Bandar Bin-Mohsin

Nonlinear radiation effects on MHD flow of nanofluid over a nonlinearly stretching/shrinking wedge

Flow over a moving wedge in a nanofluid is considered. Magneto-hydrodynamic effects are incorporated along with the passive control model of nanofluids that also takes into account the Brownian motion and thermophoresis effects. In energy equation, nonlinear radiation is taken into account. The equations governing the flow are transformed into a set of ordinary differential equations by employing suitable similarity transforms. The reduced system of equations is then solved numerically using a well-known Runge–Kutta–Fehlberg method coupled with shooting technique. Influence of parameters involved on velocity, temperature and concentration profiles is highlighted with the help of graphical aid. Expressions for skin friction coefficient, local Nusselt number and Sherwood number are obtained and presented graphically. A comparison between the passive and active control models is also provided with focus on the variations in Nusselt and Sherwood numbers.

Heat and mass transfer analysis for MHD flow of nanofluid inconvergent/divergent channels with stretchable walls using Buongiorno’s model

Abstract The present article investigates the flow, heat, and mass transfer in the convergent and divergent channels under the influence of magnetic field. The walls of the channel are also considered to be stretching/shrinking. Buongiorno’s model is used to formulate the problem for nanofluids. The equations governing the flow are transformed to a set of nonlinear ordinary differential equations by employing appropriate similarity transformations. Solution of the equations is obtained with the help of a useful and efficient numerical technique called the Runge–Kutta–Fehlberg method. Influence of the various emerging parameters on velocity, temperature and concentration profiles is described pictorially. Comprehensive discussions on the results obtained are provided. Backflow phenomena are observed for the stretching of divergent channel when angle opening and Re are increasing. This backflow can be controlled in two ways: one is by applying a strong magnetic field and other by shrinking the walls of the divergent channels. These results can be useful in various practical situations. Furthermore, expressions for skin friction coefficient, Nusselt and Sherwood numbers are obtained, and the variations in these quantities are analyzed graphically. Comparison of the results obtained here with the ones already existed in the literature confirms our solutions.

On biological population model of fractional order

In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this model, we establish a variety of exact solutions. To study the exact solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into corresponding partial differential equation and modified exp-function method is implemented to investigate the nonlinear equation. Graphical demonstrations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, unfailing, well-organized and pragmatic for fractional PDEs and could be protracted to further physical happenings.

A Study of Heat and Mass Transfer of Nanofluids Arising in Biosciences Using Buongiorno's Model

Flow in converging/diverging channels under the influence of external magnetic field is presented. The walls of the channels are taken to be stretching/shrinking. Buongiorno’s model is used to formulate the problem for nanofluids. It is to be highlighted that such models arise frequently in biosciences. The equations governing the flow are transformed to a set of nonlinear ordinary differential equations by employing appropriate similarity transformations. Two efficient techniques variational iteration method (VIM) and variation of parameters method (VPM) are employed to tackle the complexity and nonlinearity of the presented model. Comprehensive discussions on the results obtained are provided. Comparison of the obtained results with existing literature re-confirms the credibility of solution obtained via VIM and VPM.

A BIOCONVECTION MODEL FOR MHD FLOW AND HEAT TRANSFER OVER A POROUS WEDGE CONTAINING BOTH NANOPARTICLES AND GYROTATIC MICROORGANISMS

This paper is dedicated to analyze the flow of a nanofluid over a porous moving wedge in the presence of gyrotactic microorganisms. Magnetohydrodynamic (MHD) effects coupled with the viscous dissipation are taken into consideration. The passive control model is used to formulate the problem. Suitable similarity transforms are employed to transform the equations governing the flow into a set of ordinary differential equations. Solution of the transformed system is obtained numerically using a well-known Runge–Kutta–Fehlberg (RKF) method coupled with shooting technique. Influence of parameters involved on velocity, temperature, concentration and the motile microorganisms density profiles are highlighted using a graphical aid. Expressions for skin friction coefficient, Nusselt number, Sherwood number and the motile microorganisms density number are obtained and presented graphically. For the validity of results obtained, a comparison is also presented with the existing results.

Thermo-Diffusion And Diffuso-Thermo Effects On Mhd Squeezing Flow Between Parallel Disks

In this article, Magnetohydrodynamic (MHD) squeezing flow between two parallel disks is considered. The upper disk is taken to be solid and the lower one is permeable. Soret and Dufour effects are measured to explore the thermal-diffusion and diffusion-thermo effects. Governing PDEs are converted into system of ODEs with the support of suitable similarity transforms. Homotopy analysis method (HAM) has been employed to obtain the expressions for velocity, temperature and concentration profiles. Effects of different emerging parameters such as squeezing number S, Hartman number M, Prandtl number Pr, Eckert number Ec, dimensionless length δ and Schmidt number Sc on the flow are also discussed with the help of graphs for velocity, temperature and concentration. The local Nusselt and Sherwood numbers along with convergence of the series solutions are presented with the help of graphs. From the results obtained, we observed that the physical quantities like skin friction coefficient increases with increasing value of Hartmann number M in the blowing case (A 0). However, the rate of heat transfer at upper wall increases with increasing values of Dufour number Du and Soret number Sr for both the suction (A>0) and blowing flow (A 0) and blowing (A<0) cases. A numerical solution is obtained by employing Runge–Kutta method of order four (RK-4) to check the validity and reliability of the developed algorithm. A well agreement is found between both the solutions.

A finite element investigation of the flow of a Newtonian fluid in dilating and squeezing porous channel under the influence of nonlinear thermal radiation

The influence of nonlinear thermal radiation on the flow of a viscous fluid between two infinite parallel plates is investigated. The lower plate is solid, fixed and heated, while the upper is porous and capable of moving toward or away from the lower plate. The effects of nonlinear thermal radiation are incorporated in the energy equation by using Rosseland approximation. The similarity transformations have been used to obtain a system of ordinary differential equations. A finite element algorithm, known as Galerkin method, has been employed to obtain the solution of the resulting system of differential equations. It is observed that the radiation parameter Rd increases the temperature of the fluid in all the cases considered. Same is the case with temperature ratio parameter θw. The influence of the concerned parameters on the local rate of heat transfer is also displayed with the help of graphs.

Exact Controllability of Structural Acoustic Interactions with Variable Coefficients

This paper studies exact controllability properties of two coupled wave equations with variable coefficients by a Riemannian geometrical approach. One of the PDEs holds on the interior of a bounded open domain

Parametric resonances: from the Mathieu equation to QASER

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Fractal aggregation kinetics contributions to thermal conductivity of nano-suspensions in unsteady thermal convection

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