A New Idea of Fractal-Fractional Derivative with Power Law Kernel for Free Convection Heat Transfer in a Channel Flow between Two Static Upright Parallel Plates

Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.

In vitro biological screening of the stem of Desmodium elegans

Objective:To explore the medicinal importance of the stem of Desmodium elegans,methanolic extract,and its different solvent fractions were evaluated for brine shrimp lethality,insecticidal and phytotoxicity,antifungal,and antibacterial activities.Methods:The methanolic extract and its solvent fractions were tested for cytotoxic,phytotoxic,insecticidal,antifungal,and antibacterial effects using our previous published protocols.Results:The methanolic,DCM,ethyl acetate and n-butanol fractions exhibited insecticidal effect against Callosobruchus analis and Rhyzopertha dominie.The methanolic extract,n-hexane,DCM ethyl acetate and n-butanol showed 75,85,85,65 and 5%phytotoxicity at the tested concentration of 500μg/ml.respectively.The solvent fractions(DCM and ethyl acetate)were effective against F.solani(10%and 20%,inhibition respectively).All the tested samples were devoid of cytotoxic and antibacterial effects.Conclusions:It was concluded diat diis plant can be practiced for control of weeds and insects.

Influences of double diffusion upon radiative flow of thin film Maxwell fluid through a stretching channel

This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching channel.The nanoparticles of silver and alumina have mixed in the Maxwell fluid(base fluid).Magnetic field influence has been employed to channel in normal direction.Equations that are going to administer the fluid flow have been converted to dimension-free notations by using appropriate variables.Homotopy analysis method is used for the solution of the resultant equations.In this investigation it has pointed out that motion of fluid has declined with growth in magnetic effects,thin film thickness,and unsteadiness factor.Temperature of fluid has grown up with upsurge in Brownian motion,radiation factor,and thermophoresis effects,while it has declined with greater values of thermal Maxwell factor and thickness factor of the thin film.Concentration distribution has grown up with higher values of thermophoresis effects and has declined for augmentation in Brownian motion.

Influences of Marangoni convection and variable magnetic field on hybrid nanofluid thin-film flow past a stretching surface

Investigations on thin-film flow play a vital role in the field of optoelectronics and magnetic devices.Thin films are reasonably hard and thermally stable but quite fragile.The thermal stability of a thin film can be further improved by incorporating the effects of nanoparticles.In the current work,a stretchable surface is considered upon which hybrid nanofluid thin-film flow is taken into account.The idea of augmenting heat transmission by making use of a hybrid nanofluid is a focus of the current work.The flow is affected by variations in the viscous forces,along with viscous dissipation effects and Marangoni convection.A time-constrained magnetic field is applied in the normal direction to the flow system.The equations governing the flow system are shifted to a non-dimensional form by applying similarity variables.The homotopy analysis method is employed to find the solution to the resultant equations.It is noticed in this study that the flow characteristics decline with augmentation of magnetic,viscosity and unsteadiness parameters while they increase with enhanced values of thin-film parameters.Thermal characteristics are supported by increasing values of the Eckert number and the unsteadiness parameter and opposed by the viscosity parameter and Prandtl number.The numerical impact of different emerging parameters upon skin friction and the Nusselt number is calculated in tabular form.A comparison of current work with established results is carried out,with good agreement.

Heat Transfer of Casson Fluid over a Vertical Plate with Arbitrary Shear Stress and Exponential Heating

The basic objective of this work is to study the heat transfer of Casson fluid of non-Newtonian nature.The fluid is considered over a vertical plate such that the plate exhibits arbitrary wall shear stress at the boundary.Heat transfers due to exponential plate heating and natural convection are due to buoyancy force.Magnetohydrodynamic(MHD)analysis in the occurrence of a uniform magnetic field is also considered.The medium over the plate is porous and hence Darcy’s law is applied.The governing equations are established for the velocity and temperature fields by the usual Boussinesq approximation.The problem is first written in dimensionless form using some useful non-dimensional quantities and then solved.The exact analysis is performed and hence solutions via integral transform are established.The analysis of various pertinent parameters on temperature distribution and velocity field are reported graphically.It is found that pours medium permeability parameter retards the fluid motion whereas,velocity decreases with increasing magnetic parameter.Velocity and temperature decrease with increasing Prandtl number whereas the Grashof number enhances the fluid motion.Further,it is concluded from this study that the results obtained here are more general and in a limiting sense several other solutions can be recovered.The Newtonian fluid results can be easily established by taking the Casson parameter infinitely large i.e.,whenβ→∞.

可持续能源发展的指标 跟踪进展的工具

在1987年世界环境与发展委员会发表 Brundt-land 的报告《我们共同的未来》

各种能源方案的比较 机构间DECADES项目的进展情况报告

提供充分而付得起的能源服务,是可持续发展的一个基本组成部分。