Impact of Newtonian heating and Fourier and Fick’s laws on a magnetohydrodynamic dusty Casson nanofluid flow with variable heat source/sink over a stretching cylinder

The present investigation aims to deliberate the magnetohydrodynamic (MHD) dusty Casson nanofluid with variable heat source/sink and modified Fourier’s and Fick’s laws over a stretching cylinder. The novelty of the flow model is enhanced with additional effects of the Newtonian heating, activation energy, and an exothermic chemical reaction. In an exothermic chemical reaction, the energy of the reactants is higher than the end products. The solution to the formulated problem is attained numerically by employing the MATLAB software function bvp4c. The behavior of flow parameters versus involved profiles is discussed graphically at length. For large values of momentum dust particles, the velocity field for the fluid flow declines, whereas an opposite trend is perceived for the dust phase. An escalation is noticed for the Newtonian heating in the temperature profile for both the fluid and dust-particle phase. A comparison is also added with an already published work to check the validity of the envisioned problem

Magnetized suspended carbon nanotubes based nanofluid flow with bio-convection and entropy generation past a vertical cone

© 2019, The Author(s). The captivating attributes of carbon nanotubes (CNT) comprising chemical and mechanical steadiness, outstanding electrical and thermal conductivities, featherweight, and physiochemical consistency make them coveted materials in the manufacturing of electrochemical devices. Keeping in view such exciting features of carbon nanotubes, our objective in the present study is to examine the flow of aqueous based nanofluid comprising single and multi-wall carbon nanotubes (CNTs) past a vertical cone encapsulated in a permeable medium with convective heat and solutal stratification. The impacts of heat generation/absorption, gyrotactic-microorganism, thermal radiation, and Joule heating with chemical reaction are added features towards the novelty of the erected model. The coupled differential equations are attained from the partial differential equations by exercising the local similarity transformation technique. The set of conservation equations supported by the associated boundary conditions are worked out numerically by employing bvp4c MATLAB function. The sway of numerous appearing parameters in the analysis on the allied distributions is scrutinized and the fallouts are portrayed graphically. The physical quantities of interest including Skin friction coefficient, the rate of heat and mass transfers are assessed versus essential parameters and their outcomes are demonstrated in tabulated form. It is witnessed that the velocity of the fluid decreases for boosting values of the magnetic and suction parameters in case of both nanotubes. Moreover, the density of motile microorganism is decreased versus larger estimates of bio-convection constant. A notable highlight of the presented model is the endorsement of the results by matching them to an already published material in the literature. A venerable harmony in this regard is achieved

A mathematical study of boundary layer nanofluid flow using spectral quasilinearization methods.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.Heat and mass transfer enhancement in industrial processes is critical in improving the efficiency of these systems. Several studies have been conducted in the past to investigate different strategies for improving heat and mass transfer enhancement. There are however some aspects that warrant further investigations. These emanate from different constitutive relationships for different non-Newtonian fluids and numerical instability of some numerical schemes. To investigate the convective transport phenomena in nanofluid flows, we formulate models for flows with convective boundary conditions and solve them numerically using the spectral quasilinearisation methods. The numerical methods are shown to be stable, accurate and have fast convergence rates. The convective transport phenomena are studied via parameters such as the Biot number and buoyancy parameter. These are shown to enhance convective transport. Nanoparticles and microorganisms’ effects are studied via parameters such as the Brownian motion, thermophoresis, bioconvective Peclet number, bioconvective Schmidt number and bioconvective Rayleigh number. These are also shown to aid convective transport

MHD Mixed Convective Flow of Maxwell Nanofluid Past a Porous Vertical Stretching Sheet in Presence of Chemical Reaction

In this study, MHD mixed convective flow of Maxwell nanofluid past a porous vertical stretching sheet in the presence of chemical reaction is investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations via Lie group analysis. Numerical solutions of these equations are obtained by Runge-Kutta fourth order method along with shooting technique and the results obtained for different governing flow parameters are drawn graphically and their effects on velocity, temperature and concentration profiles are discussed. The values of skin-friction coefficient, Nusselt number coefficient and Sherwood number coefficient are presented in table. A comparison with previously reported data is made and an excellent agreement is noted

Numerical performance of thermal conductivity in Bioconvection flow of cross nanofluid containing swimming microorganisms over a cylinder with melting phenomenon

This study investigates the effects of melting phenomena and non-linear thermal radiation in Cross nanofluid bioconvection flow with motile microorganisms with a convective boundary over a cylinder. Brownian motion and thermophoresis diffusion are also taken into account in this mathematical model. A governing partial differential equation is used to represent the given flow phenomena. The proper dimensionless transformation is then employed to convert the PDE controlling system into an ordinary one. Bvp4c numerically solves redesigned ODE problems using a shooting strategy in the computational tool MATLAB. Figures versus velocity, temperature distribution, nanoparticle concentration, and microbe concentration profiles are used to analyze and expound on the notably involved aspects thoroughly. It has been demonstrated that increasing the estimates of a mixed convection parameter can enhance velocity. By increasing the Prandtl number, the temperature and concentration of nanoparticles decrease. A high Peclet value lowers the microorganism\u27s profile

A numerical study of entropy generation, heat and mass transfer in boundary layer flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.This study lies at the interface between mathematical modelling of fluid flows and numerical methods for differential equations. It is an investigation, through modelling techniques, of entropy generation in Newtonian and non-Newtonian fluid flows with special focus on nanofluids. We seek to enhance our current understanding of entropy generation mechanisms in fluid flows by investigating the impact of a range of physical and chemical parameters on entropy generation in fluid flows under different geometrical settings and various boundary conditions. We therefore seek to analyse and quantify the contribution of each source of irreversibilities on the total entropy generation. Nanofluids have gained increasing academic and practical importance with uses in many industrial and engineering applications. Entropy generation is also a key factor responsible for energy losses in thermal and engineering systems. Thus minimizing entropy generation is important in optimizing the thermodynamic performance of engineering systems. The entropy generation is analysed through modelling the flow of the fluids of interest using systems of differential equations with high nonlinearity. These equations provide an accurate mathematical description of the fluid flows with various boundary conditions and in different geometries. Due to the complexity of the systems, closed form solutions are not available, and so recent spectral schemes are used to solve the equations. The methods of interest are the spectral relaxation method, spectral quasilinearization method, spectral local linearization method and the bivariate spectral quasilinearization method. In using these methods, we also check and confirm various aspects such as the accuracy, convergence, computational burden and the ease of deployment of the method. The numerical solutions provide useful insights about the physical and chemical characteristics of nanofluids. Additionally, the numerical solutions give insights into the sources of irreversibilities that increases entropy generation and the disorder of the systems leading to energy loss and thermodynamic imperfection. In Chapters 2 and 3 we investigate entropy generation in unsteady fluid flows described by partial differential equations. The partial differential equations are reduced to ordinary differential equations and solved numerically using the spectral quasilinearization method and the bivariate spectral quasilinearization method. In the subsequent chapters we study entropy generation in steady fluid flows that are described using ordinary differential equations. The differential equations are solved numerically using the spectral quasilinearization and the spectral local linearization methods

Numerical studies of nanofluid boundary layer flows using spectral methods.

Doctoral Degree. University of KwaZulu-Natal, PietermaritzburgThis thesis is focused on numerical studies of heat and mass transport processes that occur in nanofluid boundary layer flows. We investigate heat and mass transfer mechanisms in the flow of a micropolar nanofluid above a stretching sheet, the squeezed nanofluid flow between two parallel plates and the impact of activation energy and binary chemical reaction on nanofluid flow past a rotating disk. We present an analysis of entropy generation in nanofluid flow past a rotating disk and nanofluid flow past a stretching surface under the influence of an inclined magnetic field. This study aims to numerically determine to a high degree of accuracy, how nanoparticles can be utilized to alter heat and transport properties of base fluids in order to enhance or achieve desirable properties for thermal systems. The heat and mass transfer processes that feature in nanofluid boundary layer flow are described by complex nonlinear transport equations which are difficult to solve. Because of the complex nature of the constitutive equations describing the flow of nanofluids, finding analytic solutions has often proved intractable. In this study, the model equations are solved using the spectral quasilinearization method. This method is relatively recent and has not been adequately utilized by researchers in solving related problems. The accuracy and reliability of the method are tested through convergence error and residual error analyses. The accuracy is further tested through a comparison of results for limiting cases with those in the literature. The results confirm the spectral quasilinearization method as being accurate, efficient, rapidly convergent and suited for solving boundary value problems. In addition, among other findings, we show that nanofluid concentration enhances heat and mass transfer rates while the magnetic field reduces the velocity distribution. The fluid flows considered in this study have significant applications in science, engineering and technology. The findings will contribute to expanding the existing knowledge on nanofluid flow

A Simplified Finite Difference Method (SFDM) Solution via Tridiagonal Matrix Algorithm for MHD Radiating Nanofluid Flow over a Slippery Sheet Submerged in a Permeable Medium

In this paper, we turn our attention to the mathematical model to simulate steady, hydromagnetic, and radiating nanofluid flow past an exponentially stretching sheet. A numerical modeling technique, simplified finite difference method (SFDM), has been applied to the flow model that is based on partial differential equations (PDEs) which is converted to nonlinear ordinary differential equations (ODEs) by using similarity variables. For the resultant algebraic system, the SFDM uses the tridiagonal matrix algorithm (TDMA) in computing the solution. The effectiveness of numerical scheme is verified by comparing it with solution from the literature. However, where reference solution is not available, one can compare its numerical results with the results of MATLAB built-in package bvp4c. The velocity, temperature, and concentration profiles are graphed for a variety of parameters, i.e., Prandtl number, Grashof number, thermal radiation parameter, Darcy number, Eckert number, Lewis number, and Brownian and thermophoresis parameters. The significant effects of the associated emerging thermophysical parameters, i.e., skin friction coefficient, local Nusselt number, and local Sherwood numbers are analyzed and discussed in detail. Numerical results are compared from the available literature and found a close agreement with each other. It is found that the Eckert number upsurges the velocity curve. However, the dimensionless temperature declines with the Grashof number. It is also shown that the SFDM gives good results when compared with the results obtained from bvp4c and results from the literature.publishedVersio

On time dependent MHD nanofluid dynamics due to enlarging sheet with bioconvection and two thermal boundary conditions

The current study pertains to heat and mass transportation of magnetic fluid flow having dilute diffusion of nanoparticles and motile microorganisms over a permeable stretched sheet to examine the influence of thermal radiation and activation energy. Similarity functions are utilized to convert the highly mixed non-linear partial differential equations into higherorder non-linear ordinary differential equations. Five coupled equations are derived to be resolved numerically by employing a computing function Bvp4c, built-in Matlab. Two sets of thermal boundaries prescribed surface temperature (PSF) and prescribed heat flux (PHF) are considered. Basic physical quantities, temperature distribution, concentration, velocity field, and motile micro-organism profiles are observed as influenced by emerging parameters. The microorganisms distribution undergoes decreasing behavior against growing values of bio-convection Lewis number and Peclet number. These results are highly useful in the application of heat-transmitting devices and microbial fuel cells. It is seen that decreasing trend is observed in velocity profile when parameters Nr and Nc are uplifted. Also, the motility of the nanofluid decreases when the Lb parameter is raised. On the other hand, an increase in Peclet number Pe showed a rising trend in motility profile. Additionally, the implications of Brownian motion, Rayleigh number, Bioconvection Lewis number thermophoresis parameter, Peclet number, and buoyancy ratio parameter are discussed. Moreover, the obtained outcomes are validated as compared to the existing ones as limiting cases. Representative findings for microorganism concentration, skin friction coefficient, temperature gradient, local Sherwood number and density number of motile microorganisms, velocity field, temperature, the volumetric concentration of nanoparticles, are discussed in tabulated and graphical form

Irreversibility minimization analysis of ferromagnetic Oldroyd-B nanofluid flow under the influence of a magnetic dipole

© 2021, The Author(s). Studies highlighting nanoparticles suspensions and flow attributes in the context of their application are the subject of current research. In particular, the utilization of these materials in biomedical rheological models has gained great attention. Magneto nanoparticles have a decisive role in the ferrofluid flows to regulate their viscoelastic physiognomies. Having such substantial interest in the flow of ferrofluids our objective is to elaborate the melting heat transfer impact in a stretched Oldroyd-B flow owing to a magnetic dipole in the presence of entropy generation optimization. Buongiorno nanofluid model expounding thermophoretic and Brownian features are considered. Moreover, activation energy with chemical reaction is also considered. The Cattaneo–Christov heat flux model is affianced instead of conventional Fourier law. The renowned bvp4c function of MATLAB is utilized to handle the nonlinearity of the system. Impacts of miscellaneous parameters are portrayed through graphical fallouts and numeric statistics. Results divulge that the velocity and temperature profiles show the opposite trend for growing estimates of the ferromagnetic parameter. It is also noticed that the temperature ratio parameter diminishes the entropy profile. Moreover, it is seen that the concentration profile displays a dwindling trend for the Brownian motion parameter and the opposite trend is witnessed for the thermophoretic parameter