Couple stress effects on the MHD oscillatory flow in a fluid-saturated porous layer

In this paper, the oscillatory flow of hydromagnetic couple stress fluid-saturated porous layer with inhomogeneous wall temperatures is studied. The flow is modeled using the modified Darcy equation. The fluid is subjected to a transverse magnetic field and the velocity slip at the lower plate is taken into deliberation. The governing coupled partial differential equations of the flow are transformed to coupled ordinary differential equations and are solved analytically. The impact of the physical parameters such as the Grashof number, Prandtl number, Darcy number, Hartmann number, and couple stress parameters on velocity profiles, temperature, rate of heat transfer, and skin friction are emphasized. The velocity field increased as either the Grashof number, the Darcy number, the suction/injection parameter, and Prandtl number increased nevertheless reverse growth can be seen by increasing the Hartmann number and the couple stress parameter. The temperature field in the channel increases with increasing the suction/injection parameter and Prandtl number but a conflicting development can be seen with increasing the oscillation amplitude. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate.     

Simultaneous heat and mass transfer on oscillatory free convection boundary layer flow

The problem of simultaneous heat and mass transfer in two-dimensional free convection from a semi-infinite vertical flat plate is investigated. An integral method is used to find a solution for zero wall velocity and for a mass transfer velocity at the wall with small-amplitude oscillatory wall temperature. Low- and high-frequency solutions are developed separately and are discussed graphically with the effects of the parameters Gr (the Grashof number for heat transfer), Gc (the Grashof number for mass transfer) and Sc (the Schmidt number) for Pr = 0–71 representing aid at 20°C.     

Simulation of Laminar Axisymmetric Buoyant Plumes: A Case Study of the Anatomy of Similarity Solutions

This article is concerned with the numerical simulation of the laminar buoyant plume created by a heated sphere situated in an otherwise quiescent environment. The limit of vanishing sphere diameter corresponds to the point source of heat, for which extensive results have been obtained in the literature. The dual objectives of this work are the attainment of an exact characterization of the buoyant plume, and the diagnosis of an existing similarity solution for the limiting problem of the point source. These objectives were fulfilled by means of a numerically exact solution of the equations representing mass, momentum, and energy conservation. The solutions were carried out over a range of the radius-based Grashof number extending from 50 to 5 × 10⁶ for a Prandtl number of 0.7, which corresponds to air. The velocities in the plume were found to increase with elevation above the sphere but approach a fully developed state characterized by congruent (similar) velocity profiles at sufficiently high elevations. The temperature profiles, while attaining a self-similar shape at high elevations, actually decay with increasing elevation. The approach to both the fully developed state for the velocity and the self-similar state for the temperature occurs more rapidly at low Grashof numbers. In general, it was found that the existing similarity solutions become viable only at very large elevations above the source of buoyancy.     

Experimental and numerical investigation of natural convection effects on confined impinging jet heat transfer

The influence of natural convection on the local and average heat transfer at increasing temperature differences between the jet and the target plate from confined impinging jets has been experimentally and numerically investigated. Local Nusselt numbers were obtained numerically for jet Reynolds numbers in the range of 250–1000, and jet to target spacings of 2, 4, 8, 12 jet diameters at various modified Grashof numbers, to determine the effect of buoyancy induced natural convection. To determine the overall effect of natural convection on the average heat transfer, experiments have been conducted for Re numbers in the range 250–5000 and dimensionless jet to target spacing 2, 4, 6, 8, and 12 at increasing modified Grashof numbers. It has been determined that buoyancy induced natural convection might have opposing or assisting influence on local heat transfer at different locations of the target plate. It has also been shown that especially at low jet inlet velocities the average heat transfer coefficient at the highest modified Grashof number, where the natural convection is effective, is higher than the value corresponding to the lowest Grashof number at which buoyancy effects are negligible, by as much as 37%.     

Numerical Study of Pressure Drop and Thermal Characteristics of Al2O3–Water Nanofluid Flow in Horizontal Annuli

In this paper the results of numerical study of the mixed convection heat transfer of Al₂O₃–water nanofluid in a horizontal annuli are presented. Steady, laminar flows in symmetric configurations are considered. Single-phase fluid approach is adopted for nanofluid modeling. The governing equations are discretized using the finite-volume method. A SIMPLE-like algorithm has been applied for pressure–velocity coupling on the collocated arrangement. In order to validate the code performance, the numerical results are compared with those available in the literature and good agreement is achieved. The effects of some important parameters such as nanoparticle volume fraction, aspect ratio, Grashof number, and heat flux ratio are studied and discussed in detail. In general, it is observed that the local Nusselt number increases with increase in nanoparticle concentration, Grashof number, and radius ratio. However, when increasing the nanoparticle concentration there are considerable increments in pressure drop and pumping power, which are not desirable. On the other hand, changes in the skin friction coefficient are negligible.     

Magnetoconvection in a square cavity with partially active vertical walls: Time periodic boundary condition

Magnetoconvection of an electrically conducting fluid in a square cavity with partially thermally active sidewalls is investigated numerically. Temperature of one of the thermally active regions of the side walls is periodic in time while the opposite wall is isothermal. The horizontal walls and the remaining parts of the side walls are thermally inactive. Nine different combinations of the relative positions of the active zones are considered. The governing equations are discretized by the control volume method with QUICK scheme and solved numerically by SIMPLE algorithm for the pressure–velocity coupling together with under relaxation technique. The tests were carried out for various values of amplitude, period, Grashof number, Hartmann number and Prandtl number. The heat transfer characteristics are presented in the form of streamlines, isotherms and velocity profiles both for transient and steady state. It is observed that the flow and the heat transfer rate in the cavity are affected by the sinusoidal temperature profile and by the magnetic field at lower values of Grashof number. The rate of heat transfer oscillates for increasing periods but it is maximum for Ω = 3 and it is found to be an increasing function of amplitude but decreases for higher values of Hartmann number. The heat transfer rate is maximum for the middle–middle thermally active locations while it is poor for the top heating and bottom cooling active locations. The average Nusselt number decreases with an increase of Hartmann number and increases with increase of Prandtl number and Grashof number.     

Coupled heat and mass transfer in mixed convection over a wedge with variable wall temperature and concentration in porous media: The entire regime

A boundary layer analysis is used to investigate both heat and mass transfer characteristics of mixed convection about a wedge in saturated porous media under the coupled effects of thermal and mass diffusion. The surface of the wedge is maintained at a variable wall temperature (VWT) and variable wall concentration (VWC). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results are presented for the local Nusselt number and the local Sherwood number. Increasing the buoyancy ratio N, the exponent of wall temperature/concentration n and the wedge angle parameter λ increases the local Nusselt number and the local Sherwood number. As mixed convection parameter χ varies from 0 to 1, the local Nusselt number and the local Sherwood number decrease initially, reach a minimum in the intermediate value of χ and then increase gradually. It is apparent that the Lewis number has a pronounced effect on the local Sherwood number than it does on the local Nusselt number. Furthermore, increasing the Lewis number decreases (increases) the local heat (mass) transfer rate.     

Thermo-Solutal Buoyancy Induced Mixed Convection in a Backward Facing Step Channel using Velocity-Vorticity Formulation

Double diffusive mixed convection in a horizontal channel with backward facing step is analyzed using velocity-vorticity formulation with a focus on the effect of recirculatory flow pattern on convective heat and mass transfer. The governing equations consist of vorticity transport equation with thermal and solutal buoyancy force terms, velocity Poisson equations, energy equation, and solutal concentration equation. Galerkin's weighted residual finite-element method has been employed to solve the equations for vorticity, velocity, temperature, and concentration fields in the computational domain. Test results are obtained to study the effect of thermal Grashof number (Gr _T ), solutal Grashof number (Gr _S ), and expansion ratio on the average Nusselt and Sherwood numbers. Results indicate that the convective heat transfer increased with increase in Gr _T only when the Gr _S number is in the aiding mode. The maximum local Nusselt number is always observed to be located adjacent to the downstream of the fluid reattachment point. Using the matched method of asymptotic expansions, correlations have also been developed for average Nusselt and Sherwood numbers for both cases of aiding and opposing buoyancy forces.     

SIMULATION OF MIXED CONVECTION HEAT TRANSFER AT THE WALL OF A PACKED BED

Numerical investigations of the effect of mixed convection on the fluid flow pattern and heat transfer at the boundary layer of a packed bed are reported. A volume-averaged Navier-Stolces equation incorporating the Boussinesq approximation is used to predict the fluid flow, and a volume-averaged heat balance equation, the heat transfer. An exponential variation in the porosity of the packing is assumed in the region near the wall. Simulations are performed using a modified penalty Galerkin finite-element method. The Nusselt number is found to depend on the Grashof to Reynolds number ratio, Graetz number, and ratio of thermal conductivity of the solid and fluid phases. The heat transfer rate is enhanced by a positive Grashof number and hindered by a negative value. The velocity and temperature profiles in the bed are also found to be strong functions of the Gr/Re² ratio. At higher values of this ratio the flow becomes unsteady     

MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition

A numerical approach has been used to study the heat and mass transfer from a vertical plate embedded in a porous medium experiencing a first-order chemical reaction and exposed to a transverse magnetic field. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The momentum, energy, and concentration equations derived as coupled second-order, ordinary differential equations are solved numerically using a highly accurate and thoroughly tested finite difference algorithm. The effects of Biot number, thermal Grashof number, mass transfer Grashof number, permeability parameter, Hartmann number, Eckert number, Sherwood number and Schmidt number on the velocity, temperature, and concentration profiles are illustrated graphically. A table containing the numerical data for the plate surface temperature, the wall shear stress, and the local Nusselt and Sherwood numbers is also provided. The discussion focuses on the physical interpretation of the results as well their comparison with the results of previous studies.     

Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate

The purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon  and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number.     

Effect of corrugation frequencies on natural convective heat transfer and flow characteristics in a square enclosure of vee-corrugated vertical walls

A numerical investigation has been carried out on natural convective heat transfer and fluid flow in a square cavity with vee-corrugated vertical surfaces. This study covers the range of corrugation frequency from 1 to 3 and Grashof number from 10³ to 10⁵. The corrugation amplitude has been fixed at 5% of the enclosure height. The vorticity stream function formulation with the control volume based finite element method has been used to analyse the effects of corrugation frequency and Grashof number. The investigation shows that the overall heat transfer through the enclosure increases with the increase of corrugation for low Grashof number; but the trend is reversed for high Grashof number.     

Natural-Convection Heat Transfer in Channels With Isoflux Convex Surfaces

Numerical solutions are presented for laminar natural convection heat transfer in channels with convex surfaces that are subjected to a uniform heat flux. Simulations are conducted for several values of Grashof number (10 to 10⁴) and radius of curvature (1 to ∞). The governing elliptic conservation equations are solved in a boundary-fitted coordinate system using a collocated control-volume-based numerical procedure. The results are presented in terms of streamline and isotherm plots, inlet mass flow rates, curved wall temperature profiles, maximum hot wall temperature estimates, and average Nusselt number values. At the lowest radius of curvature, computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. For a radius of curvature equal to or greater than 2, recirculation does not occur at any Grashof number. For values of radius of curvature between 1 and 2, the value of Grashof number at which recirculation occurs decreases with increasing values of the former. The variation in the buoyancy-induced volume flow rate is highly nonlinear with respect to the radius of curvature, and the value of the radius of curvature at which the volume flow rate is maximum increases with increasing Grashof number. The value of radius of curvature at which the maximum hot wall temperature is minimized increases with Grashof number. For all configurations studied, the average Nusselt number increases with increasing Grashof number values. Correlations for maximum wall temperature and average Nusselt number are provided.     

Free Convection in Confined Power-Law Fluids From Two Side-by-Side Cylinders in a Square Enclosure

Laminar free convection heat transfer in power-law fluids from two side-by-side cylinders (one hot and one cold) confined in a square duct has been studied numerically in the two-dimensional flow regime. For a fixed value of the ratio of cylinder radius to size of the enclosure, the effect of geometrical placement of the cylinders is studied on the resulting velocity and temperature fields in the laminar free convection regime by considering six asymmetric locations of the two cylinders. In particular, extensive results reported herein span the range of conditions of Grashof number, 10 to 10⁵; Prandtl number, 0.7 to 100, thereby yielding the range of the Rayleigh number as 7 to 10⁷; power-law index, 0.3 to 1.8; and the relative positions (dimensionless) of the cylinders with respect to the centerline, –0.25 to 0.25. The heat transfer characteristics are analyzed in terms of the local Nusselt number along the surfaces of the two cylinders and the enclosure walls. Overall, the average Nusselt number shows a positive dependence on both the Grashof number and the Prandtl number irrespective of the values of power-law index and relative positioning of the cylinders. Also, all else being equal, shear-thinning fluid behavior promotes heat transfer with reference to that in Newtonian fluids. When the two cylinders are situated close to the bottom wall, the rate of heat transfer is augmented with reference to that for the symmetric positioning of the cylinders along the horizontal mid-plane of the enclosure. Conversely, heat transfer deteriorates as the cylinders are located above the centerline of the enclosure. The present numerical results have been consolidated via the use of a modified Rayleigh number, thereby enabling the estimation of the average Nusselt number in a new application.     

Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.     

Direct numerical simulation of turbulent flow and combined convective heat transfer in a square duct with axial rotation

Direct numerical simulations (DNS) of turbulent flow and convective heat transfer in a square duct with axial rotation were carried out. The pressure-driven flow is assumed to be hydrodynamically and thermally fully developed, for which the Reynolds number based on the friction velocity and hydraulic diameter is kept at constant (Re_τ = 400). In the finite length duct, two opposite walls are perfectly insulated and another two opposite walls are kept at constant but different temperatures. Four thermal boundary conditions were chosen in combination with axial rotation to study the effects of rotation and Grashof number on mean flow, turbulent quantities and momentum budget. The results show that thermal boundary conditions have significant effects on the topology of secondary flows, profiles of streamwise velocity, distribution of temperature and other turbulent statistic quantities but have marginal effects on the bulk-averaged quantities; Coriolis force affects the statistical results very slightly because it exerts on the plane normal to main flow direction and the rotation rate is low; Buoyancy effects on the turbulent flow and heat transfer increase with the increase of Grashof number (Gr), and become the major mechanism of the development of secondary flow, turbulence increase, and momentum and energy transport at high Grashof number.     

Unsteady flow through a porous medium with the presence mass transfer

Unsteady flow through a very porous medium with the presence mass transfer is considered. The porous medium is bounded by a vertical plate and this plate absorbs the fluid with a constant velocity. Also the free stream velocity of the fluid vibrates about a mean constant value. The influences of the permeability parameter and the modified Grashof number on the velocity field are discussed.     

Effect of radiation absorption and chemical reaction on MHD-free convective flow through a porous medium past an infinite vertical porous plate in the presence of constant heat flux

An incompressible, electrically conducting, and viscous fluid flowing steadily and freely across a uniformly porous media that is partially constrained by an infinitely long vertical porous plate is studied in the present article. Additionally, chemical reaction and radiation absorption effects are seen. Here, a magnetic field of uniform strength is applied transversely to the plate, a normal suction velocity is imposed on the fluid, and the heat flux is considered to be constant. The non-dimensional momentum and energy equations are solved using the method of perturbation. The problem has been analytically resolved, and several parameters, including the Hartmann number, porosity parameter, thermal Grashof number, mass Grashof number, and transport properties like the Sherwood number, skin friction, and plate temperature, are graphically represented. The current study reveals a spike in the radiation absorption effect causes skin friction to drop, but on the other hand, a contrary effect is observed for plate temperature. One of the notable findings of this investigation is that the Sherwood number increases as chemical reaction parameter influence increases.     

Numerical investigation of laminar forced convection of water upwards in a narrow annulus at supercritical pressure

In the present work, convection heat transfer of water at supercritical pressure in a narrow annulus at low Reynolds numbers (less than 1500) has been investigated numerically. The continuity, momentum and energy equations have been solved simultaneously using computational fluid dynamics techniques with the inlet Reynolds number ranging from 250 to 1000, Grashof number from 2.5 × 10⁵ to 1 × 10⁶ and the inlet fluid temperature from 360 °C to 380 °C. In all of the case studies, a sub-cooled water flow at supercritical pressure (25 MPa) and a temperature close to the pseudo-critical point enters the annular channel with constant heat flux at inner wall surface and insulated at outer wall. To calculate the velocity and temperature distributions of the flow, discretized form of the governing equations in the cylindrical coordinate system are obtained by the finite volume method and solved by the SIMPLE algorithm. It has been shown that the effect of buoyancy is strong and causes extensive increase in velocity near the inner wall, and consequently an increase in the convective heat transfer, which is desirable. Besides, the effects of inlet Reynolds number, Grashof number and inlet temperature on the velocity distribution and also on the heat transfer have been investigated.     

Parametric study on mixed convection heat transfer in an inclined arc-shape cavity

This paper presents a parametric study on mixed convection heat transfer in an inclined arc-shape cavity subjected to a moving lid. The governing equations for the inclined arc-shape cavity were derived with the incorporation of inertia and buoyant force terms and solved by using the finite-volume method and numerical grid generation scheme. The parametric study considered three physical parameters including inclination angle, Reynolds number and Grashof number, and explored the effect of these parameters on the flow field and heat transfer characteristics. Computations were conducted for the Reynolds number ranging from 100 to 1500, Grashof number from 10⁵ to 10⁷ and inclination angle from 15⁰ to 60⁰. The numerical results show that the flow pattern becomes inertia-dominant and the strength of the primary vortex generally increases as the Reynlods number increases. As the Grashof number increases, the strength of the inertial-induced vortex decreases and the strength of the buoyancy-induced vortex increases. The strength of the vortexes decreases with the increasing inclination angle and the buoyancy-induced flow becomes more dominant. The average Nusselt number increases as the Grashof number increases for all the inclination angles studied here. The local friction increases with the increasing inclination angle, and becomes significant as the Grashof number increases.