Free convection flow with chemical reaction effect between oscillating parallel plates

This research purpose is to investigate the exact solutions for unsteady free convection flow between oscillating parallel plates with mass diffusion and chemical reaction. The governing equations are modelled and reduced using non-dimensional variables. The method used is Laplace transform method. Solutions for velocity, temperature, and concentration fields as well as skin friction, Nusselt and Sherwood number are obtained. For physical understanding, analytical results for velocity, temperature and concentration profile are plotted graphically with respect to the Schmidt number, Prandtl number, oscillating parameter, Grashof number, mass Grashof number and chemical reaction parameter. Increasing Prandtl number and Schmidt number decreases the concentration, velocity, temperature, and skin friction but increases the Sherwood and Nusselt numbers.

Development of unsteady boundary layers on the generatrices of a vertical silicon rod heated by electric current in the mode of conjugate radiation-convective heat transfer

The nonstationary conjugate radiation-convective heat transfer of a single silicon rod heated by an electric current with the surrounding gas medium is studied numerically in the axisymmetric formulation by the finite element method. The calculations were carried out at the Prandtl number Pr = 0.68, and the range of the Grashof number, determined by the temperature difference and the radius of the rod 9 703 ≤ Gr ≤ 261 977. It is shown that after a short incubation period, a circulation flow is formed. As a result, a significantly inhomogeneous temperature field in the longitudinal direction is formed in a silicon rod heated by an electric current. As the Grashof number increases, the inhomogeneity of the longitudinal distribution of the temperature field increases.

Comparative study of heat and mass transfer of generalized MHD Oldroyd-B bio-nano fluid in a permeable medium with ramped conditions

This article aims to investigate the heat and mass transfer of MHD Oldroyd-B fluid with ramped conditions. The Oldroyd-B fluid is taken as a base fluid (Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three different types of definitions of fractional differential operators, like Caputo, Caputo-Fabrizio, Atangana-Baleanu (will be called later as $$C,CF,AB$$ C , C F , A B ) are used to develop the resulting fractional nano-fluid model. The solution for temperature, concentration, and velocity profiles is obtained via Laplace transform and for inverse two different numerical algorithms like Zakian’s, Stehfest’s are utilized. The solutions are also shown in tabular form. To see the physical meaning of various parameters like thermal Grashof number, Radiation factor, mass Grashof number, Schmidt number, Prandtl number etc. are explained graphically and theoretically. The velocity and temperature of nanofluid decrease with increasing the value of gold nanoparticles, while increase with increasing the value of both thermal Grashof number and mass Grashof number. The Prandtl number shows opposite behavior for both temperature and velocity field. It will decelerate both the profile. Also, a comparative analysis is also presented between ours and the existing findings.

The Influence of Elasticity on Peristaltic Flow of Nanofluid in a Tube

In this paper, a mathematical model is proposed to study the influence of elasticity on peristaltic flow of nanofluid in a vertical tube with temperature dependent viscosity. The expressions for axial velocity, temperature, flux and pressure gradient are derived. The different nanofluids suspensions are consider to analyze the influence of elasticity on flux variation. Application of blood flow through veins is studied by expressing relationship between pressure gradient and volume flow rate in an elastic tube. The effect of different pertinent parameters on the flow characteristics of nano fluid in an elastic tube with peristalsis is analyzed through graphs. The variation in flux for different nanofluids like pure water H2O, Copper-water nanofluid CuO + H2O, Silver-water Ag + H2O and Titanium oxide-water nanofluid TiO2 + H2O are illustrated through graphs. The variation in flux for various physical parameters such as amplitude ratio, heat source parameter, Grashof number, viscosity parameter and elastic parameters are discussed. The flux takes higher values for nano particles case when compared to pure water. The flux enhances with amplitude ratio, Grashof number, heat source/sink factor and viscosity factor. The flux is more for the Titanium oxide-water nanofluid TiO2 + H2O when compared to remaining cases. The important observation is that pressure rise along mean flow rate is increase due to raise in temperature of source or sink in puming region and decreases in co pumping region. In the absence of elastic parameter (α″ = 0), the results observed in the present study are similar to that of results observed by O. A. Beg et al., Results in Physics 7, 413 (2017).

Modelling Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds Using the Lattice Boltzmann Method

Field observations and laboratory experiments have shown that ash sedimentation can be significantly affected by collective settling mechanisms that promote premature ash deposition, with important implications for dispersal and associated impacts. Among these mechanisms, settling-driven gravitational instabilities result from the formation of a gravitationally-unstable particle boundary layer (PBL) that grows between volcanic ash clouds and the underlying atmosphere. The PBL destabilises once it reaches a critical thickness characterised by a dimensionless Grashof number, triggering the formation of rapid, downward-moving ash fingers that remain poorly characterised. We simulate this process by coupling a Lattice Boltzmann model, which solves the Navier-Stokes equations for the fluid phase, with a Weighted Essentially Non Oscillatory (WENO) finite difference scheme which solves the advection-diffusion-settling equation describing particle transport. Since the physical problem is advection dominated, the use of the WENO scheme reduces numerical diffusivity and ensures accurate tracking of the temporal evolution of the interface between the layers. We have validated the new model by showing that the simulated early-time growth rate of the instability is in very good agreement with that predicted by linear stability analysis, whilst the modelled late-stage behaviour also successfully reproduces quantitative results from published laboratory experiments. The results show that the model is capable of reproducing both the growth of the unstable PBL and the non-linear dependence of the fingers’ vertical velocity on both the initial particle concentration and the particle diameter. Our validated model is used to expand the parameter space explored experimentally and provides key insights into field studies. Our simulations reveal that the critical Grashof number for the instability is about ten times larger than expected by analogy with thermal convection. Moreover, as in the experiments, we found that instabilities do not develop above a given particle threshold. Finally, we quantify the evolution of the mass of particles deposited at the base of the numerical domain and demonstrate that the accumulation rate increases with time, while it is expected to be constant if particles settle individually. This suggests that real-time measurements of sedimentation rate from volcanic clouds may be able to distinguish finger sedimentation from individual particle settling.

High Grashof number turbulent natural convection on an infinite vertical wall

The present study concerns a temporally evolving turbulent natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall, with Prandtl number 0.71. Three-dimensional direct numerical simulations (DNS) are carried out to investigate the turbulent flow up to $\textit {Gr}_\delta =1.21\times 10^8$ , where $\textit {Gr}_\delta$ is the Grashof number based on the boundary layer thickness $\delta$ . In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.g. George & Capp, Intl J. Heat Mass Transfer, vol. 22, 1979, pp. 813–826). Beyond a wall-normal distance $\delta _i$ , the NCBL can be characterised as a plume-like region. We find that this region is well described by a self-similar integral model with profile coefficients (cf. van Reeuwijk & Craske, J. Fluid Mech., vol. 782, 2015, pp. 333–355) which are $\textit {Gr}_\delta$ -independent after $\textit {Gr}_\delta =10^7$ . In this Grashof number range both the outer plume-like region and the near-wall boundary layer are turbulent, indicating the beginning of the so-called ultimate turbulent regime (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Grossmann & Lohse, Phys. Fluids, vol. 23, 2011, 045108). Solutions to the self-similar integral model are analytically obtained by solving ordinary differential equations with profile coefficients empirically obtained from the DNS results. In the present study, we have found the wall heat transfer of the NCBL is directly related to the top-hat scales which characterise the plume-like region. The Nusselt number is found to follow $\textit {Nu}_\delta \propto \textit {Gr}_\delta ^{0.381}$ , slightly higher than the empirical $1/3$ -power-law correlation reported for spatially developing NCBLs at lower $\textit {Gr}_\delta$ , but is shown to be consistent with the ultimate heat transfer regime with a logarithmic correction suggested by Grossmann & Lohse (Phys. Fluids, vol. 23, 2011, 045108). By modelling the near-wall buoyancy force, we show that the wall shear stress would scale with the bulk velocity only at asymptotically large Grashof numbers.

Effects of Magnetohydrodynamics and Heat Transfer in Casson Fluid Through a Channel

Unsteady flow of Casson fluid past through a vertical channel has been studied by some researchers due to its importance of applications in science and technology. Therefore, the main purpose of this paper is to obtain exact solutions for unsteady free convection flows of Casson fluid with effects of magnetohydrodynamics (MHD) past through vertical channel. This paper is continued study from published article [18] with additional effects of magnetohydrodynamics (MHD). Dimensional governing equations are converted into dimensionless forms by using appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid, time, Prandtl number, Grashof number and magnetic field. Laplace transform method is used to solve the dimensionless equations with associated initial and boundary conditions. Solutions for velocity and temperature profiles are obtained. Skin friction and Nusselt number are also calculated. The obtained analytical results for velocity and temperature are plotted graphically to discuss the influence of dimensionless parameters on profiles. It is observed that fluid velocity increases with increases of Grashof number, Gr and time, t whereas it decreases with increases of Casson parameter, γ, magnetic field parameter, M and Prandtl number, Pr. Besides that, it is found that temperature profiles decrease with high value of Prandtl number, Pr while increases with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and it is found to be in a mutual agreement.

Micropolar Fluid Flow Along with an Inclined Riga Plate Through a Porous Medium

This study presents the one-dimensional unsteady micropolar fluid flow set in a porous medium along with an inclined infinite Riga plate. This Riga plate is created an electric and magnetic field, where a transverse Lorentz force is generated that contributes a flow along with the plate. The explicit finite difference method is used to find the solution of the non-dimensional form of the governing equations and estimated results are analyzed in terms of Microrotation parameter, Suction parameter, thermal Grashof number, mass Grashof number, Permeability parameter, Hartmann number, Dufour number, Soret number, Schmidt number. Also, the effects of the pertinent parameters on the local and average shear stress, Nusselt number, and Sherwood number are reported numerically as well as graphically.

Optimal Homotopy Asymptotic Method for Investigation of Effects of Thermal Radiation, Internal Heat Generation, and Buoyancy on Velocity and Heat Transfer in the Blasius Flow

In this study, analytical examination of effects of internal heat generation, thermal radiation, and buoyancy force on flow and heat transfer in the Blasius flow over flat plate has been presented. The governing nonlinear partial differential equations of the problem are transformed into a set of coupled nonlinear third-order ordinary differential equations by the similarity variable method and have been systematically solved using the optimal homotopy asymptotic method. The main aim of the present study is to inspect the effects of various physical parameters in the flow model on velocity and heat transfer in steady two-dimensional laminar boundary layer flow with convective boundary conditions. The influences of the Grashof number, internal heat generation, the Biot number, radiation parameter, and the Prandtl number on the skin-friction coefficient, the fluid velocity profile, and temperature distribution have been determined and discussed in detail through several plots. The finding revealed that the fluid velocity and temperature delivery upsurge with snowballing in the values of the Biot number and internal heat generation parameters. The temperature profile of the fluid declines contrary to the value of the Grashof number and the Prandtl number but increases with thermal radiation. Moreover, it is found that the skin-friction coefficient and the rate of heat intensify with the Grashof number, internal heat generation, the Biot number, and thermal radiation parameter. The obtained result is likened with the previously published numerical results in a limited case of the problem and shows an excellent agreement.