Abdul Shakeel

Bio: Abdul Shakeel is an academic researcher from National University of Computer and Emerging Sciences. The author has contributed to research in topics: Mechanics & Fundamental solution. The author has an hindex of 2, co-authored 2 publications receiving 23 citations.

Solutions with Wright functions for time fractional convection flow near a heated vertical plate

Abstract: We investigate the unsteady flow of a viscous fluid near a vertical heated plate. The momentum and energy equations are considered as fractional differential equations with respect to the time t. Solutions of the initial-boundary values problem are determined by means of the Laplace transform technique and are represented by means of the Wright functions. The fundamental solution for the temperature field is obtained. This allows obtaining the temperature field for different conditions on the wall temperature. A numerical case is analyzed in order to obtain information regarding the influence of the fractional parameters on the temperature and velocity fields. Some physical aspects of the fluid behavior are presented by graphical illustrations.

Flows with Slip of Oldroyd-B Fluids over a Moving Plate

Abstract: A general investigation has been made and analytic solutions are provided corresponding to the flows of an Oldroyd-B fluid, under the consideration of slip condition at the boundary. The fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. The adequate integral transform approach is employed to find analytic solutions for the velocity field. Solutions for the flows corresponding to Maxwell fluid, second-grade fluid, and Newtonian fluid are also determined in both cases, namely, flows with slip on the boundary and flows with no slip on the boundary, respectively. Some of our results were compared with other results from the literature. The effects of several emerging dimensionless and pertinent parameters on the fluid velocity have been studied theoretically as well as graphically in the paper.

Rheology of peristaltic flow in couple stress fluid in an inclined tube: Heat and mass transfer analysis

Abstract: The recent investigations ensure that the effect of an endoscope on the peristaltic flow is very important for medical diagnosis and it has many clinical applications such as gastric juice motion in the small intestine when an endoscope is inserted through it. Therefore, we have studied the problem of peristaltic flow with heat and mass transfer through the gap between coaxial inclined tubes where the inner tube is rigid and the outer tube has sinusoidal wave traveling down its wall. The inner tube fulfilled the slip condition while the outer tube has a no-slip condition. The lubrication approximation theory is utilized to simplify the normalized equations. The perturbation procedure is employed to concede the results for the pressure gradient and velocity field, whereas exact outcomes are established for the energy and concentration fields. Frictional forces and pressure rise per wavelength are calculated numerically. The impacts of embedded parameters are portrayed through graphs. It is found that fluid velocity reduces by increasing the couple stress parameter however the inverse effect is noted for the slip parameter. Furthermore, better pumping is viewed in the vertical tube as compared to the horizontal tube. A validity of perturbation solutions for velocity distribution is made with the finite element method and an admirable comparison is also noticed with previously published results.

Interaction of nanoparticles with micro organisms under Lorentz force in a polymer liquid with zero mass flux

Abstract: Rheological fluids enduring bio convection are gaining great attention in modern day industrial, technological and several manufacturing industries. Such flows are evident in chemical and mining industry, biomedical flows, and many other fields of science and engineering. Among the many other rheolgical liquids, Sutterby fluid model is significant due to its characteristics of Pseudoplastic and dilatant fluids. It portrays dilute polymer solutions, which has numerous applications in industrial practice. In this theoretical research two-dimensional hydromagnetic stagnation point flow of Sutterby bio convective fluid through an elastic surface has been discussed. The mathematical model of governed problem is transformed into a set of ordinary differential equations using similarity transformation. These nonlinear coupled ordinary differential equations are handled by using shooting scheme (numerical technique). Influence of all physical constraints for temperature, concentration of gyrotactic microorganism and velocity profiles are presented graphically. Local heat & mass flux and density of microorganisms (Physical quantities of interest) are presented numerically through bar charts.

Unsteady flow of generalized Casson fluid with fractional derivative due to an infinite plate

Abstract: The Caputo time-fractional derivative is introduced in the constitutive model of a generalized Casson fluid which is moving over an infinite, oscillating flat plate. Exact solutions for the fluid velocity and shear stress are obtained using the Laplace transform method. Closed forms of solutions are written in terms of Wright functions. The obtained solutions can be easily particularized for ordinary Casson fluid, viscous fluid with fractional derivative and ordinary viscous fluid. Numerical simulations are carried out for fractional parameter and Casson fluid parameter and results are shown in graphical illustrations.

Solutions with special functions for time fractional free convection flow of Brinkman-type fluid

Abstract: The objective of this paper is to report the combined effect of heat and mass diffusion on time fractional free convectional incompressible flow of Brinkman-type fluid over an oscillating plate in the presence of first-order chemical reaction. The Laplace transform has been used to obtain the exact solutions for the fractional-order distributions. Exact expressions for temperature, concentration and velocity have been presented in terms of special functions. For instance, we presented temperature in terms of Wright function, concentration in the form of Fox-H function and velocity in terms of Mittag-Leffler and general Wright functions. The effects of various physical parameters on the fluid motion are sketched and discussed graphically. The present solutions have been reduced by taking one or more parameters approaching to zero and an excellent agreement is observed with the published work. The numerical results for skin-friction, Nusselt and Sherwood numbers have been shown in tabular form.

Functionality of circuit via modern fractional differentiations

Abstract: The significance of the modern fractional derivatives containing the singular kernel with locality and the non-singular kernel with non-locality have recently diverted the researchers because of the numerical or experimental analyses on the behavior between a system conservative and dissipative and the lack of fractionalized analytic methods. This study investigates the effects of modern fractional differentiation on the RLC electrical circuit via exact analytical approach. The modeling of governing differential equation of RLC electrical circuit has been fractionalized through three types of fractional derivatives namely Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives based on the range as $$0 \le \alpha \le 1,\,\,0 \le \beta \le 1,\,\,0 \le \gamma \le 1$$ respectively. The RLC electrical circuit is observed for exponential, periodic and unit step sources via three classified modern fractional derivatives. The exact analytical solutions have been investigated by invoking mathematical Laplace transforms and presented in terms of convolutions product and special function namely Fox-H function. The Comparative mathematical analysis of RLC electrical circuit is based on Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives which exhibit the presence of heterogeneities in the electrical components causing irreversible dissipative effects. Finally, the several similarities and differences for the periodic and exponential sources have been rectified on the basis of the Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives for the current.

Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium

Abstract: This research article investigates that how heat flow changes versus temperature or time on the rheology of magnetohydrodynamic Brinkman fluid embedded in porous medium for the oscillations of heated plate. A fractional approach namely Caputo–Fabrizio fractional operator is applied for developing the governing partial differential equations of Brinkman fluid flow. The fractional governing partial differential equations have been modeled for temperature distribution, mass concentration and velocity field along with imposed initial and boundary conditions. The solutions are obtained by integral transforms and presented in special and elementary functions. In the limiting sense, the analytical solutions are particularized in the presence and absence of heat and mass transfer, magnetic field and porous medium. The parametric graphs have been depicted for the influence of different embedded rheological parameters on fluid flow. The results show few interesting differences and similarities by comparative analysis for fractional and ordinary Brinkman fluid flow, such as physically higher Prandtl (Pr) number that leads to decay thermal diffusivity which results in the reduction in thermal field; this means that better quality of production can be achieved through proper choice of Prandtl (Pr) and Schmidt (Sc) numbers.

Heat transfer flow of Maxwell hybrid nanofluids due to pressure gradient into rectangular region.

Abstract: In this work, influence of hybrid nanofluids (Cu and $$\mathrm{Al}_{2}\mathrm{O}_{3}$$ ) on MHD Maxwell fluid due to pressure gradient are discussed. By introducing dimensionless variables the governing equations with all levied initial and boundary conditions are converted into dimensionless form. Fractional model for Maxwell fluid is established by Caputo time fractional differential operator. The dimensionless expression for concentration, temperature and velocity are found using Laplace transform. As a result, it is found that fluid properties show dual behavior for small and large time and by increasing volumetric fraction temperature increases and velocity decreases respectively. Further, we compared the Maxwell, Casson and Newtonian fluids and found that Newtonian fluid has greater velocity due to less viscosity. Draw the graphs of temperature and velocity by Mathcad software and discuss the behavior of flow parameters and the effect of fractional parameters.