Dynamic of Two-phase Dusty Nanofluid Flow Past a Vertical Wavy Surface

An analysis is performed to study two-phase natural convection flow with heat transfer of nanofluid along a vertical way surface. The model includes equations expressing conservation of total mass, momentum and thermal energy for two-phase nano fluid. Primitive variable formulations (PVF) are used to transform the dimensionless boundary layer equations into convenient coordinate system and resulting equations are integrated numerically via implicit finite difference iterative scheme. The effects of the controlling parameters on the dimensionless quantities such as skin friction coeffcient, rate of heat transfer and rate of mass transfer are explored. It is concluded from present analysis, that the diffusivity ratio parameter, NA and particle-density increment number, NB has pronounced effect in reduction of heat transfer rate

Numerical estimation of thermal radiation effects on Marangoni Convection of dusty fluid

In this paper, numerical solutions to thermally radiating Marangoni convection of dusty fluid flow along a vertical wavy surface are established. The results are obtained with the understanding that the dust particles are of uniform size and dispersed in optically thick fluid. The numerical solutions of the dimensionless transformed equations are obtained through straightforward implicit finite difference scheme. In order to analyze the influence of various controlling parameters, results are displayed in the form of rate of heat transfer, skin friction coeffcient, velocity and temperature profiles, streamlines and isotherms. It is observed that the variation in thermal radiation parameter significantly alters the corresponding particle pattern and extensively promotes the heat transfer rate

Singularity in Gravitational Collapse of Plane Symmetric Charged Vaidya Spacetime

We study the final outcome of gravitational collapse resulting from the plane symmetric charged Vaidya spacetime. Using the field equations, we show that the weak energy condition is always satisfied by collapsing fluid. It is found that the singularity formed is naked. The strength of singularity is also investigated by using Nolan's method. This turns out to be a strong curvature singularity in Tipler's sense and hence provides a counter example to the cosmic censorship hypothesis.Comment: 8 pages, accepted for publication in Mod. Phys. Lett

Influence of Variable Thermophysical Properties on Nanofluid Bioconvection along a Vertical Isothermal Cone

The prime purpose of this analysis is to investigate the effect of variable thermophysical properties of nano fluid on bioconvection boundary layer flow past a uniformly heated vertical cone. The governing equations with associated boundary conditions for this phenomenon are cast into a non-dimensional form via continuous transformation, which are then solved by using the implicit finite difference method. How does the phenomena of heat transfer is effected due to the temperature-dependent thermophysical properties of the fluid is the question investigated in this manuscript. Comprehensive numerical computations are carried out for wide range of the parameters that are describing the flow characteristics. The influence of the governing physical parameters on the distribution of velocity and temperature profiles, wall skin friction and local rate of heat transfer is explored. Tabular comparison with some special cases of published data is done and good agreement is found. It is recorded that, the variable thermophysical properties of the fluid are more likely to promote the rate of heat transfer, Q_w as compared to fluid having constant properties

Thermal Maragoni Convection of Two-phase Dusty Fluid Flow Along a Vertical Wavy Surface

The paper considers the inuence of thermal Maragoni convection on boundary layer flow of two-phase dusty fluid along a vertical wavy surface. The dimensionless boundary layer equations for two-phase problem are reduced to a convenient form by primitive variable transformation (PVF) and then integrated numerically by employing the implicit finite difference method along with the Thomas Algorithm. The effect of thermal Maragoni convection, dusty water 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 water-particle mixture reduces the rate of heat transfer, significantly

Natural convection of gas along a vertical wavy surface with effect of variable thermophysical properties

The intent of this paper is to establish the detailed parametric study for laminar natural convection ow along a vertical wavy plate. Typical sinusoidal surface is used to elu- cidate the heat transport phenomena for the gas having variable thermophysical properties. From the present analysis, we will interrogate whether the presence of roughness element disturbs the gas ow and alter the physical characteristics associates with the wavy surface or not? The numerical solutions are obtained after converting the governing equations into a suitable coordinate system. The results are interpreted for the parameters which emerge from the temperature dependent physical properties of the gases and transverse curvature of the surface. In order to ensure the accuracy, the present numerical results are also compared with some special cases and are found in good agreement. The key observation from the present analysis is that the amplitude of wavy surface parameter, a contributes in reduction of heat transfer rate

Two-phase Dusty Fluid Flow Along a Rotating Axi-symmetric Round-Nosed Body

This article is concerned with the class of solutions of gas boundary layer containing uniform, spherical solid particles over the surface of rotating axi-symmetric roundnosed body. By using the method of transformed coordinates, the boundary-layer equations for two-phase flow are mapped into a regular and stationary computational domain and then solved numerically by using implicit finite difference method. In this study, a rotating hemisphere is used as a particular example to elucidate the heat transfer mechanism near the surfaces of round nosed bodies. We will also investigate whether the presence of dust particles in carrier fluid disturb the flow characteristics associated with rotating hemisphere or not. A comprehensive parametric analysis is presented to show the influence of the particle loading, the buoyancy ratio parameter and the surface of rotating hemisphere on the numerical findings. In the absence of dust particles, the results are graphically compared with existing data in the open literature and an excellent agreement has been found. It is noted that, the concentration of dust particles parameter, D_p, strongly influence the heat transport rate near the leading edge

How to understand Pakistan’s hybrid regime: the importance of a multidimensional continuum

Pakistan has had a chequered democratic history but elections in 2013 marked a second turnover in power, and the first transition in Pakistan’s history from one freely elected government to another. How do we best categorize (and therefore understand) political developments in Pakistan? Is it now safe to categorize it as an electoral democracy or is it still a hybrid case of democracy? Using the Pakistani case as an example, this article argues that hybrid regimes deserve consideration as a separate case (rather than as a diminished sub type of democracy or authoritarianism), but must be categorised along a multidimensional continuum to understand the dynamics of power within the political system