Sadia Siddiqa

Natural Convection Flow with Surface Radiation Along a Vertical Wavy Surface

In this study, natural convection boundary layer flow of thermally radiating fluid along a heated vertical wavy surface is analyzed. Here, the radiative component of heat flux emulates the surface temperature. Governing equations are reduced to dimensionless form, subject to the appropriate transformation. Resulting dimensionless equations are transformed to a set of parabolic partial differential equations by using primitive variable formulation, which are then integrated numerically via iterative finite difference scheme. Emphasis has been given to low Prandtl number fluid. The numerical results obtained for the physical parameters, such as, surface radiation parameter, R, and radiative length parameter, ξ, are discussed in terms of local skin friction and Nusselt number coefficients. Comprehensive interpretation of velocity distribution is also given in the form of streamlines.

Radiation effects from an isothermal vertical wavy cone with variable fluid properties

Numerical solutions are presented for the natural convection flow along a vertical wavy cone situated in the thermally radiating fluid. The fluid flow and heat transfer characteristics are analyzed for the fluid having temperature dependent viscosity and thermal conductivity. After the primitive variable formulations, the transformed equations are integrated numerically through implicit finite difference method. Computational results are carried out for a range of physical parameters and interpreted in the form of skin friction coefficient, Nusselt number coefficient, streamlines and isotherms. The calculations show strong influence of thermal radiation parameter on the velocity and temperature fields. It is also reported that variable fluid properties sufficiently alter the important physical quantities and the quantitative analysis determines that it is likely to be more than 50%.

Two-phase natural convection flow of a dusty fluid

Purpose – The purpose of this paper is to conduct a detailed investigation of the two-dimensional natural convection flow of a dusty fluid. Therefore, the incompressible boundary layer flow of a two-phase particulate suspension is investigated numerically over a semi-infinite vertical flat plate. Comprehensive flow formations of the gas and particle phases are given in the boundary layer region. Primitive variable formulation is employed to convert the nondimensional governing equations into the non-conserved form. Three important two-phase mechanisms are discussed, namely, water-metal mixture, oil-metal mixture and air-metal mixture. Design/methodology/approach – The full coupled nonlinear system of equations is solved using implicit two point finite difference method along the whole length of the plate. Findings – The authors have presented numerical solution of the dusty boundary layer problem. Solutions obtained are depicted through the characteristic quantities, such as, wall shear stress coefficient...

Radiation effects on natural convection flow over an inclined flat plate with temperature-dependent viscosity:

The effect of radiation on laminar natural convection flow of a viscous incompressible fluid over a semi-infinite flat plate inclined at a small angle to the horizontal with strong temperature-dependent viscosity has been investigated. The Rosseland approximation is considered while modelling the problem. The non-similar equations are obtained for upstream, downstream, and entire regimes, which are then solved numerically. For constant viscosity, the series solution technique has been employed in order to obtain solutions that are valid near the leading edge as well as in the downstream regime. Later, solutions of the governing equations have been obtained using the finite difference method along with the Keller box technique, taking into consideration variable viscosity. Effects of physical parameters like conduction—radiation para-meter R d, surface temperature parameter θw, variable viscosity parameter λ, and Prandtl number Pr are shown on the local skin-friction coefficient C f and the local Nusselt number, Nu. Effects of the parameters on the streamlines are also shown around the point of separation that occurs along the negatively inclined surface.

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.

Natural Convection Flow over Wavy Horizontal Surface

In this paper boundary layer analysis is performed over a heated horizontal wavy surface. The governing boundary layer equations are transformed into parabolic partial differential equations with the help of appropriate coordinate transformation. Parabolic partial differential equations are then solved numerically with finite difference scheme, seeking details of the momentum and energy fields. Step by step computations are done for the upstream, downstream, and entire regimes. The numerical results are thoroughly discussed in terms of local skin friction and local Nusselt number coefficients for various parameters, like phase shift parameter, φ, and amplitude of the wavy surface, a. In addition, streamlines and isotherms are also drawn in order to visualize velocity and temperature distributions, respectively, within the boundary layer region.

Natural convection flow over an inclined flat plate with internal heat generation and variable viscosity

The present investigation deals with study of laminar natural convection flow of a viscous fluid over a semi-infinite flat plate inclined at a small angle to the horizontal with internal heat generation and variable viscosity. The dimensionless boundary layer equations are solved numerically for a negatively inclined plate using a very efficient marching order implicit finite difference scheme. Some results obtained numerically are, also, presented graphically at the point of separation in terms of velocity and temperature profiles. Several physically important quantities, specifically the local skin-friction coefficient and local Nusselt number are discussed with the effects of the physical parameters, namely, heat generation parameter, Q, viscosity-variation parameter, @l, and inclination parameter, @L, for a fluid of high Prandtl number, Pr. It is found that for a severely large Prandtl number Pr > 1000.0, which is appropriate for geophysical problems, both local skin friction and local Nusselt number coefficients get enhanced. It is interesting to see that the heat generation parameter, Q, as well as the viscosity-variation parameter, @l, have a significant role in the velocity and temperature distributions.

Compressible dusty gas along a vertical wavy surface

This analysis deals with the numerical solutions for the compressible natural convection flow of two-phase dusty gas. In particular, it gives the solutions for the flow having spherical particles suspended in the gas (air) over the surface with sharp lateral curvatures. The governing equations are converted into dimensionless equations by using a set of suitable continuous transformations and solved through the implicit finite difference method. The effect of compressibility, dusty gas and sinusoidal waveform are discussed in detail in terms of local heat transfer rate, skin friction coefficient, velocity and temperature distributions. This investigation reveals the fact that the air-particle mixture reduces the rate of heat transfer, significantly.

Radiation Effect on Free Convection Laminar Flow from an Isothermal Sphere

Natural convection laminar flow from an isothermal sphere immersed in a viscous incompressible optically dense fluid in the presence of radiation effects has been investigated. The governing boundary layer equations are transformed into a non dimensional form and the resulting nonlinear systems of partial differential equations are reduced to local non-similarity boundary layer equations, which are solved numerically by two distinct, efficient methods, namely, (i) implicit finite difference method together with the Keller box scheme and (ii) local non-similarity method. Numerical results of the velocity and temperature profiles of the fluid are presented. The results of the shearing stress and the heat transfer rate in terms of skin-friction coefficient and Nusselt number respectively are also presented for a wide range of the radiation-conduction parameter or Planck number R d (=0.0, 1.0, 2.0, 3.0), the surface heating parameter θ w (=1.1, 1.2, 1.4), and Prandtl number Pr (=7.0, 10.0, 15.0, 20.0).

Natural convection from a vertical plate embedded in a stratified medium with uniform heat source

Natural convection flow from an isothermal vertical plate with uniform heat source embedded in a stratified medium has been discussed in this paper. The resulting momentum and energy equations of boundary layer approximation are made non-similar by introducing the usual non-similarity transformations. Numerical solutions of these equations are obtained by an implicit finite difference method for a wide range of the stratification parameter, X. The solutions are also obtained for different values of pertinent parameters, namely, the Prandtl number, Pr and the heat generation or absorption parameter, λ and are expressed in terms of the local skin-friction and local heat transfer, which are shown in the graphical form. Effect of heat generation or absorption on the streamlines and isotherms are also shown graphically for different values of λ.