Numerical Analysis of Free Convection Casson Fluid Flow from a Spinning Cone in non-Darcy Porous Medium with Partial Slip and Viscous Dissipation Effects

Published Conference ProceedingsIn the present study, a numerical analysis on free convection Casson fluid flow from a spinning cone in non-Darcy porous medium with radiation, partial slip, cross diffusion and viscous dissipation is considered. The surface of the cone is heated under linear surface heat flux (LSHF). The boundary layer partial differential equations were converted into a system of ordinary differential equations which were then solved using spectral relaxation method (SRM). In this study, we demonstrate the accuracy of the SRM as an alternative method in solving boundary value problems. The results obtained in this study were compared with others in the literature and found to be in excellent agreement. The boundary layer velocity, temperature and concentration profiles are computed for different values of the physical parameters. In particular, the effect of the Casson parameter, spin parameter, Eckert number, Soret number, velocity slip factor, thermal slip factor and concentration slip factor on velocity, temperature and concentration profiles was studied. It is shown that increasing the Casson parameter decrease velocity profiles. Increasing the velocity slip factor tend to assist the flow, while increasing the thermal and concentration slip factors tend to reduce temperature and concentration profiles respectively

Natural convection from a spinning cone in Casson fluid embedded in porous medium with injection, temperature dependent viscosity and thermal conductivity

ArticleIn the present study, a numerical analysis on natural convection Casson fluid flow from a spinning cone in porous medium with injection, temperature-dependent viscosity and thermal conductivity is considered. The surface of the cone is heated under linear surface temperature (LST). The boundary layer partial differential equations were converted into a system of ordinary differential equations which were then solved using spectral relaxation method (SRM). In this study, we study the effects of varying fluid parameters on logarithm of the SRM decoupling error. The results obtained in this study were compared with others in the literature and found to be in excellent agreement. The application of the SRM on a spinning cone has not been studied. The boundary layer velocity, temperature and concentration profiles are computed for different values of the physical parameters. In particular, the effect of the Casson parameter, spin parameter, Eckert number, temperature dependent viscosity parameter, thermal conductivity parameter on rotational velocity and temperature profiles was studied. Increasing the Casson and temperature-dependent viscosity parameters both reduce the logarithm of the SRM decoupling error. Increasing the Eckert and spin parameters both increase the logarithm of the SRM decoupling error

Heat transfer in viscoplastic boundary layer flow from a vertical permeable cone with momentum and thermal wall slip : numerical study

A mathematical model is presented for the laminar free convection boundary layer flow of Casson viscoplastic non-Newtonian fluid external to a vertical penetrable circular cone in the presence of thermal and hydrodynamic slip conditions. The cone surface is maintained at non-uniform surface temperature. The boundary layer conservation equations, which are parabolic in nature, are transformed into non-dimensional form via appropriate similarity variables, and the emerging boundary value problem is solved computationally with the second order accurate implicit Keller-box finite-difference scheme. The influence of velocity (momentum) slip, thermal slip and Casson non-Newtonian parameter on velocity, temperature, skin friction and Nusselt number are illustrated graphically. Validation of solutions with earlier published work is included. The computations show that the flow near the cone surface is strongly decelerated with increasing momentum slip whereas the temperature and thermal boundary layer thickness are increased. Increasing Casson parameter generally decelerates the flow and also decreases temperatures. Both velocity and thermal boundary layer thickness are reduced with greater Prandtl number. The study is relevant to petro-chemical engineering (polymer) processing systems

Study of the Chemical Fabrication Process of NSOM Probes and the Modification of the Probe Surface

Near-field scanning optical microscopy (NSOM) merges scanning probe technology with the power of high-resolution optical microscopy and provides a natural view into the nanoworld. NSOM requires tapered probes with subwavelength optical apertures and wide cone angles to efficiently channel the illumination light to the tip apex so that it can acquire optical images beyond the diffraction limit. Tapered probes with a range of cone angles can be fabricated through chemical etching of optical fibers using hydrofluoric acid (HF) by varying the etching time. Apart from their use for NSOM imaging, such optical probes can also be transformed into nanosensors by attaching sensing elements to the NSOM probe surface. This work seeks to identify the maximum obtainable cone angle in an NSOM probe fabricated by chemical etching of an optical fiber and to create a nanosensor using this kind of probe. We investigate the progression of cone angles with etching time and propose a model of the etching process. We find that the variation of cone angle as a function of etching time does not follow the expected exponential plateau curve and we compare the experimental result to simulations with multiphysics models of the etching process of an optical fiber. Additionally, functionalization of NSOM probes with different fluorescent molecules is investigated and a fluorescent nanosensor is developed. We observe that the nanosensor is able to detect concentration changes of Cu^(2+) and Fe^(3+) ions in a droplet of sample solution

On paired decoupled quasi-linearization methods for solving nonlinear systems of differential equations that model boundary layer fluid flow problems.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.Two numerical methods, namely the spectral quasilinearization method (SQLM) and the spectral local linearization method (SLLM), have been found to be highly efficient methods for solving boundary layer flow problems that are modeled using systems of differential equations. Conclusions have been drawn that the SLLM gives highly accurate results but requires more iterations than the SQLM to converge to a consistent solution. This leads to the problem of figuring out how to improve on the rate of convergence of the SLLM while maintaining its high accuracy. The objective of this thesis is to introduce a method that makes use of quasilinearization in pairs of equations to decouple large systems of differential equations. This numerical method, hereinafter called the paired quasilinearization method (PQLM) seeks to break down a large coupled nonlinear system of differential equations into smaller linearized pairs of equations. We describe the numerical algorithm for general systems of both ordinary and partial differential equations. We also describe the implementation of spectral methods to our respective numerical algorithms. We use MATHEMATICA to carry out the numerical analysis of the PQLM throughout the thesis and MATLAB for investigating the influence of various parameters on the flow profiles in Chapters 4, 5 and 6. We begin the thesis by defining the various terminologies, processes and methods that are applied throughout the course of the study. We apply the proposed paired methods to systems of ordinary and partial differential equations that model boundary layer flow problems. A comparative study is carried out on the different possible combinations made for each example in order to determine the most suitable pairing needed to generate the most accurate solutions. We test convergence speed using the infinity norm of solution error. We also test their accuracies by using the infinity norm of the residual errors. We also compare our method to the SLLM to investigate if we have successfully improved the convergence of the SLLM while maintaining its accuracy level. Influence of various parameters on fluid flow is also investigated and the results obtained show that the paired quasilinearization method (PQLM) is an efficient and accurate method for solving boundary layer flow problems. It is also observed that a small number of grid-points are needed to produce convergent numerical solutions using the PQLM when compared to methods like the finite difference method, finite element method and finite volume method, among others. The key finding is that the PQLM improves on the rate of convergence of the SLLM in general. It is also discovered that the pairings with the most nonlinearities give the best rate of convergence and accuracy

Numerical Solutions of Free Convective Flow from a Vertical Cone with Mass Transfer under the Influence of Chemical Reaction and Heat Generation/Absorption in the Presence of UWT/UWC

The purpose of this paper is to present a mathematical model for the combined effects of chemical reaction and heat generation/absorption on unsteady laminar free convective flow with heat and mass transfer over an incompressible viscous fluid past a vertical permeable cone with uniform wall temperature and concentration (UWT/UWC).The dimensionless governing boundary layer equations of the flow that are transient, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicholson type. The velocity, temperature, and concentration profiles have been studied for various parameters viz., chemical reaction parameter , the heat generation and absorption parameter , Schmidt number Sc , Prandtl number Pr , buoyancy ratio parameter N . The local as well as average skin friction, Nusselt number, Sherwood number, are discussed and analyzed graphically. The present results are compared with available results in open literature and are found to be in excellent agreemen

Effects of chemical reactions on unsteady free convective and mass transfer flow from a vertical cone with heat generation/absorption in the presence of VWT/VWC

A mathematical model for the effects of chemical reaction and heat generation/absorption on unsteady laminar free convective flow with heat and mass transfer over an incompressible viscous fluid past a vertical permeable cone with nonuniform surface temperature T w '(x) = T ∞' + a x n and concentration C w '(x) = C ∞' + b x m is considered here. The dimensionless governing boundary layer equations of the flow that are transient, coupled, and nonlinear partial differential equations are solved by an efficient, accurate, and unconditionally stable finite difference scheme of Crank-Nicholson type. The velocity, temperature, and concentration profiles have been studied for various parameters, namely, chemical reaction parameter, the heat generation and absorption parameter Δ, Schmidt number Sc, Prandtl number Pr, buoyancy ratio parameter N, surface temperature power law exponent n, and surface concentration power law exponent m. The local as well as average skin friction, Nusselt number, and Sherwood number are discussed and analyzed graphically. The present results are compared with available results in open literature and are found to be in excellent agreemen

Reservoir Description of a Middle Eastern CO2 Storage Aquifer

Imperial Users onl

Numerical study of convective fluid flow in porous and non-porous media.

Ph. D. University of KwaZulu-Natal, Pietermaritzburg 2015.Abstract available in PDF file