scholarly journals Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 449 ◽  
Author(s):  
Muhammad Asif ◽  
Sami Ul Haq ◽  
Saeed Islam ◽  
Tawfeeq Abdullah Alkanhal ◽  
Zar Khan ◽  
...  
Keyword(s):  
Shear Stress ◽  
Constitutive Equations ◽  
Integral Transformation ◽  
Rectangular Channel ◽  
Fourier Integral ◽  
Momentum Equation ◽  
Bottom Plate ◽  
Fractional Models ◽  
Physical Background ◽  
Time Fractional Derivative

In this article, unidirectional flows of fractional viscous fluids in a rectangular channel are studied. The flow is generated by the shear stress given on the bottom plate of the channel. The authors have developed a generalized model on the basis of constitutive equations described by the time-fractional Caputo–Fabrizio derivative. Many authors have published different results by applying the time-fractional derivative to the local part of acceleration in the momentum equation. This approach of the fractional models does not have sufficient physical background. By using fractional generalized constitutive equations, we have developed a proper model to investigate exact analytical solutions corresponding to the channel flow of a generalized viscous fluid. The exact solutions for velocity field and shear stress are obtained by using Laplace transform and Fourier integral transformation, for three different cases namely (i) constant shear, (ii) ramped type shear and (iii) oscillating shear. The results are plotted and discussed.

scholarly journals Exact Solutions of Brinkman Type Fluid Between Side Walls Over an Infinite Plate

2018 ◽  
Author(s):  
Saeed Islam ◽  
Muhammad Asif ◽  
Samiul Haq
Keyword(s):  
Integral Transformation ◽  
Infinite Plate ◽  
Fourier Integral ◽  
Bottom Plate ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Special Cases ◽  
Depth Analysis ◽  
Side Walls ◽  
Oscillating Shear Stress

In this paper Brinkman type fluid over an infinite plate between side walls is being investigated. The flow is generated by oscillating shear stress of the bottom plate and the solutions are obtained by using Fourier integral transformation. The obtained results are presented in steady and transient states for both sin and cos shear stresses. The general solutions are reduced to some special cases corresponding, namely to the Brinkman type fluid over an infinite plate and flow of a Newtonian viscous fluid. Graphical illustrations are carried out to have in depth analysis of the involved physical parameters

scholarly journals Assessing Machine Learning versus a Mathematical Model to Estimate the Transverse Shear Stress Distribution in a Rectangular Channel

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 596
Author(s):  
Babak Lashkar-Ara ◽  
Niloofar Kalantari ◽  
Zohreh Sheikh Khozani ◽  
Amir Mosavi
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Fuzzy Inference ◽  
Rectangular Channel ◽  
Tsallis Entropy ◽  
Shear Stress Distribution ◽  
Data Series ◽  
Shear Stresses ◽  
Inference System ◽  
Aspect Ratios

One of the most important subjects of hydraulic engineering is the reliable estimation of the transverse distribution in the rectangular channel of bed and wall shear stresses. This study makes use of the Tsallis entropy, genetic programming (GP) and adaptive neuro-fuzzy inference system (ANFIS) methods to assess the shear stress distribution (SSD) in the rectangular channel. To evaluate the results of the Tsallis entropy, GP and ANFIS models, laboratory observations were used in which shear stress was measured using an optimized Preston tube. This is then used to measure the SSD in various aspect ratios in the rectangular channel. To investigate the shear stress percentage, 10 data series with a total of 112 different data for were used. The results of the sensitivity analysis show that the most influential parameter for the SSD in smooth rectangular channel is the dimensionless parameter B/H, Where the transverse coordinate is B, and the flow depth is H. With the parameters (b/B), (B/H) for the bed and (z/H), (B/H) for the wall as inputs, the modeling of the GP was better than the other one. Based on the analysis, it can be concluded that the use of GP and ANFIS algorithms is more effective in estimating shear stress in smooth rectangular channels than the Tsallis entropy-based equations.

scholarly journals Pulsating Flow of an Ostwald—De Waele Fluid between Parallel Plates

Water ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 932
Author(s):  
Rodrigo González ◽  
Aldo Tamburrino ◽  
Andrea Vacca ◽  
Michele Iervolino
Keyword(s):  
Shear Stress ◽  
Analytical Solution ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Momentum Equation ◽  
Parallel Plates ◽  
Analytical Computation ◽  
Pulsatile Pressure ◽  
Pulsatile Pressure Gradient

The flow between two parallel plates driven by a pulsatile pressure gradient was studied analytically with a second-order velocity expansion. The resulting velocity distribution was compared with a numerical solution of the momentum equation to validate the analytical solution, with excellent agreement between the two approaches. From the velocity distribution, the analytical computation of the discharge, wall shear stress, discharge, and dispersion enhancements were also computed. The influence on the solution of the dimensionless governing parameters and of the value of the rheological index was discussed.

Casson Model of MHD Flow of SA-Based Hybrid Nanofluid Using Caputo Time-Fractional Models

2019 ◽  
Vol 390 ◽  
pp. 83-90 ◽  
Author(s):  
Sidra Aman ◽  
Syazwani Mohd Zokri ◽  
Zulkhibri Ismail ◽  
Mohd Zuki Salleh ◽  
Ilyas Khan
Keyword(s):  
Fractional Derivatives ◽  
Volume Fraction ◽  
Vertical Channel ◽  
Mhd Flow ◽  
Hybrid Nanoparticles ◽  
Hybrid Nanofluid ◽  
Caputo Fractional Derivatives ◽  
Fractional Models ◽  
Hybrid Nanofluids ◽  
Time Fractional Derivative

In this paper MHD flow of Casson hybrid nanofluids are investigated with Caputo time-fractional derivative. Alumina (Al) and copper (Cu) are used as nanoparticles in this study with heat, mass transfer and MHD flow over a vertical channel in a porous medium. The problem is modeled using Caputo fractional derivatives and thermophysical properties of hybrid nanoparticles. The influence of concerned parameters is investigated physically and graphically on the heat, concentration and flow. The effect of volume fraction on thermal conductivity of hybrid nanofluids is observed.

Experimental and Numerical Investigation on Natural Convection in Horizontal Channels Partially Filled With Aluminium Foam and Heated From Below

2016 ◽  
Author(s):  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Sergio Nardini ◽  
Alessandra Diana
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Wall Temperature ◽  
Aluminum Foam ◽  
Rectangular Channel ◽  
Lower Surface ◽  
Heated Wall ◽  
Working Fluid ◽  
Bottom Plate ◽  
Uniform Heat Flux

Natural convection in horizontal rectangular channel without or with aluminum foam is experimentally and numerically investigated. In the case with aluminum foam the channel is partially filled. In both cases, the bottom wall of the channel is heated at a uniform heat flux and the upper wall is unheated and it is not thermally insulated to the external ambient. The experiments are performed with working fluid air. Different values of wall heat flux at lower surface are considered in order to obtain some Grashof numbers and different heated wall temperature distributions. Two different aluminum foams are considered in the experimental investigation, one from “M-pore”, with 10 and 30 pore per inch (PPI), and the other one from “ERG”, with 10, 20 and 40 PPI. The numerical simulation is carried out by a simplified two-dimensional model. It is found that the heat transfer is better when the channel is partially filled and the emissivity is low, whereas the heated wall temperature values are higher when the channel is partially filled and the heated bottom plate has high emissivity. The investigation is achieved also by flow visualization which is carried out to identify the main flow shape and development and the transition region along the channel. The visualization of results, both experimental and numerical, grants the description of secondary motions in the channel.

scholarly journals Studying Disturbance Wave Velocity and Wall Shear Stress of Vertical Upward Annular Flow in Narrow Rectangular Channel

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Antai Liu ◽  
Changqi Yan ◽  
Fuqiang Zhu ◽  
Haifeng Gu ◽  
Suijun Gong
Keyword(s):  
Experimental Data ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Wave Velocity ◽  
Annular Flow ◽  
Rectangular Channel ◽  
Disturbance Wave ◽  
New Correlation ◽  
Current Experimental Data ◽  
Wall Shear

As two important parameters, the velocity of disturbance wave and the wall shear stress in annular flow are very important to solve the closed equations of the mechanical model for annular flow. In this study, the disturbance wave velocity and wall shear stress of annular flow in a vertical narrow rectangular channel with a cross section of 70 mm × 2 mm were studied. According to the experimental results, it is found that the wave velocity and wall shear stress of disturbance wave increase with increasing gas phase velocity and liquid phase velocity. Also, existing correlations for predicting the velocity of disturbance wave were summarized and evaluated using the current experimental data. A new correlation for wall shear stress based on the disturbance wave velocity has been proposed. Compared with the existing correlation for predicting wall shear stress, this new correlation can well predict the current experimental data and MAPE is only 7.32%.

scholarly journals Consideration of wear in plane contact of rectangular punch and elastic half-plane

2019 ◽  
pp. 138-141
Author(s):  
V. M. Onyshkevych ◽  
G. T. Sulym
Keyword(s):  
Half Plane ◽  
Integral Transformation ◽  
Initial Approximation ◽  
Vertical Displacement ◽  
Fourier Integral ◽  
Mean Value ◽  
Theory Of Elasticity ◽  
Contact Stresses ◽  
Dual Integral Equations ◽  
Plane Contact

The plane contact problem on wear of elastic half-plane by a rigid punch has been considered. The punch moves with constant velocity. Arising thermal effects are neglected because the problem is investigated in stationary statement. In this case the crumpling of the nonhomogeneities of the surfaces and abrasion of half-plane take place. Out of the punch the surface of half-plane is free of load. The solution for problem of theory of elasticity is constructed by means of Fourier integral transformation. Contact stresses are found in Fourier series which coefficients satisfy the dual integral equations. It leads to the system of nonlinear algebraical equations for unknown coefficients by a method of collocations. This system is reduced to linear system in the partial most interesting cases for computing of maximum and minimum wear. The iterative scheme is considered for investigation of other nonlinear cases, for initial approximation the mean value of boundary cases is used. The evolutions of contact stresses, wear and abrasion in the time are given. For both last cases increase or invariable of vertical displacement correspondently is obtained. In the boundary cases coincidence of results with known is obtained.

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