scholarly journals Numerical Scrutinization of Darcy-Forchheimer Relation in Convective Magnetohydrodynamic Nanofluid Flow Bounded by Nonlinear Stretching Surface in the Perspective of Heat and Mass Transfer

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 374
Author(s):  
Ghulam Rasool ◽  
Anum Shafiq ◽  
Marei S. Alqarni ◽  
Abderrahim Wakif ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Biot Number ◽  
Mass Flux ◽  
Flow Direction ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Forchheimer Number ◽  
Highly Nonlinear ◽  
Non Linear ◽  
Thermal Layer

The aim of this research is mainly concerned with the numerical examination of Darcy-Forchheimer relation in convective magnetohydrodynamic nanofluid flow bounded by non-linear stretching sheet. A visco-elastic and strictly incompressible liquid saturates the designated porous medium under the direct influence of the Darcy-Forchheimer model and convective boundary. The magnetic effect is taken uniformly normal to the flow direction. However, the model is bounded to a tiny magnetic Reynolds number for practical applications. Boundary layer formulations are taken into consideration. The so-formulated leading problems are converted into highly nonlinear ordinary problems using effectively modified transformations. The numerical scheme is applied to solve the governing problems. The outcomes stipulate that thermal layer receives significant modification in the incremental direction for augmented values of thermal radiation parameter Rd. Elevation in thermal Biot number γ1 apparently results a significant rise in thermal layer and associated boundary layer thickness. The solute Biot number is found to be an enhancing factor the concentration profile. Besides the three main profiles, the contour and density graphs are sketched for both the linear and non-linear cases. Furthermore, skin friction jumps for larger porosity and larger Forchheimer number. Both the heat and mass flux numbers receive a reduction for augmented values of the Forchheimer number. Heat flux enhances, while mass flux reduces, the strong effect of thermal Biot number. The considered problem could be helpful in any several industrial and engineering procedures, such as rolling, polymeric extrusion, continuously stretching done in plastic thin films, crystal growth, fiber production, and metallic extrusion, etc.

Impact of Convective Boundary Condition on Heat and Mass Transfer of Nanofluid Flow Over a Thin Needle Filled with Carbon Nanotubes

2020 ◽  
Vol 9 (4) ◽  
pp. 282-292
Author(s):  
P. Sreedevi ◽  
P. Sudarsana Reddy
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Finite Element Scheme ◽  
Convective Boundary ◽  
Non Linear ◽  
Layer Flow ◽  
Linear Differential

In the current study, we have scrutinized the sway of non-linear thermal radiation and Biot number on boundary layer flow along a continuously moving thin needle filled with carbon based nanotubes by considering water as regular fluid. The main system of partial differential equations is first reduced to the system of ordinary non-linear differential equations with the help of similarity conversion technique. The transmuted boundary layer ordinary differential equations are answered numerically by implementing Finite element scheme. The influence of pertinent constraints involved on heat, hydro-dynamic and solutal boundary layers are analysed in depth and the outcomes are revealed through plots. Moreover, the effect of these parameters on the values of Sherwood number, Nusselt number and skin-friction coefficient is also inspected and the results are exposed through tables. It is seen that velocity sketches depreciates with improving values of size of the needle parameter.

A Thermal Plume Model for the Convective Boundary Layer: Representation of Cumulus Clouds

2008 ◽  
Vol 65 (2) ◽  
pp. 407-425 ◽  
Author(s):  
Catherine Rio ◽  
Frédéric Hourdin
Keyword(s):  
Boundary Layer ◽  
Mass Flux ◽  
Convective Boundary Layer ◽  
Turbulent Transport ◽  
Thermal Plume ◽  
Cumulus Clouds ◽  
Convective Boundary ◽  
Near Surface ◽  
Plume Model ◽  
Surface Drying

Abstract The “thermal plume model,” a mass-flux scheme combined with a classical diffusive approach, originally developed to represent turbulent transport in the dry convective boundary layer, is extended here to the representation of cloud processes. The modified parameterization is validated in a 1D configuration against results of large eddy simulations (LES), as well as in a 3D configuration against in situ measurements, for a series of cases of dry and cloudy convective boundary layers. Accounting for coherent structures of the mixed layer with the mass-flux scheme improves the representation of the diurnal cycle of the boundary layer, particularly its progressive deepening during the day and the associated near-surface drying. Results also underline the role of the prescription of the mixing of air between the plume and its environment, and of submean-plume fluctuations.

scholarly journals Evaluation of PBL Parameterizations in WRF at Subkilometer Grid Spacings: Turbulence Statistics in the Dry Convective Boundary Layer

2016 ◽  
Vol 144 (3) ◽  
pp. 1161-1177 ◽  
Author(s):  
Hyeyum Hailey Shin ◽  
Jimy Dudhia
Keyword(s):  
Boundary Layer ◽  
Mass Flux ◽  
Weather Prediction ◽  
Wrf Model ◽  
Eddy Diffusivity ◽  
Weather Research And Forecasting ◽  
Turbulence Statistics ◽  
Convective Boundary ◽  
Large Eddies ◽  
Horizontal Grid

Abstract Planetary boundary layer (PBL) parameterizations in mesoscale models have been developed for horizontal resolutions that cannot resolve any turbulence in the PBL, and evaluation of these parameterizations has been focused on profiles of mean and parameterized flux. Meanwhile, the recent increase in computing power has been allowing numerical weather prediction (NWP) at horizontal grid spacings finer than 1 km, at which kilometer-scale large eddies in the convective PBL are partly resolvable. This study evaluates the performance of convective PBL parameterizations in the Weather Research and Forecasting (WRF) Model at subkilometer grid spacings. The evaluation focuses on resolved turbulence statistics, considering expectations for improvement in the resolved fields by using the fine meshes. The parameterizations include four nonlocal schemes—Yonsei University (YSU), asymmetric convective model 2 (ACM2), eddy diffusivity mass flux (EDMF), and total energy mass flux (TEMF)—and one local scheme, the Mellor–Yamada–Nakanishi–Niino (MYNN) level-2.5 model. Key findings are as follows: 1) None of the PBL schemes is scale-aware. Instead, each has its own best performing resolution in parameterizing subgrid-scale (SGS) vertical transport and resolving eddies, and the resolution appears to be different between heat and momentum. 2) All the selected schemes reproduce total vertical heat transport well, as resolved transport compensates differences of the parameterized SGS transport from the reference SGS transport. This interaction between the resolved and SGS parts is not found in momentum. 3) Those schemes that more accurately reproduce one feature (e.g., thermodynamic transport, momentum transport, energy spectrum, or probability density function of resolved vertical velocity) do not necessarily perform well for other aspects.

Effects of NP Shapes on Non-Newtonian Bio-Nanofluid Flow in Suction/Blowing Process with Convective Condition: Sisko Model

2020 ◽  
Vol 45 (2) ◽  
pp. 97-108 ◽  
Author(s):  
Mohamed R. Eid
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Biot Number ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Nanofluid Flow ◽  
Au Nps ◽  
Non Linear ◽  
Flow Similarity ◽  
The One

AbstractThe present mathematical simulation deals with the study of heat transfer characteristics of the shape of gold nanoparticles (Au-NPs) on blood flow past an exponentially stretching sheet using Sisko nanofluid taking into account the Biot number effect. Influences of non-linear thermal radiation and suction/injection are considered. The one-phase model is used to describe the Sisko nanofluid flow. Similarity variables are performed to convert the non-linear PDEs into ordinary ones. These equations together with initial and boundary conditions are provided in a non-dimensional form and then resolved numerically utilizing the fourth–fifth-order Runge–Kutta–Fehlberg (RKF45) technique. The attitude of diverse flow quantities is investigated and examined via the study of parameters like the Au-NP volume fraction, the non-linear stretching parameter, and the Biot number. It is found that the Biot number improves the heat transfer rate markedly. In the blowing case, the blade-shaped Au-NPs show the highest heat transfer rate; in the suction case, the contrary is observed for spherical Au-NPs.

scholarly journals Significance of Thermal Slip and Convective Boundary Conditions in Three Dimensional Rotating Darcy-Forchheimer Nanofluid Flow

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 741 ◽  
Author(s):  
Anum Shafiq ◽  
Ghulam Rasool ◽  
Chaudry Masood Khalique
Keyword(s):  
Activation Energy ◽  
Boundary Conditions ◽  
Skin Friction ◽  
Three Dimensional ◽  
Brownian Diffusion ◽  
Thermal Slip ◽  
Convective Boundary Conditions ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Forchheimer Number

This article is concerned with the nanofluid flow in a rotating frame under the simultaneous effects of thermal slip and convective boundary conditions. Arrhenius activation energy is another important aspect of the present study. Flow phenomena solely rely on the Darcy–Forchheimer-type porous medium in three-dimensional space to tackle the symmetric behavior of viscous terms. The stretching sheet is assumed to drive the fluid. Buongiorno’s model is adopted to see the features of Brownian diffusion and thermophoresis on the basis of symmetry fundamentals. Governing equations are modeled and transformed into ordinary differential equations by suitable transformations. Solutions are obtained through the numerical RK45-scheme, reporting the important findings graphically. The outputs indicate that larger values of stretching reduce the fluid velocity. Both the axial and transverse velocity fields undergo much decline due to strong retardation produced by the Forchheimer number. The thermal radiation parameter greatly raises the thermal state of the field. The temperature field rises for a stronger reaction within the fluid flow, however reducing for an intensive quantity of activation energy. A declination in the concentration profile is noticed for stronger thermophoresis. The Forchheimer number and porosity factors result in the enhancement of the skin friction, while both slip parameters result in a decline of skin friction. The thermal slip factor results in decreasing both the heat and mass flux rates. The study is important in various industrial applications of nanofluids including the electro-chemical industry, the polymer industry, geophysical setups, geothermal setups, catalytic reactors, and many others.

scholarly journals A Simple Model of a Balanced Boundary Layer Coupled to a Large-Scale Convective Circulation

2019 ◽  
Vol 76 (3) ◽  
pp. 837-849
Author(s):  
Robert J. Beare ◽  
Michael J. P. Cullen
Keyword(s):  
Boundary Layer ◽  
Simple Model ◽  
Surface Temperature ◽  
Mass Flux ◽  
Time Scale ◽  
Large Scale ◽  
Climate Models ◽  
Convective Boundary ◽  
Convective Circulation ◽  
Convective Mass Flux

Abstract Many simple models of large-scale tropical circulations do not include a frictional boundary layer. A simple model is presented where the convective circulation is coupled to the boundary layer convergence. In the free troposphere, convection and boundary layer heating try to relax to a moist adiabat from the local sea surface temperature with a time scale τc, but other processes act to maintain a weak temperature gradient. There is a mass balance between radiatively driven subsidence and the large-scale convective mass flux. For a prescribed Gaussian surface temperature, the model predicts a mass flux that varies as and a convective width proportional to its reciprocal. In the boundary layer, there can be significant horizontal temperature gradients and a balance between the pressure gradient and drag is assumed. Coupling between the two layers is mediated by the vertical velocity at the top of the boundary layer. The boundary layer constrains the circulation in three ways. First, it may lengthen the relaxation time scale compared to deep convection. Second, the evaporation in the nonconvecting region constrains the horizontal moisture advection. Third, it maintains a convective boundary layer where there is a convective mass flux; this condition cannot be satisfied if τc is too small or if the drag is too large, thus showing that such values are physically impossible. These results provide testable hypotheses concerning the physics and large-scale dynamics in weather and climate models.

Numerically framing the impact of magnetic field on nanofluid flow over a curved stretching surface with convective heating

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sanatan Das ◽  
Akram Ali ◽  
Rabindra Nath Jana
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Magnetic Parameter ◽  
Convective Boundary Condition ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Content Type ◽  
Curvature Parameter

Purpose Outstanding features such as thermal conductivity and superior electrical conductivity of nanofluids unfold a new window in the context of their extensive applications in engineering and industrial domains. The purpose of this study to simulate numerically the magneto-nanofluid flow and heat transfer over a curved stretching surface. Heat transport is explored in the presence of viscous dissipation. At the curved surface, the convective boundary condition is adopted. Three different nanoparticles, namely, copper, aluminium oxide and titanium dioxide are taken into consideration because of easily available in nature. Design/methodology/approach The basic flow equations are framed in terms of curvilinear coordinates. The modelled partial differential equations are transformed into a system of non-linear ordinary differential equations by means of appropriate similarity transformation. The subsequent non-linear system of equations is then solved numerically by using the Runge–Kutta–Felhberg method with the shooting scheme via bvp4c MATLAB built-in function. Impacts of various physical parameters on velocity, pressure and temperature distributions, local skin-friction coefficient, local Nusselt number and wall temperature are portrayed through graphs and tables followed by a comprehensive debate and physical interpretation. Findings Graphical results divulge that augmenting values of the magnetic parameter cause a decline in velocity profiles and stream function inside the boundary layer. The magnitude of the pressure function inside the boundary layer reduces for higher estimation of curvature parameter, and it is also zero when the curvature parameter goes to infinity. Furthermore, the temperature is observed in a rising trend with growing values of the magnetic parameter and Biot number. Practical implications This research study is very pertinent to the expulsion of polymer sheet and photographic films, metallurgical industry, electrically-conducting polymer dynamics, magnetic material processing, rubber and polymer sheet processing, continuous casting of metals, fibre spinning, glass blowing and fibre, wire and fibre covering and sustenance stuff preparing, etc. Originality/value Despite the huge amount of literature available, but still, very little attention is given to simulate the flow configuration due to the curved stretching surface with the convective boundary condition. Very few papers have been examined on this topic and found that its essence inside the boundary layer is not any more insignificant than on account of a stretching sheet. A numerical comparison with the published works is conducted to verify the accuracy of the present study.

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