Three-dimensional flow of a nanofluid over a permeable stretching/shrinking surface with velocity slip: A revised model

A reformulation of the three-dimensional flow of a nanofluid by employing Buongiorno’s model is presented. A new boundary condition is implemented in this study with the assumption of nanoparticle mass flux at the surface is zero. This condition is practically more realistic since the nanoparticle fraction at the boundary is latently controlled. This study is devoted to investigate the impact of the velocity slip and suction to the flow and heat transfer characteristics of nanofluid. The governing partial differential equations corresponding to the momentum, energy, and concentration are reduced to the ordinary differential equations by utilizing the appropriate transformation. Numerical solutions of the ordinary differential equations are obtained by using the built-in bvp4c function in Matlab. Graphical illustrations displaying the physical influence of the several nanofluid parameters on the flow velocity, temperature, and nanoparticle volume fraction profiles, as well as the skin friction coefficient and the local Nusselt number are provided. The present study discovers the existence of dual solutions at a certain range of parameters. Surprisingly, both of the solutions merge at the stretching sheet indicating that the presence of the velocity slip affects the skin friction coefficients. Stability analysis is carried out to determine the stability and reliability of the solutions. It is found that the first solution is stable while the second solution is not stable

Magnetohydrodynamic boundary layer flow and heat transfer of nanofluids past a bidirectional exponential permeable stretching/shrinking sheet with viscous dissipation effect

The problem of boundary layer flow and heat transfer of magnetohydrodynamic (MHD) nanofluids which consist of Fe3O4, Cu, Al2O3, and TiO2 nanoparticles and water as the base fluid past a bidirectional exponentially permeable stretching/shrinking sheet is studied numerically. The mathematical model of the nanofluid incorporates the effect of viscous dissipation in the energy equation. By employing a suitable similarity transformation, the conservative equations for mass, momentum, and energy are transformed into the ordinary differential equations. These equations are then numerically solved with the utilization of bvp4c function in MATLAB. The effects of the suction parameter, magnetic parameter, nanoparticle volume fraction parameter, Eckert number, Prandtl number, and temperature exponent parameter to the reduced skin friction coefficient as well as the local Nusselt number are graphically presented. Cu is found to be prominently good in the thermal conductivity. Nevertheless, higher concentration of nanoparticles leads to the deterioration of heat transfer rate. The present result negates the previous literature on thermal conductivity enhancement with the implementation of nanofluid. Stability analysis is conducted since dual solutions exist in this study, and conclusively, the first solution is found to be stable

Dual solutions of magnetohydrodynamic stagnation point flow and heat transfer of viscoelastic nanofluid over a permeable stretching/shrinking sheet with thermal radiation

The present study is intended to encompass the stagnation point flow and heat transfer of viscoelastic nanofluid with the presence of thermal radiation. The viscous incompressible electrically conducting and Jeffrey fluid model is taken into account. The governing partial differential equations are reduced to ordinary differential equations by using the appropriate similarity variables. The resulting differential equations are solved numerically using the built in bvp4c function in Matlab. Dual solutions are discovered for a certain range of the governing parameters. Numerical results for the velocity and temperature profiles as well as the skin friction coefficients and the local Nusselt number are elucidated through tables and graphs

Numerical solver of A(alpha)-stable for stiff ordinary differential equations

In this paper, a numerical solver for stiff ordinary differential equations (ODEs) known as the Extended Singly Diagonally Implicit Block Backward Differentiation Formulas (ESDIBDDF) is developed. Objectives of this study are to analyse the A( ) − stability of the ESDIBBDF method and enhance its accuracy by employing a strategy that minimizes the error norm to optimize the values of free parameters. In addition to that, accuracy of the method is to be enhanced by approximating solutions by implementing extra functions to be evaluated. The formula is specifically designed in a lower triangular form with equal diagonal coefficients, enabling faster computation of numerical solutions. Numerical experiments are conducted to assess the efficiency of this method as a solver for stiff ODEs, comparing it with existing methods. The A( ) − stability analysis is verified and conditions for convergence are discussed. The conclusive works efficiently as an alternate solver for stiff ODEs. The research recommended extended application of the developed method to solve applied problems

Mathematical analysis of AG-TIO2/blood hybrid nanofluid with inclusion of viscous dissipation over a permeable surface

The remarkable efficiency of hybrid nanofluids in heat transfer has made them a prominent research topic. This study investigates the boundary layer flow and heat transfer of AgTiO2/blood hybrid nanofluid while taking viscous dissipation into account. The governing partial differential equations of the hybrid nanofluid are transformed into ordinary differential equations using the requisite similarity transformations. The bvp4c function is then used in Matlab to generate numerical and graphical output. The accurate initial guessing values are then used to calculate the dual solutions. The existence of viscous dissipation considerably reduces the rate of heat transfer in this model. The effects of nanoparticle concentration have also been studied. The thickness of the boundary layer diminishes as the suction parameter rises, whereas different patterns of results are obtained as the concentration of argentum and titania nanoparticles changes

Effects of Heat Generation/Absorption on a Stagnation Point Flow Past a Stretching Sheet Carbon Nanotube Water-Based Hybrid Nanofluid with Newtonian Heating

This study investigates the mathematical modelling of heat generation/absorption effect on the convective flow of single wall carbon nanotube-copper (SWCNT-Cu)/water hybrid nanofluid towards a stagnation point past a stretching sheet with Newtonian heating. The set of governing equations in the form of non-linear partial differential equations are first transform using the similarity transformation technique then solved numerically by the Runge-Kutta-Fehlberg (RKF45) method in Maple software. The numerical solutions were obtained for the surface temperature, the heat transfer coefficient and the skin friction coefficient as well as the velocity and the temperature profiles. The features of the flow and heat transfer characteristics for various values of the stretching parameter, the conjugate parameter, the nanoparticle volume fraction parameter and the heat source/sink parameter are analyzed and discussed. It is found that effects of hybrid nanoparticles are more significant for lower stretching parameter and for large conjugate parameter values, as well as the heat generation/absorption

Recent advances in photocatalyst for photocatalytic degradation of organic pollutants : Short review

Wastewater from industries that predominantly consist of organic pollutants significantly contributes to water pollution and harms the environment, which should be urgently solved. Among available wastewater treatment technologies, photocatalysis has attracted much interest because of its high efficiency, cleanliness, and sustainability. Various metal oxides photocatalysts have been explored, but each of the metal oxides photocatalyst has its limitation, such as agglomeration, rapid electron-hole recombination, and photo corrosion. Thus, practical design and facile synthesis of photocatalysts are still significant challenges. Due to that, various researchers have introduced and studied photocatalyst modification, such as doping with noble metal or nonnoble metal, crystal facet engineering, surface modification, dye sensitization, and Z-scheme photocatalyst system to enhance the photocatalyst’s catalytic properties. It was also reported that modifying the photocatalyst’s catalytic properties would able to enhance the degradation of organic pollutants. In this review article, the recent advances in photocatalysts for photocatalytic degradation of organic pollutants are reported. The future prospect and conclusions are also discussed. This review is expected to provide an in- depth understanding of photocatalyst development, thus accelerating the evolution of the photodegradation field for pollutant degradation

Magnetohydrodynamics flow of Ag-TiO2 hybrid nanofluid over a permeable wedge with thermal radiation and viscous dissipation

Hybrid nanofluids, which are made by suspending non-identical nanoparticles, have been a prominent research area because of their high efficiency in heat transfer. The analysis of the magnetohydrodynamics flow of Ag-TiO2 hybrid nanofluid over a permeable wedge with heat radiation and viscous dissipation is mathematically examined in this paper. Ordinary differential equations are deduced by applying the corresponding similarity transformations to the mathematical modelling of the governing partial differential equations. The dimensionless governing equations are solved using the built-in bvp4c function in the MATLAB package to compute the dual solutions and the stability analysis. A respectable degree of agreement has been obtained after comparing the current results with the earlier study. Prandtl number, magnetic parameter, radiation parameter, Eckert number, and other governing factors have all been studied, along with their physical impacts on fluid flow. The graphical results have been demonstrated and described in relation to the profiles of temperature and velocity distribution, skin friction as well as the Nusselt number. It has been established that the higher volume percentage of titania nanoparticles has the potential to improve thermal conductivity, and the first solution has been found to be stable in this flow

U-slot microstrip patch array antenna for UHF RFID reader

This paper aims to design and analyze a microstrip patch array antenna for the application of Radio Frequency Identification (RFID). Array antennas are widely used in the RFID applications as it offers high gain and directivity to allow long distance read range. The microstrip patch is arranged in 2 × 2 array and is printed on FR-4 materials. In compliance with the Malaysian RFID regulated range of frequency of 919 to 923 MHz, the antenna is designed to meet its specifications. The operating frequency of the microstrip patch antenna array is 921 MHz. The FR-4 substrate with a dielectric constant of 4.7 and height of 0.16 cm. Theoretical studies and calculations on this topic have been done in order to design the microstrip patch antenna array with the correct dimensions. By using the CST Microwave Studio 2014 as the primary software to model and simulate the results, there are a few parameters that are going to be analyze which includes reflection coefficient, Voltage Standing Ratio (VSWR), gain, directivity, radiation pattern and bandwidth

Influence of viscous dissipation on the boundary layer flow of Cu-Al2O3 hybrid nanofluid

This study presents the mathematical modelling of two dimensional boundary layer flow of hybrid nanofluid where the impact of viscous dissipation has been accentuated in the energy equation. The copper and aluminium oxide nanoparticles are considered in this study. The surface of the model is stretched and shrunk at certain values of stretching/shrinking parameter. The partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the utilization of the suitable similarity transformations. Then Matlab software is utilized to produce the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are obtained with the correct guess values. The insertion of viscous dissipation in this model tremendously lessens the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter and concentration of copper enhance the magnitude of the reduced skin friction coefficient while the augmentation of the aluminium oxide nanoparticles shows a different trend