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 Conditions of cracking of a stringer

2005 ◽  
Vol 2005 (3) ◽  
pp. 377-389 ◽  
Author(s):  
D. I. Bardzokas ◽  
G. I. Sfyris
Keyword(s):  
Contact Problem ◽  
Brittle Failure ◽  
Integral Transformation ◽  
Infinite Plate ◽  
Fourier Integral ◽  
Contact Stresses ◽  
Accurate Solution ◽  
Theory And Practice ◽  
External Loading ◽  
Distributed Forces

In the limits of brittle failure of materials, we investigate the problem of possible cracking of an infinite stringer on the boundary of an elastic half-infinite plate. The plate is exposed to tensioning by uniformly distributed forces, and also to contact stresses due to application of forces on the stringer. The accurate solution of a contact problem of interaction of an infinitely continuous stringer is constructed. With the help of this solution, we formulate the condition of cracking of a stringer and the necessary restrictions for external loading, which provide the contacts of a broken stringer with a plate without propagation of a crack inside the stringer. The problem considered here is of interest for theory and practice. We firstly formulate the modified problem of E. Melan and with the help of Fourier integral transformation, we construct its acoustic solution and then formulate the condition of cracking of an infinite stringer. After that, reveal the necessary restrictions on external loadings, which provide the contact of the failed stringer with a plate without propagation of the crack inside the plate.

scholarly journals Convection heat mass transfer and MHD flow over a vertical plate with chemical reaction, arbitrary shear stress and exponential heating

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sehra ◽  
Sami Ul Haq ◽  
Syed Inayat Ali Shah ◽  
Kottakkaran Sooppy Nisar ◽  
Saeed Ullah Jan ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Vertical Plate ◽  
Mhd Flow ◽  
Convection Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Transform Method ◽  
Molecular Diffusivity ◽  
Special Cases ◽  
Infinite Vertical Plate

AbstractThe present research article is directed to study the heat and mass transference analysis of an incompressible Newtonian viscous fluid. The unsteady MHD natural convection flow over an infinite vertical plate with time dependent arbitrary shear stresses has been investigated. In heat and mass transfer analysis the chemical molecular diffusivity effects have been studied. Moreover, the infinite vertical plate is subjected to the phenomenon of exponential heating. For this study, we formulated the problem into three governing equations along with their corresponding initial and boundary conditions. The Laplace transform method has been used to gain the exact analytical solutions to the problem. Special cases of the obtained solutions are investigated. It is noticed that some well-known results from the published literature are achieved from these special cases. Finally, different physical parameters’ responses are investigated graphically through Mathcad software.

Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Corina Fetecau
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Viscous Fluid ◽  
Fourier Transforms ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Unsteady Motion ◽  
Side Walls ◽  
Oscillating Shear Stress ◽  
Similar Solutions

AbstractThe velocity field corresponding to the unsteady motion of a viscous fluid between two side walls perpendicular to a plate is determined by means of the Fourier transforms. The motion of the fluid is produced by the plate which after the time t = 0, applies an oscillating shear stress to the fluid. The solutions that have been obtained, presented as a sum of the steady-state and transient solutions satisfy the governing equation and all imposed initial and boundary conditions. In the absence of the side walls they are reduced to the similar solutions corresponding to the motion over an infinite plate. Finally, the influence of the side walls on the fluid motion, the required time to reach the steady-state, as well as the distance between the walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence, are established by means of graphical illustrations.

Effects of Side Walls on the Motion Induced by an Infinite Plate that Applies Shear Stresses to an Oldroyd-B Fluid

2013 ◽  
Vol 68 (12) ◽  
pp. 725-734 ◽  
Author(s):  
Mehwish Rana ◽  
Nazish Shahid ◽  
Azhar Ali Zafar
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Integral Transforms ◽  
Second Grade ◽  
Shear Stresses ◽  
Transient Solutions ◽  
Side Walls ◽  
Similar Solutions

Unsteady motions of Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies two types of shears to the fluid are studied using integral transforms. Exact solutions are obtained both for velocity and non-trivial shear stresses. They are presented in simple forms as sums of steady-state and transient solutions and can easily be particularized to give the similar solutions for Maxwell, second-grade and Newtonian fluids. Known solutions for the motion over an infinite plate, applying the same shears to the fluid, are recovered as limiting cases of general solutions. Finally, the influence of side walls on the fluid motion, the distance between walls for which their presence can be neglected, and the required time to reach the steady-state are graphically determined.

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 Time Fractional Analysis of Channel Flow of Couple Stress Casson Fluid using Fick’s and Fourier’s Laws

2021 ◽  
Author(s):  
Shafiq Ahmad ◽  
Sami Ul Haq ◽  
Farhad Ali ◽  
Ilyas Khan ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Channel Flow ◽  
Couple Stress ◽  
Integral Transformation ◽  
Physical Phenomenon ◽  
Classical Model ◽  
Fourier Integral ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fractional Model ◽  
Stress Parameter

Abstract This study aim to examine the channel flow of a couple stress Casson fluid. The flow is generated due to the motion of the plate at y = o, while the plate at y = d is at rest. This physical phenomenon is derived in terms of partial differential equations. The subjected governing PDE’s are non-dimensionalized with the help of dimensionless variables. The dimensionless classical model is generalized by transforming it to the time fractional model using Fick’s and Fourier’s Laws. The general fractional model is solved by applying the Laplace and Fourier integral transformation. Furthermore, the parametric influence of various physical parameters like Casson parameter, couple stress parameter, Grashof number, Schmidt number and Prandtl number on velocity, temperature, and concentration distributions is shown graphically and discussed. The heat transfer rate, skin friction, and Sherwood number are calculated and presented in tabular form. It is worth noting that the increasing values of the couple stress parameter λ deaccelerate the velocity of Couple stress Casson fluid.

scholarly journals Sliding Contact Between a Cylindrical Punch and a Graded Half-Plane With an Arbitrary Gradient Direction

2015 ◽  
Vol 82 (4) ◽  
Author(s):  
Chen Peijian ◽  
Chen Shaohua ◽  
Peng Juan
Keyword(s):  
Half Plane ◽  
Integral Transformation ◽  
Contact Region ◽  
Fourier Integral ◽  
Graded Materials ◽  
Special Cases ◽  
Cylindrical Punch ◽  
The Moment ◽  
Gradient Variation ◽  
Stable Sliding

Contact behavior of a rigid cylindrical punch sliding on an elastically graded half-plane with shear modulus gradient variation in an arbitrary direction is investigated. The governing partial differential equations and the boundary conditions are achieved with the help of Fourier integral transformation. As a result, the present problem is reduced to a singular integral equation of the second kind, which can be solved numerically. Furthermore, the presently general model can be well degraded to special cases of a lateral gradient half-plane and a homogeneous one. Normal stress in the contact region is predicted with different material parameters, which is usually used to estimate the possibility of surface crack initiation. The moment that is needed to ensure stable sliding of the cylindrical punch on the contact surface is further predicted. The result in the present paper should be helpful for the design of novel graded materials with surfaces of strong abrasion resistance.

scholarly journals Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 334
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Exponential Dependence ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Pressure Dependent Viscosity ◽  
Laplace Transform Technique ◽  
Dependent Viscosity

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

scholarly journals Heat Transfer in Nanomaterial Suspension (CuO and Al2O3) Using KKL Model

Coatings ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 417
Author(s):  
Muhammad Awais ◽  
Saeed Ehsan Awan ◽  
Muhammad Asif Zahoor Raja ◽  
Muhammad Nawaz ◽  
Wasim Ullah Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Angular Momentum ◽  
Diffusion Theory ◽  
Shear Thickening ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Nonlinear Conservation Laws ◽  
Error Analyses ◽  
Flexible Surface ◽  
Flux Model

Novel nonlinear power-law flux models were utilized to model the heat transport phe-nomenon in nano-micropolar fluid over a flexible surface. The nonlinear conservation laws (mass, momentum, energy, mass transport and angular momentum) and KKL cor-relations for nanomaterial under novel flux model were solved numerically. Computed results were used to study the shear-thinning and shear-thickening nature of nano pol-ymer suspension by considering n-diffusion theory. Normalized velocity, temperature and micro-rotation profiles were investigated under the variation of physical parame-ters. Shear stresses at the wall for nanoparticles (CuO and Al2O3) were recorded and dis-played in the table. Error analyses for different physical parameters were prepared for various parameters to validate the obtained results.

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

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