Complexiton solutions for complex KdV equation by optimal Homotopy Asymptotic Method

Shutaywi

et al. 2020

Sci Rep

nanotechnology research has a huge impact upon biomedicine and at the forefront of this area are micro and nano devices that use active/controlled motion. In this connection, it is focus to investigate steady three dimensional rotating flow with heat and mass transfer incorporating gyrotactic microorganisms. Buongiorno's nanofluid formulation is followed for thermophoresis and Brownian motion, porous space, Arrhenius activation energy and binary chemical reaction with some other effects. An enhanced analytical method is applied to solve the nondimensional equations. The nondimensional parameters effects on the fields of velocity, temperature, nanoparticles concentration and gyrotactic microorganisms concentration are shown graphically. Velocity decreases while temperature and nanoparticles concentration increase with magnetic field strength. Gyrotatic microorganisms motion becomes slow with rotation parameter. Due to rotation, the present problem can be applied in microbial fuel cells, food processing, microbiology, biotechnology and environmental sciences, electric power generating and turbine systems, computer disk drives, mass spectromentries and jet motors.

Section: Computation Methodologymentioning

confidence: 99%

A comprehensive study to the assessment of Arrhenius activation energy and binary chemical reaction in swirling flow

Shutaywi

et al. 2020

Sci Rep

“…Figure 10 2 each in Eqs. (9) and (10) respectively. So in non-dimensional form (M) of these terms does a lot to motion and heating.…”

Section: Resultsmentioning

confidence: 99%

“…′ Illustration of different mathematical letters and notations used in Eqs. (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) are given in Table 1. Substituting the values from Eq.…”

Section: Methodsmentioning

confidence: 99%

“…Sankar et al 9 documented a report on the double diffusive convection in a vertical annulus filled with a fluid-saturated porous medium accompanying the effects of discrete source of heat and solute on the fluid flow, heat and mass transfer rates in which the location of stronger flow circulation is independent of the higher heat and mass transfer rates in the porous region. Zuhra et al 10 used the OHAM solution to develop the special form of initial value problems to complex KdV equation in which three different types of semi analytic complextion solutions from complex KdV equation have been achieved. Sankar et al 11 carried out the work on Brinkman extended Darcy equation for the natural convection heat transfer due to two discrete heat sources showing that the bottom heater is found to dissipate higher heat transfer compared to top heater.…”

mentioning

confidence: 99%

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Entropy generation in bioconvection nanofluid flow between two stretchable rotating disks

Bhaumik

et al. 2020

Sci Rep

Buongiorno's nanofluid model is followed to study the bioconvection in two stretchable rotating disks with entropy generation. Similarity transformations are used to handle the problem equations for nondimensionality. For the simulation of the modeled equations, Homotopy Analysis Method is applied. The biothermal system is explored for all the embedded parameters whose effects are shown through different graphs. There exists interesting results due to the effects of different parameters on different profiles. Radial velocity decreases with increasing stretching and magnetic field parameters. Temperature increases with Brownian motion and thermophoresis parameters. Nanoparticles concentration decreases on increasing Lewis number and thermophoresis parameter while motile gyrotactic microorganisms profile increases with increasing Lewis and Peclet numbers. Convergence of the solution is found and good agreement is obtained when the results are compared with published work. Natural convection has an outstanding applications in daily life. These applications are exist in petrochemical processes, cooling of electronic components, geothermal engineering, crystal growth processes, in the annular gap between the rotor and stator, thermal insulation system, food industry, growth of single silicon crystals, packed bed chemical reactors, grain storage installations, rotating systems, porous heat exchangers, fuel cells, solar ponds etc. Researchers paid extensive attention to work on convection. Venkatachalappa et al. 1 performed a study to analyze the role of rotation on the axisymmetric gravity driven complex flow in a cylindrical annulus whose side walls rotate about their axis with different angular velocities. They obtained the results for Grashof number, rotational speeds, Prandtl number, aspect ratio and compared the results with the existing data. Khan et al. 2 treated the movement in heating prevailing system of a differential type dispersion on an expanding medium using series solution. Sankar et al. 3 tested numerically the hydromagnetic field influence in axial or radial forms for natural convection of a low Prandtl number electrically conducting fluid in a vertical cylindrical annulus. Their outcomes showed that in shallow cavities the flow and heat transfer were suppressed sufficiently through an axial magnetic field and in tall cavities the radial magnetic field had an excellent output. Khan et al. 4 tested the thermal disorder, heat and mass transfer tiny dispersion movement with gyrotactic microorganisms in porous medium using heating wall information. Using the Brinkman-extended Darcy equation, Sankar et al. 5 investigated the natural convection flows in a vertical annulus filled with a fluid-saturated porous medium in which the inner wall was subjected to discrete heating, outer wall was subjected to isothermally at lower temperature and the adiabatic parts were the bottom and top walls including

“…Some similar literature on Newtonian, non-Newtonian fluids, and nanofluid comes into sight in previous works. [35][36][37][38][39][40][41][42] All the aforementioned studies except, 30 engage the classical heat and mass transfer equations by Fourier 43 that restrict the energy and concentration to parabolic type equations through which an initial distribution provides an instant experience by the system, called a paradox of heat and mass flux. This restriction was tackled by Cattaneo 44 innovating a modification with relaxation time quantity.…”

Section: Introductionmentioning

confidence: 99%

Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

Advances in Mechanical Engineering

Sohail

2014

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.