quasilinearization technique. The effects of various dimensionless parameters are shown graphically, such as buoyancy force (), concentration buoyancy force , Casson parameter (), magnetic parameter (), thermal radiation (), Darcy parameter (), Forchheimer (fr), Dufour (), Soret (Sor), Brownian motion (), thermopohersis (), and Lewis number (). Prevention of heat transfer in the industrial system is critical, the velocity behavior (), thermal variation (), and concentration profile () are more prominent in the roles of coal, gas, and solar thermal collectors.

Radiative MHD flow of Casson hybrid nanofluid over an infinite exponentially accelerated vertical porous surface

The radiative unsteady magnetohydrodynamic (MHD) flow of an incompressible viscous electrically conducting non-Newtonian Casson hybrid nanofluid over an infinite exponentially accelerated vertical moving porous surface under the influence of slip velocity in a rotating frame has been explored in this paper. Water and ethylene glycol mixture have been considered as a base Casson fluid. A steady homogeneous magnetic field is applied under the assumption of low magnetic Reynolds number. The ramped temperature and time varying concentration at the surface is made into consideration. First order consistent chemical reaction and thermal absorption are also considered. Silver and Titania nanoparticles are disseminated in base fluid water and ethylene glycol mixture to be formed as hybrid nanofluid. Laplace transformation technique is employed on the non-dimensional governing equations for the closed form solutions. Based on those outcomes, the expressions for non-dimensional shear stress, rates of heat and mass transfer are also evaluated. The graphical representations are presented to scrutinize the effects of physical parameters on the significant flow characteristics. The computational values of the shear stresses, rate of heat transfer and rate of mass transfer at the surface are tabulated by the different implanted parameters. The resultant velocity is increasing with an increasing in thermal and concentration buoyancy forces, whereas rotation and slip parameters have overturn result on it for both cases of uniform wall temperature and ramped wall temperature. Species concentration of Casson hybrid Ag-TiO2/WEG nanofluid is decreased with an increase in Schmidt number and chemical reaction parameter. The Nusselt number is increased with an increase in heat absorption at the surface.

Hall and induced magnetic field effects on MHD buoyancy-driven flow of Walters’B fluid over a magnetised convectively heated inclined surface

In this paper we discussed the impacts of Hall current and induced magnetic field on the steady flow of Walters’B fluid, driven by the thermal and concentration buoyancy forces, over a magnetised convectively heated inclined surface in a uniform porous regime. Suitable non-dimensional transformations are used to convert the problem to a similar non-dimensional problem. The resulting flow governing equations are solved by implementing the regular perturbation method. The flow behaviours for various system parameters are discussed with the help of graphs and tables that are computed and generated using MATHEMATICA software. It is examined that the rising values of angle of inclination reduce the buoyancy force that causes the reduction of the flow. Furthermore, it is noted that the current density at the magnetised inclined surface reduces as the angle of inclination rises.

MHD mixed convection on an inclined stretching plate in Darcy porous medium with Soret effect and variable surface conditions

AbstractThis work is concerned with a steady 2D laminar MHD mixed convective flow of an electrically conducting Newtonian fluid with low electrical conductivity along with heat and mass transfer on an isothermal stretching semi-infinite inclined plate embedded in a Darcy porous medium. Along with a strong uniform transverse external magnetic field, the Soret effect is considered. The temperature and concentration at the wall are varying with distance from the edge along the plate, but it is uniform at far away from the plate. The governing equations with necessary flow conditions are formulated under boundary layer approximations. Then a continuous group of symmetry transformations are employed to the governing equations and boundary conditions which determine a set of self-similar equations with necessary scaling laws. These equations are solved numerically and similar velocity, concentration, and temperature for various values of involved parameters are obtained and presented through graphs. The momentum boundary layer thickness becomes larger with increasing thermal and concentration buoyancy forces. The flow boundary layer thickness decreases with the angle of inclination of the stretching plate. The concentration increases considerably for larger values of the Soret number and it decreases with Lewis number. The skin friction coefficient increases for increasing angle of inclination of the plate, magnetic and porosity parameters, however it decreases for rise of thermal and solutal buoyancy parameters. In this double diffusive boundary layer flow, Nusselt and Sherweed numbers increase for rise of thermal and solutal buoyancy parameters, Prandtl number, but they behave opposite nature in case of angle of inclination of the plate, magnetic and porosity parameters. The Sherwood number increases for increasing Lewis number but it decreases for increasing Soret number.

Hall and ion slip effects on magnetohydrodynamic convective rotating flow of Jeffreys fluid over an impulsively moving vertical plate embedded in a saturated porous medium with Ramped wall temperature

AbstractIn the present study, it is explored theoretically Hall and ion slip effects on the unsteady magnetohydrodynamic (MHD) rotating flow of a viscous, incompressible electrically conducting, and optically thick radiating Jeffreys fluid over an impulsively, moving vertical plate embedded in a saturated porous medium, when the temperature of the plate has a provisionally ramped profile. The exact solutions of the governing equations for the flow domain are attained by making use of the Laplace transform method. The specified analytical solutions are also acquired for some limiting cases. The research phrases of engineering curiosity for skin friction and Nusselt number are originated for both ramped wall temperature and the isothermal plate. Sherwood number is also obtained. The numerical results of velocity, temperature, and concentration distributions are exhibited graphically whereas skin friction, Nusselt number, and also Sherwood number are mentioned in a table form. It is observed that on either cases of ramped wall temperature and isothermal plate, the resultant velocity enhances with an increase in Hall and ion slip parameters. Reversal behavior is observed with an increase in magnetic field parameter, Jeffreys fluid parameter and Prandtl number. Thermal and concentration buoyancy forces and thermal radiation tend to accelerate the resultant velocity throughout the boundary layer region. The temperature reduces with an increase in Prandtl number and reverse effect is observed with an increase in thermal radiation parameter. Mass diffusion tends to enhance to species concentration. The rotation and Jeffreys fluid parameters tend to enhance both stress components. Nusselt number enables to lessen with growing in thermal radiation parameter and is magnified on escalating in time. The Sherwood number is improved with increasing in Schmidt number at the plate and it is refused on increasing in time.

Hall and ion‐slip effects on MHD free convection flow of rotating Jeffrey fluid over an infinite vertical porous surface

AbstractAn attempt has been made to explore Hall and ion‐slip effects on an unsteady magnetohydrodynamic rotating flow of an electrically conducting, viscous, incompressible, and optically thick radiating Jeffrey fluid past an impulsively vertical moving porous plate. Analytical solutions of the governing equations are obtained by Laplace transform technique. The analytical expressions for skin friction, Nusselt number, and Sherwood number are also evaluated. The velocity, temperature, and concentration distributions are displayed graphically in detail. From engineering point of view, the changes in skin friction, Nusselt number, and Sherwood number are observed with the computational results presented in a tabular manner. It is observed that the effects of rotation and Hall current tend to accelerate secondary velocity and decelerate primary velocity throughout the boundary layer region. Thermal and concentration buoyancy forces tend to accelerate both velocity components. Thermal radiation and thermal diffusion tend to enhance fluid temperature throughout the boundary layer region. Rotation and Jeffrey fluid parameters tend to enhance both stress components.

Effect of double-diffusive convection with cross gradients on heat and mass transfer in a cubical enclosure with adiabatic cylindrical obstacles

We investigate natural convection driven by a horizontal temperature gradient and a vertical concentration gradient in fluid-filled enclosures with obstructions inside it. Within the domain, nine adiabatic and impermeable cylinders are placed, occupying 30% of the domain volume. The Boussinesq approximation is used to account for density variations within the fluid and the flow is fully resolved. The solutal Rayleigh number has been fixed at RaC=106 and the Prandtl number at Pr=5.4. The Lewis number has been varied in the range of 1 ≤ Le ≤ 100 and the buoyancy ratio in the range of 0.1 ≤ |N| ≤ 10. The rate of heat and mass transfer are compared to those found in single-scalar natural convection, i.e solely thermal or concentration driven convection. Besides, the obtained heat and mass transfer rate in the cylinder-packed enclosure have been compared to those found in a fluid-only domain. We observe that the addition of a destabilizing concentration gradient to a side-heated enclosure results in heat transfer enhancement, which decreases with Lewis number and thermal Rayleigh number. Similarly, the temperature gradient increases the mass transfer, especially at high Lewis numbers and lower concentration buoyancy force over its thermal counterpart. Although the presence of the cylindrical obstacles reduced the flow velocity, the mass transfer was enhanced at lower buoyancy ratio.

Impacts of time varying wall temperature and concentration on MHD free convective flow of a rotating fluid due to moving free-stream with hall and ion-slip currents

Present paper mathematically discusses unsteady MHD free convection flow of thermally conducting, chemically reacting, and rotating fluid over a vertical plate due to moving free-stream. The applied magnetic field is considered to be strong enough to generate Hall and ion-slip currents. The wall temperature and concentration are considered to be linearly varying with time. Laplace transform technique is successfully implemented to solve the resulting partial differential equations representing the fluid motion. The expression for fluid velocity is derived in four special cases., i.e. (i) for those fluids whose viscosity, thermal diffusivity and molecular diffusivity are not of same order of magnitude, (ii) for those fluids whose viscosity and thermal diffusivity are of same order of magnitude while molecular diffusivity is of different order, (iii) for those fluids whose viscosity and molecular diffusivity are of same order of magnitude while thermal diffusivity is of different order, and (iv) for those fluids whose viscosity, thermal diffusivity and molecular diffusivity are of same order of magnitude. To discuss the specific features of the flow, numerical computation is carried out. The variations in fluid velocity, fluid temperature and concentration are presented through graphs whereas skin friction coefficient, rate of heat and mass transfer are presented in tables. A notable observation recorded that in the absence of thermal buoyancy force there appears reverse flow in the secondary flow direction while in the absence of concentration buoyancy force there does not exists reverse flow in the secondary flow direction.

On the evaluation of heat and mass transfer effects on the migration behavior of neutrally buoyant particles in a Couette flow

The effects of thermal and concentration buoyancy forces on the migration of a cold particle and multi-cold particles in a Couette flow were investigated in this paper using the combination of the Thermal-Concentration Smoothed Profile-Lattice Boltzmann Method (TCSPM-LBM). The two-dimensional Lattice Boltzmann Method was also applied for the computations related to fluid velocity, temperature, and concentration. In addition, Smoothed Profile, Thermal Smoothed Profile, and Concentration Smoothed Profile Methods were applied to calculate the hydrodynamic force, temperature exchange, and concentration exchange between the fluid and the particle, respectively. The effect of the coupling between the thermal and concentration convection on the migration path of the neutrally buoyant particle was shown by five mechanisms; these included a repulsion force due to the effect of lubrication, a Saffman lift due to the shear slip, a Magnus lift due to the particle rotation, a thermal convection, and the concentration convection. Initially, the proposed combined method was validated by comparing the obtained numerical results with the ones found in the literature, showing a good agreement. Then the effects of the forced convection, natural convection, the dimensionless numbers, the particle Reynolds number (Rep), the thermal Grashof number (GrT), the concentration Grashof number (Grc), and the Richardson number (Ri) on the equilibrium position of the neutrally buoyant particle were evaluated. Overall, the results indicated that with the increase of the Richardson number, the forced flow became weaker, leading to the increasing effect of the natural convection.

Numerical Analysis of Double-Diffusive Natural Convection in Shallow and Deep Open-Ended Cavities Using Lattice Boltzmann Method

In this work, the double-diffusive natural convection was studied in an open-ended cavity with the help of the lattice Boltzmann method. In this study, the driven force is developed by a change in the temperature gradient and concentration gradient on the left side of the cavity, which is the closed end. The temperature and concentration are maintained high at this end. The study is carried out for various parameters such as Rayleigh number (Ra) ranging from 103 to 106, aspect ratio (Ar) of 0.5, 1 and 2 and constant Prandtl number (Pr) of 0.7 and Lewis number (Le) of 2. The results are concentrated on for different buoyancy ratios (N = − 1, 0, 1) also. The results obtained are validated with existing literature results. The results show that when N value is negative, two buoyancy forces oppose each other and also the influence of concentration buoyancy force on fluid flow behavior gets dominant, and for aspect ratios 1 and 2, this effect was suppressed when Ra is increased but for the shallow cavity increasing in Ra helps the concentration force to become more dominant.

Development of self-label method to distinguish supply air from room air without tracer in numerical simulations

Traditionally, the tracer method has been used to distinguish the supply air and room air in buildings by labeling the target air with a tracer. However, due to difference in the physical properties of the target air and the tracer, use of the tracer method inevitably produces tracer error. Furthermore, due to the lack of an exact comparative reference, it is difficult to determine which tracer is the best to represent the target air distribution. In this study, a method (i.e. self-label method) which can distinguish supply air from ambient air without tracer in numerical simulations has been developed. In this paper, the principle, governing equations, accuracy, and applications of the self-label method are presented. Further, due to its simple and typical mixing characteristics of supply air and ambient air, a jet has been used to validate the numerical model by comparing the numerical results with the classical theoretical and experimental results in the earlier studies. The validity of the self-label method has been verified by comparing the flow rate and the velocity field of the jet with those by the single air approach. The tracer gas error has been compared with the exact reference obtained by self-label method. The results show that the tracer gas error increases with increasing tracer concentration or decreasing air velocity under isothermal conditions. Finally, the dynamic mechanism of the tracer gas error has been analyzed. It shows that an additional concentration buoyancy force can occur, which can cause tracer gas error under isothermal conditions.

Effect of Thermal Radiation, Chemical Reaction and Viscous Dissipation on MHD Flow

This study examines the effect of thermal radiation, chemical reaction and viscous dissipation on a magnetohydro- dynamic flow in between a pair of infinite vertical Couette channel walls. The momentum equation accounts the effects of both the thermal and the concentration buoyancy forces of the flow. The energy equation addresses the effects of the thermal radiation and viscous dissipation of the flow. Also, the concentration equation includes the effects of molecular diffusivity and chemical reaction parameters. The gray colored fluid considered in this study is a non-scattering medium and has the property of absorbing and emitting radiation. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The velocity of flow transforms kinetic energy into heat energy. The increment of the velocity due to internal energy results in heating up of the fluid and consequently it causes increment of the thermal buoyancy force. The Eckert number being the ratio of the kinetic energy of the flow to the temperature difference of the channel walls is directly proportional to the thermal energy dissipation. It can be observed that increasing the Eckert number results in increasing velocity. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall is high enough due to the presence of thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. These techniques help to convert partial differential equations to a set of ordinary differential equations in dimensionless form and thus they are solved analytically. The following results are obtained: from the simulation study it is observed that the flow pattern of the fluid is affected due to the influence of the thermal radiation, the chemical reaction and viscous dissipation. The increment in the Hartmann number results in the increment of the Lorentz force but a decrement in velocity of the flow. An increment in the radiative parameter results in a decrement in temperature. An increment in the Prandtl number results in a decrement in thermal diffusivity. An increment in both the chemical reaction parameter and molecular diffusivity results in a decrement in concentration.

Unsteady MHD Natural Convective Flow of a Rotating Fluid over an Infinite Vertical Plate due to Oscillatory Movement of the Free-Stream with Hall and Ion-Slip Currents

In the present research study a mathematical analysis has been presented for unsteady MHD natural convective flow of a rotating fluid over an infinite vertical plate immersed in a fluid saturated porous medium with oscillating free-stream. The effects of Hall and ion-slip currents also considered on the fluid flow. The unsteady MHD flow over the vertical plate is induced due to thermal and concentration buoyancy forces and oscillatory movement of the free-stream. The partial differential equations governing the motion for the fluid flow are solved analytically. The effects of various pertinent flow parameters on the fluid velocity, fluid temperature and species concentration are presented in graphical form whereas that on skin friction and rate of heat and mass transfer at the plate are presented in tabular form. An interesting observation recorded from the present analysis that there appears reversal flow in the secondary flow direction due to presence of thermal and/or concentration buoyancy forces. However, in the absence of both reversals flow does not exist in the secondary flow direction. It is also noted that the thickness of momentum boundary layer decreases with rise in frequency of oscillations of the free-stream.

Stratified flow of an Oldroyd-B nanoliquid with heat generation

Here modeling and computations are made to explore the characteristics of mixed convection flow of Oldroyd-B nanoliquid. Linear stretchable surface creates the flow. Brownian motion and thermophoretic aspects in nanoliquid modeling are retained. Thermal and solutal stratifications along with heat generation/absorption are considered for heat and mass transfer processes. Boundary layer approach is implemented in the mathematical formulation. The resulting problems are computed by homotopic algorithm. Salient features of Deborah numbers, mixed convection parameter, ratio of thermal to concentration buoyancy forces, Brownian motion parameter, Prandtl number, thermophoretic parameter, thermal/concentration stratification parameter, heat generation/absorption parameter and Schmidt number on the velocity, temperature, nanoparticles concentration and Nusselt and Sherwood numbers are reported through graphs and tables. Besides this the results of presented analysis have been compared with the available works in limiting situations and good agreement is noted.

Instability of opposing double diffusive convection in 2D boundary layer stagnation point flow

The objective of the present paper is to examine the effects of mass transfer on the thermal instability of a two-dimensional boundary layer stagnation point flow. We furthermore restrict our attention to thermal and concentration buoyancy forces which are of opposite sign. The basic flow has been obtained by processing the governing equations of continuity, momentum, energy and concentration using similarity analysis, then solved numerically by means of the fourth-order Runge–Kutta method with shooting technique. The linear stability of the basic flow is investigated in the usual fashion by making use of the normal mode decomposition within the Görtler–Hammerlin framework. The resulting eigenvalue problem is solved numerically using a pseudo spectral collocation method based upon Laguerre's polynomials. This procedure is warranted by the exponential damping of disturbances far from the boundary layer and the appropriate distribution of the roots of Laguerre's polynomials to treat boundary layer problems. It is found through the calculation of neutral stability curves that buoyancy ratio parameter (Nc) acts to increase the stability of the basic flow, however Lewis number (Le) acts to either increase or decrease it. Thus, Increasing Lewis number acts to increase the stability of the basic flow for Le < 1, or to decrease it for Le > 1. For Le = 1 the basic flow is always stable when Nc ≤ −1.

Numerical Modelling of Non-similar Mixed Convection Heat and Species Transfer along an Inclined Solar Energy Collector Surface with Cross Diffusion Effects

An analysis is performed to study thermo-diffusion and diffusion-thermo effects on mixed convection heat and mass transfer boundary layer flow along an inclined (solar collector) plate. The resulting governing equations are transformed and then solved numerically using the local nonsimilarity method and Runge-Kutta shooting quadrature. A parametric study illustrating the influence of thermal buoyancy parameter (&#950), Prandtl number (Pr), Schmidt number (Sc), Soret number (Sr), Dufour number (Du) and concentration-to- thermal-buoyancy ratio parameter, N, on the fluid velocity, temperature and concentration profiles as well as on local skin-friction, Nusselt and Sherwood numbers is conducted. For positive inclination angle of the plate (&#947 = 70 degrees), flow velocity (f') is strongly increased i.e. accelerated, with thermal buoyancy force parameter (&#950), in particular closer to the plate surface; further into the boundary layer, &#950 has a much reduced effect. Conversely temperature (&#952) and concentration (&#968) is decreased with increasing thermal buoyancy parameter, &#950. For negative plate inclination, the flow is accelerated whereas for positive inclination it is decelerated i.e. velocity is reduced. Conversely with negative plate inclination both the temperature and concentration in the boundary layer is reduced with the opposite apparent for positive inclination. Increasing Prandtl number strongly reduces temperature in the regime whereas an increase in Schmidt number boosts temperatures with temperature overshoots near the plate surface for Sc = 3 and 5 (i.e. for Sc > 1). Concentration is reduced continuously throughout the boundary layer, however, with increasing Schmidt number. A positive increase in concentration-to-thermal-buoyancy ratio parameter, N, significantly accelerates the flow in the domain, whereas negative N causes a deceleration. A velocity overshoot is also identified for N = 20, at intermediate distance from the plate surface. Negative N (thermal and concentration buoyancy forces oppose each other) induces a slight increase in both fluid temperature and concentration, with the reverse observed for positive N (thermal and concentration buoyancy forces assisting each other). Increasing Dufour number respectively causes a rise in temperature and a decrease in concentration, whereas an increase in Soret number cools the fluid i.e. reduces temperature and enhances concentration values. In the absence of Soret and Dufour effects, positive N causes a monotonic increase in local Nusselt number, NuxRex-1/2 with &#950 Cos &#947, for N = -1 the local Nusselt number remains constant for all values of parameter, &#950 Cos &#947. Local Sherwood number, ShxRex-1/2 is boosted considerably with higher Schmidt numbers and also with positive N values. The computations in the absence of Soret and Dufour effects correlate accurately with the earlier study by Chen et al. (1980).