scholarly journals Mixed Convection of Silica–Molybdenum Disulphide/Water Hybrid Nanoliquid over a Rough Sphere

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 236
Author(s):  
Prabhugouda M. Patil ◽  
Hadapad F. Shankar ◽  
Mikhail A. Sheremet
Keyword(s):  
Temperature Distribution ◽  
Velocity Distribution ◽  
Energy Transport ◽  
Finite Difference Approximation ◽  
Maximum Temperature ◽  
Difference Approximation ◽  
Hybrid Nanofluid ◽  
Molybdenum Disulphide ◽  
Shaped Nanoparticles ◽  
Rough Sphere

A steady combined convective motion over a rough sphere with hybrid nanoparticles is analyzed. We have considered silica (SiO2) and molybdenum disulphide (MoS2) nanoadditives which are added in H2O to form MoS2–SiO2/H2O hybrid nanoliquid. The partial differential equations describing the boundary layer flow characteristics are reduced into non-dimensional form with appropriate non-similar reduction. It should be noted that the governing equations have been written using the conservation laws of mass, momentum and energy. These considered equations allow simulating the analyzed phenomenon using numerical techniques. Implicit finite difference approximation and technique of Quasilinearization are utilized to work out the dimensionless control equations. The influence of various physical characteristics included in this challenge, such as the velocity fields and temperature patterns, is investigated. The study of border gradients is performed, which deals with the skin friction and energy transport strength. The plots of computational outcomes are considered, which ascertain that velocity distribution reduces, whilst coefficient of friction at the surface, energy transport strength and temperature distribution augment for enhancing values of hybrid nanofluid. For enhancing magnitude of combined convection parameter, dimensionless velocity distribution, surface drag coefficient and energy transport strength enhance, while temperature distribution diminishes. High impact of hybrid nanofluid on energy transport strength and the surface friction compared to the host liquid and mono nanofluid in presence/absence of surface roughness is shown. Velocity distribution enhances for rising values of velocity ratio parameter. Enhancing values of frequency parameter rise the friction at the surface and energy transport strength. It is also examined that the hybrid nanofluid has a maximum temperature for the blade-shaped nanoparticles and has a low temperature for the spherical-shaped nanoparticles.

scholarly journals Natural Convection Numeric Simulation on Metal Freezing Using Differential Method

2017 ◽  
Vol 16 (2) ◽  
Author(s):  
Heri Suprianto ◽  
Eko Prasetyo Budiana ◽  
Purwadi Joko Widodo
Keyword(s):  
Fluid Flow ◽  
Natural Convection ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Governing Equation ◽  
Solidification Process ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Flow Profile ◽  
Metal Solidification

The research of modeling of natural convection in metal solidification process with finite different method was conducted to determine temperature distribution and fluid flow profil with variations value Rayleigh number. The research conducted by solving governing equation of natural convection with finite difference approximation. Governing equation of natural convection consist of continuity equation, momentum equations, and energy equation. The ADI (Alternating Directional Implicit) method was used to discriteze for governing equation of natural convection. Finite difference method was written in Fortran language whereas the temperature distribution and fluid flow profile were visualized with Matlab software. The results of this research was validated by comparing the results obtained with Rajiv Sampath research. Comparison of the results of research showed good agreement. The result showed that solidification process occurs faster at Ra 10^4 compared with 10^5 and 10^6

Simulation Model for Calculating Pavement Temperatures Including Maximum Temperature

2000 ◽  
Vol 1699 (1) ◽  
pp. 134-141 ◽  
Author(s):  
Åke Hermansson
Keyword(s):  
Heat Transfer ◽  
Solar Radiation ◽  
Simulation Model ◽  
Wind Velocity ◽  
Air Temperature ◽  
Input Data ◽  
Finite Difference Approximation ◽  
Maximum Temperature ◽  
Difference Approximation ◽  
Pavement Surface

A simulation model has been developed to calculate the temperatures of asphalt concrete during summer. Input data to the simulation model are hourly values for solar radiation, air temperature, and wind velocity. Longwave radiation incident to and outgoing from the pavement surface is calculated from the air and pavement surface temperatures, respectively. The portion of the incident shortwave radiation absorbed by the pavement surface is calculated from the albedo of the surface. By means of a finite difference approximation of the heat transfer equation, the temperatures are calculated under the surface. Apart from radiation and heat transfer, convection losses from the pavement surface are also calculated depending on wind velocity, air temperature, and surface temperature. The formulas used for the calculation of radiation and the simulation model as a whole are validated by comparison with measurements, showing good agreement. A method for the calculation of direct solar radiation from a clear sky, at an arbitrary location and time, is used to create input data to the simulation model in order to calculate maximum pavement temperatures. The formulas used with Superpave to calculate maximum pavement temperatures are based on the assumption that there is an equilibrium when a maximum temperature is reached. Such an equilibrium assumption can be strongly questioned, and its consequences are discussed.

Nanoscale energy transport of inclined magnetized 3D hybrid nanofluid with Lobatto IIIA scheme

Heat Transfer ◽  
2021 ◽  
Author(s):  
Assad Ayub ◽  
Adil Darvesh ◽  
Gilder C. Altamirano ◽  
Zulqurnain Sabir
Keyword(s):  
Energy Transport ◽  
Hybrid Nanofluid

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

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