scholarly journals Significance of Bioconvective and Thermally Dissipation Flow of Viscoelastic Nanoparticles with Activation Energy Features: Novel Biofuels Significance

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 214 ◽  
Author(s):  
Hassan Waqas ◽  
Sami Ullah Khan ◽  
Iskander Tlili ◽  
Muhammad Awais ◽  
Mostafa S. Shadloo
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Lewis Number ◽  
Vertical Surface ◽  
Second Order ◽  
Biomedical Science ◽  
Viscoelastic Parameter ◽  
Interdisciplinary Field ◽  
Viscoelastic Nanofluid ◽  
Local Sherwood Number

The analysis of bioconvection flow nanofluids is the topic of concern in recent decades as it involves a variety of physical significance in biotechnology. Bioconvection has many applications in the interdisciplinary field of sciences such as in biomedical science, biofuel biotechnology, and enzyme-based biosensors, among others. The aim of the current work is to analyze the bioconvection phenomenon in the two-dimensional steady flow of viscoelastic nanofluid over a vertical surface. Here, the effects of activation energy, second-order slip, and nanoparticles zero mass flux conditions are considered to investigate the flow problem. Based on dimensionless variables, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) which are further solved numerically by using a built-in BVP4C approach in MATLAB software. Various controlling parameters like Hartman number, viscoelastic parameter, first and second-order slip factors, buoyancy ratio parameter, thermophoresis parameter, Brownian motion constant, bioconvection Lewis number and Peclet number are graphically illustrated for the distributions of velocity, temperature, concentration, and motile microorganism. Moreover, the variation of local Nusselt number, local Sherwood number, and motile density number are numerically investigated for the involved parameters.

An Integral Treatment for Dissipative Boundary Layer Flow along a Radiating Vertical Surface by Natural Convection in a Porous Medium

2017 ◽  
Vol 11 ◽  
pp. 191-207 ◽  
Author(s):  
Shoeb R. Sayyed ◽  
B.B. Singh ◽  
Nasreen Bano
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Radiation Effects ◽  
Lewis Number ◽  
Vertical Surface ◽  
Integral Treatment ◽  
Layer Flow ◽  
Dissipative Boundary ◽  
Local Sherwood Number

In the present study, an integral method of Von Karman type has been used to analyse the phenomenon of natural convection heat and mass transfer near a vertical surface embedded in a fluidsaturated porous medium considering the viscous dissipation and radiation effects. The buoyancy effect is due to the variation of temperature and concentration across the boundary layer. The effects of the governing parameters e.g. buoyancy ratio (N), Lewis number (Le), Eckert number (Ec) and radiation parameter (R) on local Nusselt number, local Sherwood number, velocity profile, temperature profile and concentration profile have been investigated. The results obtained in the present analysis have been compared with the published results available in the literature and they have been found in precise agreement.

scholarly journals Numerical simulation for bioconvectional flow of burger nanofluid with effects of activation energy and exponential heat source/sink over an inclined wall under the swimming microorganisms

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hassan Waqas ◽  
Umar Farooq ◽  
Aqsa Ibrahim ◽  
M. Kamran Alam ◽  
Zahir Shah ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Activation Energy ◽  
Differential Equations ◽  
Heat Source ◽  
Lewis Number ◽  
Numerical Results ◽  
Solid Particles ◽  
Liquid Component ◽  
Pharmaceutical Industries ◽  
The Impact

AbstractNanofluids has broad applications such as emulsions, nuclear fuel slurries, molten plastics, extrusion of polymeric fluids, food stuffs, personal care products, shampoos, pharmaceutical industries, soaps, condensed milk, molten plastics. A nanofluid is a combination of a normal liquid component and tiny-solid particles, in which the nanomaterials are immersed in the liquid. The dispersion of solid particles into yet another host fluid will extremely increase the heat capacity of the nanoliquid, and an increase of heat efficiency can play a significant role in boosting the rate of heat transfer of the host liquid. The current article discloses the impact of Arrhenius activation energy in the bioconvective flow of Burger nanofluid by an inclined wall. The heat transfer mechanism of Burger nanofluid is analyzed through the nonlinear thermal radiation effect. The Brownian dispersion and thermophoresis diffusions effects are also scrutinized. A system of partial differential equations are converted into ordinary differential equation ODEs by using similarity transformation. The multi order ordinary differential equations are reduced to first order differential equations by applying well known shooting algorithm then numerical results of ordinary equations are computed with the help of bvp4c built-in function Matlab. Trends with significant parameters via the flow of fluid, thermal, and solutal fields of species and the area of microorganisms are controlled. The numerical results for the current analysis are seen in the tables. The temperature distribution increases by rising the temperature ratio parameter while diminishes for a higher magnitude of Prandtl number. Furthermore temperature-dependent heat source parameter increases the temperature of fluid. Concentration of nanoparticles is an decreasing function of Lewis number. The microorganisms profile decay by an augmentation in the approximation of both parameter Peclet number and bioconvection Lewis number.

Stagnation point flow of a nanofluid past a non-aligned stretching/shrinking sheet with a second-order slip velocity

2019 ◽  
Vol 29 (2) ◽  
pp. 738-762 ◽  
Author(s):  
Alin V. Roşca ◽  
Natalia C. Roşca ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Slip Velocity ◽  
Lewis Number ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose The purpose of this study is to investigate the influence of the second order slip velocity on the boundary layer stagnation point flow of a nanofluid past a non-aligned stretching/shrinking sheet. Design/methodology/approach Proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved numerically using the bvp4c solver in MATLAB software. As in the papers by Kuznetsov and Nield (2010, 2013) and Fang et al. (2009), the authors considered the stretching/shrinking parameter λ, the first-order (a1, a2) and second-order (b1) slip parameters and the Lewis number Le, Nb the Brownian parameter and Nt the thermophoresis parameter fixed at Le = 10, Nb = Nt = 0.5 when the Prandtl number Pr is fixed at Pr = 1. Findings Dual solutions are found as the sheet is shrunk in the horizontal direction. Stability analysis shows that the first solution is physically realizable, whereas the second solution is not practicable. Originality/value The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Wang (2008) and Lok et al. (2011) to the case of nanofluids.

scholarly journals Sensitivity Analysis on Thermal Conductivity Characteristics of a Water-Based Bionanofluid Flow Past a Wedge Surface

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Sze Qi Chan ◽  
Fazlina Aman ◽  
Syahira Mansur
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Lewis Number ◽  
Motion Parameter ◽  
Nonlinear Ordinary Differential Equations ◽  
Shooting Technique ◽  
Wedge Surface ◽  
Water Based ◽  
Local Sherwood Number ◽  
Brownian Motion Parameter

Thermobioconvection boundary layer flow in a suspension of water-based bionanofluid holding both nanoparticles and motile microorganisms past a wedge surface was studied. The governing nonlinear partial differential equations on reference of the Buongiorno model were transformed into a set of coupled nonlinear ordinary differential equations. Shooting technique was then used to solve the transformed nonlinear ordinary differential equations numerically. The solutions were found to be contingent on several values of the governing parameters. As highlighted, the velocity profile as well as the skin friction coefficient was affected by the pressure gradient parameter, the function of the wedge angle parameter. On the other hand, the temperature, nanoparticle concentration, and density of motile microorganism’s distributions together with its corresponding local Nusselt number, local Sherwood number, and local density of the motile microorganisms change with the thermophoresis and Brownian motion parameter and so Lewis number, Schmidt number, and bioconvection Péclet number. An experimental scheme together with sensitivity analysis on the basis of Response Surface Methodology (RSM) was applied to examine the dependency of the response parameters of interest to the input parameters’ change. Obviously, local Nusselt number was more sensitive towards the Brownian motion parameter when the Brownian motion parameter was at 0.2 and 0.3. However local Sherwood number was more sensitive towards the Lewis number for all values of Brownian motion parameter. Compatibility found by comparing results between RSM and shooting technique gave confidence for the model’s accuracy. The findings would provide initial guidelines for future device fabrication. Finally, the numerical results obtained were thoroughly inspected and verified with the existing values reported by some researchers.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

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