Combined effects of internal heat generation and buoyancy force on boundary layer over a vertical plate with a convective surface boundary condition

This paper considers the effect of buoyancy force and internal heat generation on laminar thermal boundary layer over a vertical plate with a convective surface boundary condition. We assumed that left surface of the plate is in contact with a hot fluid while a stream of cold fluid flows steadily over the right surface with a heat source that decays exponentially. Using a similarity variable, the steady state governing non-linear partial differential equations have been transformed into a set of coupled non-linear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth order Runge-Kutta integration scheme. The effects of Prandtl number, local Biot number, the internal heat generation parameter and the local Grashof number on the velocity and temperature profiles are illustrated and interpreted in physical terms. A comparison with previously published results on special case of the problem shows excellent agreemen

The effects of lawsonia inermis pigmentation for superhydrophobic properties on cotton fabrics

Nowadays, there are many things that can be produced easily by the help of modern technologies. This include the synthetic materials that can be developed by using any advance machine that was manufactured [1]. However, those synthetics materials that was developed may bring harm to the environment. Their particles can be spread resulting an unhealthy atmosphere. Thus, the natural resources was used to produce an authentic materials (Calarge, 2018). In the recent years, textile industry has been developed significantly and contributes to the growth of Malaysia’s economy [2]. It can be categorized as one of the complicated industries among the manufacturing industries such as food, cosmetics and pharmaceutical industries [3]. Thus, the textile industries require high water consumption and resulting on high discharge rate of wastewater that loaded with contaminants [2]. The generation of wastewater from textile industry comes from the manufacturing process of textile fabrics such as washing scouring bleaching, mercerizing, and dyeing and finishing process. The highest amount of wastewater that produced from textile industries come from the process of dyeing and finishing. The contaminants of water that produced by dyeing and finishing process include high suspended solids (SS), chemical oxygen demand (COD), biochemical oxygen demand (BOD), heat, colour, acidity, basicity, and other organic pollutants [4]. This matter has to be seriously concerned as it may lead to allergic responses, eczema, and also affect the liver, lungs, and immune system of humans as well as animals [3]. The purpose for the project of the effects of Lawsonia Inermis was basically to produce a natural pigment that may not harm the environmen

Heat Transfer in Boundary Layer Viscolastic Fluid Flow Over Anexponentially Stretching Sheet

The paper presents the study of momentum and heat transfer characteristics in a visco-elastic boundary layer fluid flow over an exponentially stretching continuous sheet with non-uniform heat source. The flow is generated solely by the application of two equal and opposite forces along the x-axis such that stretching of the boundary surface is of exponential order in x and influenced by uniform magnetic field applied vertically. The non-linear boundary layer equation for momentum is converted into ordinary differential equation by means of similarity transformation. Approximate analytical similarity solutions is obtained for the dimensionless stream function and velocity distribution function after transforming the boundary layer equation into Riccati type and solving it sequentially. Heat transfer equation is then solved using Runge-Kutta fourth order method. The accuracy of the analytical solutions is also verified by comparing the solutions obtained to those in literature when Hartmann number is zero. The effects of various physical parameters on velocity, skin friction, temperature and Nusselt number profiles are presented graphically

MHD Boundary Layer Slip Flow over a Flat Plate with Soret and Dufour Effects

The present paper studies the effects of Soret and Dufour on MHD boundary layer slip flow over a flat plate. The governing partial differential equations are converted to a set of nonlinear ordinary differential equations by using similarity transformations. Then, these equations are solved numerically by implicit Finite Difference Scheme. The numerical solutions for Velocity, Temperature and Concentration profiles for the related essential physical parameters are visualized through graphs and discussed. Results show that the velocity rises whereas the temperature and concentration reduces with the respective slip parameters. The increase in Soret number or decrease in Dufour number reduces the temperature and enhances the concentration of the fluid

Heat Transfer in a Nanofluid Flow past a Permeable Continuous Moving Surface

The main purpose of this paper is to introduce a boundary layer analysis for the fluid flow and heat transfer characteristics of an incompressible nanofluid flowing over a permeable isothermal surface moving continuously. The resulting system of non-linear ordinary differential equations is solved numerically using Runge-Kutta method with shooting techniques. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the friction factor, local Nusselt number and local Sherwood number for several values of the parameters, namely the velocity ratio parameter, suction/injection parameter and nanofluid parameters. The obtained results are presented graphically and in tabular form and the physical aspects of the problem are discusse

Diffusion of a chemically reactive species of a power-law fluid past a stretching surface

A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the KellerBox method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress. © 2011 Elsevier Ltd. All rights reserved

Non-Newtonian Prandtl fluid over stretching permeable surface

An analysis is made of the velocity and temperature distribution in the flow of a viscous incompressible fluid caused by the stretching permeable surface which issues in the Prandtl fluid. Parandtl fluid is a pseudoplastic visco-inelastic non-Newtonian fluid. The governing partial differential equations are reduced to ordinary differential equations using deductive group transformation and similarity solution is derived. Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity and temperature profiles. The corresponding skin friction coefficient and the Nusselt number are also calculated

Non-Newtonian power-law fluid flow and heat transfer over a non-linearly stretching surface.

The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by an implicit finite-difference scheme known as Keller-Box method. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, velocity exponent parameter, temperature exponent parameter, Modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena

MHD Boundary Layer Flow and Heat Transfer to Sisko Nanofluid Past a Nonlinearly Stretching Sheet with Radiation

The steady flow of a Sisko fluid model in the presence of nanoparticles is studied. The governing partial differential equations are converted to a set of coupled non-linear ordinary differential equations by using suitable similarity transformations. Numerical solutions for the coupled non-linear ordinary differential equations are carried out by a variational finite element method. A suitable comparison has been made with previously published results in the literature as a limiting case of the considered problem. The comparison confirmed an excellent agreement. The results for the local Nusselt number are tabulated and discussed. Behavior of essential physical parameters are presented graphically and discussed for velocity, temperature and nanoparticle volume fraction

Mathematical models for heat and mass transfer in nanofluid flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The behaviour and evolution of most physical phenomena is often best described using mathematical models in the form of systems of ordinary and partial differential equations. A typical example of such phenomena is the flow of a viscous impressible fluid which is described by the Navier-Stokes equations, first derived in the nineteenth century using physical approximations and the principles of mass and momentum conservation. The flow of fluids, and the growth of flow instabilities has been the subject of many investigations because fluids have wide uses in engineering and science, including as carriers of heat, solutes and aggregates. Conventional heat transfer fluids used in engineering applications include air, water and oil. However, each of these fluids has an inherently low thermal conductivity that severely limit heat exchange efficiency. Suspension of nanosized solid particles in traditional heat transfer fluids significantly increases the thermophysical properties of such fluids leading to better heat transfer performance. In this study we present theoretical models to investigate the flow of unsteady nanofluids, heat and mass transport in porous media. Different flow configurations are assumed including an inclined cylinder, a moving surface, a stretching cone and the flow of a polymer nanocomposite modeled as an Oldroyd-B fluid. The nanoparticles assumed include copper, silver and titanium dioxide with water as the base fluid. Most recent boundary-layer nanofluid flow studies assume that the nanoparticle volume fraction can be actively controlled at a bounding solid surface, similar to temperature controls. However, in practice, such controls present significant challenges, and may, in practice, not be possible. In this study the nanoparticle flux at the boundary surface is assumed to be zero. Unsteadiness in fluid flows leads to complex system of partial differential equations. These transport equations are often highly nonlinear and cannot be solved to find exact solutions that describe the evolution of the physical phenomena modeled. A large number of numerical or semi-numerical techniques exist in the literature for finding solutions of nonlinear systems of equations. Some of these methods may, however be subject to certain limitations including slow convergence rates and a small radius of convergence. In recent years, innovative linearization techniques used together with spectral methods have been suggested as suitable tools for solving systems of ordinary and partial differential equations. The techniques which include the spectral local linearization method, spectral relaxation method and the spectral quasiliearization method are used in this study to solve the transport equations, and to determine how the flow characteristics are impacted by changes in certain important physical and fluid parameters. The findings show that these methods give accurate solutions and that the speed of convergence of solutions is comparable with methods such as the Keller-box, Galerkin, and other finite difference or finite element methods. The study gives new insights, and result on the influence of certain events, such as internal heat generation, velocity slip, nanoparticle thermophoresis and random motion on the flow structure, heat and mass transfer rates and the fluid properties in the case of a nanofluid