Steady and unsteady aligned magnetohydrodynamics free convection flows of magnetic and non magnetic nanofluids along a wedge, vertical and inclined plates

Nanofluids are a new type of heat transfer fluid engineered by uniform and stable suspension of nanometer sized particles into liquids. The heat transfer in nanofluids is important especially in the context of chemical engineering, aerospace engineering and industrial manufacturing processes. The reason is that, nanofluids were found to transfer heat more efficiently than the conventional fluids. Therefore, nanofluids research could lead to a major breakthrough in developing next generation coolants for numerous engineering applications. Due to this reason, several flow problems related to heat transfer over vertical flat plate, inclined plate and wedge were studied in this thesis. The main purpose of this study was to investigate the characteristics of two dimensional flow and surface heat transfer for two cases which are steady and unsteady convection flows. Nanofluids with two different base fluids (water and kerosene) containing magnetic and non magnetic nanoparticles were considered. The effect of magnetohydrodynamics (MHD) on the flow and heat transfer was also studied. The study starts with the formulation of the mathematical models that governed the fluid flow and heat transfer. Next, the governing nonlinear equations in the form of partial differential equations were reduced into ordinary differential equations using appropriate similarity transformation. The resulting systems of ordinary differential equations were then solved numerically using Keller box method. The numerical values of the skin friction coefficient, the local Nusselt number which represents the heat transfer rate at the surface as well as the velocity and temperature profiles were obtained for various values of the magnetic field inclination angle, magnetic interaction, plate inclination angle, nanoparticles volume fraction, wedge angle, moving wedge, unsteadiness, Grashof number and thermal buoyancy. All results obtained, were displayed graphically in addition to tabular form. The comparisons of results with previous studies were made to validate the results. For both steady and unsteady problems, it is found that magnetic field inclination angle can be used as controlling factor for certain situation because it enhances the skin friction and heat transfer rate. The plate inclination angle parameter and nanoparticles volume fraction parameter have tendency to increase momentum and thermal boundary layers thickness. For unsteady problems, it is observed that the unsteadiness parameter has significant effect on the nanofluids motion and heat transfer characteristic

Steady Aligned MHD free convection of ferrofluids flow over an inclined plate / Mohd Rijal Ilias, Noraihan Afiqah Rawi and Sharidan Shafie

Numerical investigation is carried out for the MHD free convection laminar boundary layer flow that allows heat transfer of an electrically conducting Fe₃O₄–kerosene and Fe₃O₄–water-based ferrofluids. For this, an inclined plate is employed that has aligned magnetic effect as well as transverse magnetic field effect. Suitable similarity transformations are used to convert governing partial differential equations into coupled nonlinear ordinary differential equation. The Keller Box method, a well-known explicit finite difference scheme, is then employed to solve transformed equations numerically. For different values of physical parameters, a detailed parametric study is conducted. Means of graphs are extrapolated to determine the effects of all these parameters over temperature and the flow field. For various values of physical parameters, the numerical values are obtained and tabulated for skin friction coefficient and the rate of heat transfer as well. The results when compared with previously published studies were found to be in excellent agreement

Combined convective transport of brinkman-viscoelastic fluid across horizontal circular cylinder with convective boundary condition

Traditional heat transfer fluids frequently encounter several limitations in the heat transfer process, due to the lower thermal conductivity in heat transfer process industries, and also has an impact on the performance of heat transfer in industrial sectors. In order to overcome the problem, researchers have currently considered an alternative development of heat transfer of fluids. Hence, this study will concentrate on the problem of steady combined convective transport. In particular, the flow of Brinkman-viscoelastic fluid over a horizontal circular cylinder with the influence of convective boundary condition (CBC) was investigated. Using the necessary similarity transformation, the governing equations were converted into a less complicated form and numerically solved by using Runge-Kutta-Fehlberg-method, which was programmed in Maple software. The influence of Biot number, combined convection, Brinkman and viscoelastic parameters are analyzed and demonstrated in graphs and tables. Numerical result showed that the fluid velocity increased with improving conjugate and combined convection parameter, but decreased with increasing Brinkman and viscoelastic parameter. It is also discovered the reverse trend on temperature profiles

Stress intensity factors for a crack in bonded dissimilar materials subjected to various stresses

The modified complex variable function method with the continuity conditions of the resultant force and displacement function are used to formulate the hypersingular integral equations (HSIE) for an inclined crack and a circular arc crack lies in the upper part of bonded dissimilar materials subjected to various remote stresses. The curve length coordinate method and appropriate quadrature formulas are used to solve numerically the unknown crack opening displacement (COD) function and the traction along the crack as the right hand term of HSIE. The obtained COD is then used to compute the stress intensity factors (SIF), which control the stability behavior of bodies or materials containing cracks or flaws. Numerical results showed the behavior of the nondimensional SIF at the crack tips. It is observed that the nondimensional SIF at the crack tips depend on the various remote stresses, the elastic constants ratio, the crack geometries and the distance between the crack and the boundary

Radiation Effects on Inclined Magnetohydrodynamics Mixed Convection Boundary Layer Flow of Hybrid Nanofluids over a Moving and Static Wedge

Nowadays, hybrid nanofluids play an important role in heat transfer systems. They are a good alternative to increase the efficiency of heat transfer and save the energy. Thermal radiation and mixed convection flow of hybrid nanofluids past a permeable moving and stationary wedge were studied in this research. This research uses water as a base fluid to investigate the effects of silver (Ag) and magnesium oxide (MgO) nanoparticles. Similarity transformation techniques are used to convert the partial differential equations of hybrid nanofluids to ordinary differential equations, which is then solved numerically by applying the implicit finite difference Keller box method. The results of the research are illustrated graphically to show the behavior of velocity and temperature profiles, as well as skin friction and Nusselt number. Increasing the parameters of the aligned magnetic field, magnetic field interaction, mixed convection, and wedge angle parameter results in higher velocity profiles but lower temperature profiles. As the radiation parameter and the nanoparticle volume fraction increase, the temperature rises and the velocity decreases. With the exception of the radiation parameter, the skin friction and Nusselt number increase as the alignment angle of the magnetic field, the interaction of the magnetic field, the mixed convection, the wedge angle parameter, and the volume fraction of nanoparticle Ag and MgO rise. As a result of these findings, the velocity profiles and Nusselt numbers of moving wedges are higher, but the temperature profiles and skin friction are lower than those of stationary and moving against flow wedges. In addition, a comparison with previously published research is presented, with excellent agreement discovered. The results of this research will contribute to the field of knowledge in mathematics by bringing additional information for mathematician interested in future research on hybrid nanofluids

Magnetohydrodynamics (MHD) Flow And Heat Transfer Of A Doubly Stratified Nanofluid Using Cattaneo-Christov Model

The present study utilized Cattaneo-Christov heat flux model for solving nanofluid flow and heat transfer towards a vertical stretching sheet with the presence of magnetic field and double stratification. Thermal and solutal buoyancy forces are also examined to deal with the double stratification effects. Buongiorno’s model of nanofluid is used to incorporate the effects of Brownian motion and thermophoresis. The boundary layer with non-Fourier energy equations are reduced into a system of nonlinear ordinary (similarity) differential equations using suitable transformations and then numerically solved using bvp4c solver in MATLAB software. The local Nusselt and Sherwood numbers of few limited cases are tabulated and compared with the earlier published works. It showed that a positive agreement was found with the previous study and thus, validated the present method. Numerical solutions are graphically demonstrated for several parameters namely magnetic, thermal relaxation, stratifications (thermal and solutal), thermophoresis and Brownian motion on the velocity, temperature and nanoparticles volume fraction profiles. An upsurge of the heat transfer rate was observed with the imposition of the thermal relaxation parameter (Cattaneo-Christov model) whereas the accretion of thermal and solutal stratification parameters reduced the temperature and nanoparticles concentration profiles, respectively

Numerical Solutions on Reiner–Philippoff (RP) Fluid Model with Velocity and Thermal Slip Boundary Condition

Non-Newtonian fluid model was created against the Newton’s Law of viscosity where the viscosity is no more constant and dependent on the shear rate. The existing such fluid can be found in many industrial claims especially in food manufacturing, lubrication, biomedical flows and oil and gas. Besides, the used of non-Newtonian fluid occurs in mining industry where the slurries and muds are often handled. There are many models on non-Newtonian fluid available in literature where some of them capture the specific properties. The Reiner–Philippoff (RP) fluid model is considered in this endeavour due to the capabilities of the model which can be acted in three different family of fluid which are viscous, shear thickening and the shear-thinning. Mathematical model is constructed using continuity, momentum and energy equations where in form of partial differential equations (PDEs). The complexity of the proposed model is abridged by deduced the equations into ordinary differential equations (ODEs) by adopting similarity variables before the computation is done by bvp4c function drive in MATLAB software. To ratify the validity of the proposed model as well as numerical outputs, the comparative study is performed and it found to be in very strong agreement under limiting case where the present model is condensed to be identical with the reported model previously. The consequences of pertinent parameters on fluid’s characteristics are analyzed in details through the plotted graphic visuals and tabular form. © 2022, Penerbit Akademia Baru. All rights reserved

Flow and heat transfer analysis on reiner-philippoff fluid flow over a stretching sheet in the presence of first and second order velocity slip and temperature jump effects

Most of the fluid used in industrial application (i.e. Oils and gas industry, food manufacturing, lubrication and biomedical) do not conform to the Newtonian postulate. In contrast to the Newtonian fluid, the viscosity of the fluid can change when under force to either more liquid or more solid and dependent on shear rate history. This behaviour of fluids is commonly known as non-Newtonian fluid. The non-Newtonian fluid is so widespread in nature and technology resulting in very high interest of investigating among scientist. The Reiner-Philippoff fluid is one of the types of non-Newtonian fluid models that exhibiting the dilatant, pseudoplastic and Newtonian behaviors. Hence, this study is devoted to analyze the flow and heat transfer of Reiner-Philippoff fluid with the presence of first and second order velocity slip together with the temperature jump effects over a stretching sheet. Partial differential equations of continuity, momentum and energy equations were transformed into the similarity equations. The obtained equations were then solved via bvp4c function in MATLAB software. For the validation purpose, the present model and its numerical solution were compared with previous established solutions under limiting case where the present model is condensed to be identical with the reported model and turn to be in very strong agreement. The consequences of pertinent parameters on fluid’s characteristics are analyzed in details through the plotted graphic visuals and tabular form

Carbon nanotubes flow on mixed convection of aligned magnetohydrodynamics over a static/moving wedge with convective boundary conditions

Nanotubes have been designed to be significantly larger than any other material, and these cylindrical carbon molecules have exceptional properties that are important for nanoscience and nanotechnology. Due to their exceptional thermal conductivity and mechanical and electrical properties, carbon nanotubes are used as additives to improve heat transfer in various industrial applications. The study analyzed a steady, two-dimensional, carbon nanotubes (CNTs) flow on aligned magnetohydrodynamics mixed convection over a static or moving wedge with convective boundary conditions. The CNTs used are single-wall carbon nanotubes (SWCNTs), multi-wall carbon nanotubes (MWCNTs), and water as the base fluid. The similarity transformation was used to reduce the partial differential governing equations into ordinary differential equations. Then, the reduced equations were solved using fourth-fifth order Runge– Kutta–Fehlberg and coded into Maple Software. The results of velocity and temperature profiles were illustrated graphically while the results of skin friction coefficient and Nusselt number were presented in tabulated data. It is found that the velocity profiles increase, and temperature profiles decrease when the angle of aligned magnetic field parameter, the interaction of magnetic parameter, convective parameter, and total angle of the wedge parameter number increase. For case where Biot number and volume fraction of nanoparticles parameters increase, the velocity profiles decrease, and temperature profiles increase. SWCNTs have increased skin friction and Nusselt numbers due to their higher density and thermal conductivity compared to MWCNTs. The finding of this study will benefit the who works in research and development in a range of industries and the mathematics body of knowledge as it provides new information to people who are interested in this field

Analysis of Heat Transfer in Non-Coaxial Rotation of Newtonian Carbon Nanofluid Flow with Magnetohydrodynamics and Porosity Effects

The study analyzed the heat transfer of water-based carbon nanotubes in non-coaxial rotation flow affected by magnetohydrodynamics and porosity. Two types of CNTs have been considered; single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). Partial differential equations are used to model the problem subjected to the initial and moving boundary conditions. Employing dimensionless variables transformed the system of equations into ordinary differential equations form. The resulting dimensionless equations are analytically solved for the closed form of temperature and velocity distributions. The obtained solutions are expressed in terms of a complementary function error. The impacts of the embedded parameters are graphically plotted in different graphs and are discussed in detail. The Nusselt number and skin friction are also evaluated. The temperature and velocity profiles have been determined to meet the initial and boundary conditions. An augment in the CNTs’ volume fraction increases both temperature and velocity of the nanofluid as well as enhances the rate of heat transport. SWCNTs provides high values of Nusselt number compared to MWCNTs. For verification, a comparison between the present solutions and a past study is conducted and achieved excellent agreement