modified darcy’s law
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2021 ◽  
Author(s):  
BIPLAB BHATTACHARJEE ◽  
PRASUN CHAKRABORTI ◽  
KISHAN CHOUDHURY

Abstract In this article a mathematical model of single layered nano-fluid lubricated PJB (porous journal bearing) has been formulated. The nano-lubricant's impact on the efficiency of said journal bearing has been studied using modified Darcy's law and boundary conditions. The different nanoparticles often used as an additive in industrial lubricating oils improve their viscosity significantly. The brief description of dimensionless performance characteristics of the investigated bearing was obtained by the use of the nano-lubricant's modified Krieger-Dougherty viscosity model. The observations revealed that the output characteristics are substantially improved by using nano-lubricant. The present study was validated by comparing the findings of recently published data with micropolar fluid and was found to be completely compatible since data with nano-lubricant are still unavailable.


Unsteady flow of viscous stratified liquid in a channel with the porous bed has been studied in this paper. To study the effects of the stratification factor and slip parameter on the flow. We divide the entire flow region into two zones, zone 1 relates to the region between the impermeable upper plate and the lower one being the porous bed where the flow is governed by Navier Stokes equations, zone 2 is the porous region where the flow is governed by the modified Darcy’s law. In this paper, we have studied the effects of the stratification factor(η) and porosity factor(σ) on the velocity profile of the flow generated by an oscillating pressure gradient. Here we have taken an oscillating pressure gradient and applied Lighthill’s technique for obtaining the velocity profile of the flow.


Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 989-1002
Author(s):  
Aamir Farooq ◽  
Muhammad Kamran ◽  
Yasir Bashir ◽  
Hijaz Ahmad ◽  
Azeem Shahzad ◽  
...  

Abstract The purpose of this proposed investigation is to study unsteady magneto hydrodynamic (MHD) mixed initial-boundary value problem for incompressible fractional Maxwell fluid model via oscillatory porous rectangular duct. Considering the modified Darcy’s law, the problem is simplified by using the method of the double finite Fourier sine and Laplace transforms. As a limiting case of the general solutions, the same results can be obtained for the classical Maxwell fluid. Also, the impact of magnetic parameter, porosity of medium, and the impact of various material parameters on the velocity profile and the corresponding tangential tensions are illuminated graphically. At the end, we will give the conclusion of the whole paper.


2020 ◽  
pp. 100872
Author(s):  
M.Z. Kiyani ◽  
T. Hayat ◽  
I. Ahmad ◽  
M. Waqas ◽  
A. Alsaedi

2020 ◽  
Vol 10 (8) ◽  
pp. 3849-3863 ◽  
Author(s):  
Arifur Rahman ◽  
Salim Ahmed ◽  
M. Enamul Hossain ◽  
Fatema Akter Happy

Abstract The development of new scaling criteria for steam flooding process is presented in this paper. The mathematical development is done by using modified Darcy’s law, constitutive relationships, constraints, and the initial and boundary conditions. Dimensional and inspectional analyses are used to develop sets of dimensionless groups by incorporating rock and fluid memory concept. The variety of scaling criteria and their comparative advantages and limitations are discussed. Currently available scaling criteria development for steam flooding processes used the same fluid, same porous media in model and prototype. However, it requires a high-pressure model with different porous media, which causes difficulties in scaling properties, and therefore, largely depends on pressure and the porous media itself. In this paper, different methods are presented which permit scaling of all properties dependent on pressure or temperature by relaxing the requirements of geometric similarity. A set of relaxed scaling criteria is determined to satisfy a major mechanism. A comparative study of different approaches and their relative merits and demerits are discussed. Approach 2 (same fluids, same pressure drop, same porous medium, and geometric similarity) seems to be the most appropriate for the steam flooding process; however, gravitational forces cannot be scaled properly with this approach. Approach 3 (same fluids, same pressure drop, same porous media, and relaxed geometric similarity) is suitable for this process if the effect of transverse dispersion is considered negligible. Finally, a table is developed which can act as a guideline to select an appropriate approach that best scales a major mechanism for a specific steam flooding recovery process.


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