Nepal C. Roy

Unsteady mixed convection dusty fluid flow past a vertical wedge due to small fluctuation in free stream and surface temperature

We examine the unsteady characteristics of the mixed convection boundary layer flow of dusty fluid past a vertical wedge. The free stream and surface temperature are assumed to be fluctuating with small amplitude in time about a steady non-zero mean surface temperature and free stream velocity. The set of governing equations has been solved by two distinct methods, namely, the straightforward finite difference method for the entire frequency range, and the extended series solution for low frequency range and the asymptotic series expansion method for high frequency range. The effects of varying the ratio of the particle density to the gas density, ź, and Richardsons number, Ri, are discussed in terms of the amplitudes and phase angles of the skin friction and heat transfer and the transient skin friction and heat transfer. The unsteady behaviors of streamlines and isolines of temperature are also observed with the change of these physical parameters as well as of the amplitude of oscillation, ź. The results show that the presence of particle into the fluid, buoyancy caused mixed convection and fluctuations of free stream and surface temperature significantly enhance the time-dependent skin friction and heat transfer.

The effect of conduction—radiation on the oscillating natural convection boundary layer flow of viscous incompressible fluid along a vertical plate

Abstract The natural convection boundary layer flow with conduction—radiation interaction of a viscous incompressible fluid along a vertical plate to surface temperature oscillations has been studied. Three distinct methods are used in the investigation, namely (a) the perturbation method for low frequency range and the asymptotic series expansion method for high frequency range, (b) the direct finite difference method for primitive variable formulations, and (c) the implicit finite difference method for stream-function formulation together with the Keller-box elimination technique for the entire frequency range. The effects of varying the Prandtl number Pr, the conduction—radiation parameter R d, and the surface temperature parameter θw, are discussed in terms of amplitude and phase of the rate of heat transfer for fluid having the Prandtl number equal to 0.1. Also the effects of these parameters on the amplitude of oscillation of the transient skin-friction and transient heat transfer have been investigated.

Unsteady laminar mixed convection boundary layer flow near a vertical wedge due to oscillations in the free-stream and surface temperature

Abstract The unsteady laminar boundary layer characteristics of mixed convection flow past a vertical wedge have been investigated numerically. The free-stream velocity and surface temperature are assumed to be oscillating in the magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the straightforward finite difference method for the entire frequency range, and the extended series solution for low frequency range and the asymptotic series expansion method for high frequency range. The results demonstrate the effects of the Richardson number, Ri, introduced to quantify the influence of mixed convection and the Prandtl number, Pr, on the amplitudes and phase angles of the skin friction and heat transfer. In addition, the effects of these parameters are examined in terms of the transient skin friction and heat transfer.

Modelling of a closed two-dimensional reactor bounded by a wavy wall

In this paper, we propose a model for a two-dimensional closed reactor bounded by a wavy wall. The left, right and top walls of the reactor are assumed to be flat surfaces while the bottom wall is a wavy surface. In order to formulate a model for such a reactor, we introduce a coordinate transformation into the dimensionless equations of a rectangular closed domain. Then the resulting equations illustrate the phenomena for a closed reactor bounded by a wavy wall. We solve these equations using the finite difference method. The astonishing results are that the intensity of streamlines and the maximum temperature within the reactor significantly increase with an increase of the number of waves in the bottom wall, the amplitude of waves and the Frank-Kamenetskii number. Converse characteristics are observed for higher values of the enlargement of a wave. Moreover, larger Rayleigh number induces stronger vortices in the flow field and reduces the maximum temperature. The Nusselt number at the bottom wavy wall is found to increase for higher values of the Frank-Kamenetskii number and the amplitude of a wave. A transition from the steady-state to the oscillatory convection is identified for a certain value of the Frank-Kamenetskii number. However, for a low value of the Rayleigh number, there occurs a transition from the steady-state to an explosion for increasing value of the Frank-Kamenetskii number. Results also demonstrate that the critical value of the Frank-Kamenetskii number, for which a transition from the steady-state to the oscillatory convection occurs, is higher for increasing values of the number of waves, the enlargement of a wave and the amplitude of a wave.

Effects of Viscous Dissipation on Unsteady Mixed Convection Heat Transfer from a Circular Cylinder for Parallel and Contra Flows

Unsteady mixed convection heat transfer from a circular cylinder has been investigated in the presence of viscous dissipation. The isothermal horizontal cylinder is placed to the oncoming free stream whose direction is considered in the free convection flow (parallel flow) and opposite to it (contra flow). The system of dimensionless governing equations for unsteady, two-dimensional flow is reduced to a suitable form for integration and the resulting equations are solved employing finite difference method. For both parallel and contra flows the influences of the viscous dissipation on the Nusselt number are found to be strong, however, it has rather weak effect on the vorticity distribution. In the presence of the viscous dissipation, the isotherms are significantly changed while there is less effect on the streamlines. Under the same conditions, the size of the vortex for the contra flow is larger than that for parallel flow.

Modeling of a reactor with exothermic reaction bounded by two concentric cylinders

A model is developed to investigate the natural convection flow in a reactor bounded by two concentric cylinders. Using a simple transformation, the governing equations for a rectangular closed domain are transformed into a system of equations which are valid for a reactor of concentric annulus. These equations have been solved using an implicit finite difference method. Numerical solutions reveal that two counter-rotating vortices are built up in each half of the annulus. The clockwise flow circulation in the inner vortex and the anticlockwise flow circulation in the outer vortex are found in the left half of the annulus. However, the reverse characteristics are observed in the right half of the annulus. The remarkable results are that the concentric characteristics of isotherms are not maintained for higher values of the Frank-Kamenetskii number, Rayleigh number, and outer radius of the annulus. In this case, a local maximum value of the Nusselt number at the inner cylinder wall is identified at the bottom of the annulus. For a fixed value of the Rayleigh number and outer radius of the annulus, an explosion occurred in the system for a higher value of the Frank-Kamenetskii number. With the increase of the Rayleigh number, the critical limit of the Frank-Kamenetskii number for the explosion of the system is found to increase. On the contrary, it significantly reduces owing to the increase of the outer radius of the annulus.

Theoretical Approach to the Onset of Convection in a Porous Layer

A new theory is proposed to determine the critical wave number and the critical Rayleigh number at the onset of convection. We consider a problem of the onset of instability in convection in a horizontal layer embedded in a fluid-saturated porous medium. The upper wall of the layer is maintained at uniform temperature and concentration. On the lower wall, an Arrhenius-type exothermic surface reaction and surface radiation are assumed to occur. The heat released from the surface reaction and surface radiation causes convection in the porous medium and thereby can lead instability in the system. Results showed that the new theory can reasonably predict the critical wave number and the critical Rayleigh number. Moreover the influences of the heat release parameter, the mass diffusion parameter, the activation energy parameter and the conduction–radiation parameter on the critical wave number and the critical Rayleigh number have been presented. In the presence of surface radiation there must have a maximum value of the heat release parameter and the activation energy parameter while there must a minimum value of the mass diffusion parameter for the onset of convection in a porous medium.

Unsteady Magnetohydrodynamic Mixed Convection Flow of Micropolar Fluid Past a Permeable Sphere

In this paper, the flow and heat transfer characteristics for unsteady mixed convection flow of an electrically conducting micropolar fluid past a permeable sphere are investigated in detail. The e...

Conjugate Heat and Mass Transfer on Fluctuating Mixed Convection Flow along a Vertical Wedge with Thermal Radiation

Abstract We study the boundary layer characteristics of heat and mass transfer flow past a vertical wedge in the presence of thermal radiation. The surface temperature and the species concentration are assumed to be oscillating in the magnitude but not in the direction of oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the straightforward finite difference method for the entire frequency range, and the series solution for the low frequency range and the asymptotic series expansion method for the high frequency range. Numerical solutions have been presented in terms of the amplitudes and phase angles of the skin friction, the rate of heat transfer and the mass transfer with the variations of Richardson’s number, the Prandtl number, the conduction–radiation parameter, the surface temperature parameter and the Schmidt number. Furthermore, the effects of these parameters are examined in terms of the transient skin friction, heat transfer and mass transfer.

Unsteady MHD Mixed Convection Flow of a Micropolar Fluid Over a Vertical Wedge

Abstract An analysis is presented to investigate the unsteady magnetohydrodynamic (MHD) mixed convection boundary-layer flow of a micropolar fluid over a vertical wedge in the presence of thermal radiation and heat generation or absorption. The free-stream velocity and surface temperature are assumed to be oscillating in magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the finite difference method for the entire frequency range, and the series solution for low frequency range and the asymptotic series expansion method for the high frequency range. Numerical solutions provide a good agreement with the series solutions. The amplitudes of skin friction and couple stress coefficients are found to be strongly dependent on the Richardson number and the vortex viscosity parameter. The Prandtl number, the conduction-radiation parameter, the surface temperature parameter and the pressure gradient parameter significantly affect the amplitudes of skin friction, couple stress and surface heat transfer rates. However, the amplitudes of skin friction coefficient are considerably affected by the magnetic field parameter, whereas the amplitudes of heat transfer rate are appreciably changed with the heat generation or absorption parameter. In addition, results are presented for the transient skin friction, couple stress and heat transfer rate with the variations of the Richardson number, the vortex viscosity parameter, the pressure gradient parameter and the magnetic field parameter.