Misconception as barrier in understanding index and logarithm: the case of pre-tertiary education students / Wan Norliza Wan Bakar and Siti Farah Haryatie Mohd Kanafiah

Misconception is an opinion that is wrong because it has been failure to understand the concept. Index and logarithm are the basic mathematical concept that is very important in advanced mathematics.It is being taught in the subject of additional mathematics at school level and refreshed again at university level. In Universiti Teknologi Mara Cawangan Kelantan (UiTMCK), index and logarithm is one of the topics in the subject of essential mathematics (MAT 037) . This research aims to explore and identify the misconception in understanding index and logarithm among pre diploma students. There were 120 pre diploma students taking Essential Mathematics on Semester September 2019 until January 2020 at UiTMCK involved in the diagnostic test. A set of diagnostic tests on the topic of index and logarithms developed by the experts were given to pre diploma students. The results revealed that the students do understand the topic of index and index equation very well. Unfortunately, when it comes to the topic of logarithm students became confused and the arrangement of BODMAS is not in appropriate order. Most of the students confused and they have their own interpretation in determine the meaning of variable

Generalized mathematical model of Brinkman fluid with viscoelastic properties: Case over a sphere embedded in porous media

The process of heat transfer that involves non-Newtonian fluids in porous regions has attracted considerable attention due to its practical application. A mathematical model is proposed for monitoring fluid flow properties and heat transmission in order to optimize the final output. Thus, this attempt aims to demonstrate the behavior of fluid flow in porous regions, using the Brinkman viscoelastic model for combined convective transport over a sphere embedded in porous medium. The governing partial differential equations (PDEs) of the proposed model are transformed into a set of less complex equations by applying the non-dimensional variables and non-similarity transformation, before they are numerically solved via the Keller-Box method (KBM) with the help of MATLAB software. In order to validate the model for the present issue, numerical values from current and earlier reports are compared in a particular case. The studied parameters such as combined convection, Brinkman and viscoelastic are analyzed to obtain the velocity and temperature distribution. Graphs are used to illustrate the variation in local skin friction and the Nusselt number. The results of this study showcase that when the viscoelastic and Brinkman parameters are enlarged, the fluid velocity drops and the temperature increases, while the combined convection parameter reacts in an opposite manner. Additionally, as the Brinkman and combined convection parameters are increased, the physical magnitudes of skin friction and Nusselt number are increased across the sphere. Of all the parameters reported in this study, the viscoelastic parameter could delay the separation of boundary layers, while the Brinkman and combined convection parameters show no effect on the flow separation. The results obtained can be used as a foundation for other complex boundary layer issues, particularly in the engineering field. The findings also can help researchers to gain a better understanding of heat transfer analysis and fluid flow properties

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

Non-similarity solutions of non-Newtonian Brinkman–viscoelastic fluid

The exploration of heat transference in relation to fluid flow problems is important especially for non-Newtonian type of fluid. The use of the particular fluid can be found in many industrial applications such as oil and gas industries, automotives and manufacturing processes. Since the experimental works are costly and high-risk procedures, the mathematical study is proposed to counter the limitations. Therefore, this work aims to study the characteristics of a fluid that combines the properties of viscosity and elasticity, together with the porosity conditions, called the Brinkman–viscoelastic model. The flow is assumed to move over a horizontal circular cylinder (HCC) under consideration of the convective thermal boundary condition. The mathematical model is transformed to the less complex form by utilising a non-dimensionless and non-similarity variable. The resulting equations are in the partial differential equation (PDE) form. Subsequently, the equations are required to be solved by employing the Keller-box method (KBM). The solutions were conveniently evaluated by observing the plotted graphs in order to capture the propensity of the fluid’s behavior in response to the adjusting parameters. The study discovered that the viscoelastic and Brinkman variables had the impact of decreasing the fluid’s velocity and increasing the temperature distribution. Nevertheless, when mixed convection and Biot numbers increased, the velocity profile exhibited the opposite pattern. Furthermore, increasing the Biot number raises the Nusselt number while decreasing the skin friction coefficient. These numerical results are critical for assisting engineers in making heat transfer process decisions and accurately verifying experimental investigations

The bibliometric review on convective heat transfer of nanofluid

Since convective heat transfer of nanofluids research has advanced significantly, it is helpful to have a brief overview of what has been done, who has been engaged, and how much they have contributed in order to choose our future course of action. Therefore, the objective of this study is to do a bibliometric analysis of the convective heat transfer of nanofluids. The reviewed articles were extracted using the advanced documents search function in SCOPUS database. The search keywords employed in this investigation encompass “convective heat transfer” and “nanofluids”. The first set of documents searched are sorted by article type and year, from 2002 to 2023. VOSviewer is then used to conduct the bibliometric analysis. Findings discovered that current and future research is moving towards investigating hybrid nanofluids flowing through microchannels and porous media, along with the influence of external factors such as pumping power

Free convection boundary layer flow of Brinkman-viscoelastic fluid over a horizontal circular cylinder with constant wall temperature

The demand on the complex model on the study of fluid flow problem is crucial since the real fluid exist in industry applications cannot be presented by the conventional fluid anymore due to the complex properties of the materials. Since then, many mathematicians and scientist try to create the model that can be presented those fluids. Fluid which having characteristics viscous and elasticity can be categorized as non-Newtonian type of fluid due to its relations which against Newton’s Law of viscosity. The application of the fluid is widespread in industrial applications including oils and gas sectors, the automobile industry and manufacturing processes. Paints is one of the examples of viscoelastic fluid since almost wall is painted by the materials polymer and solvents. Therefore, this work is intended to investigate the viscoelastic fluid flow with the porosity condition which then called as Brinkman-viscoelastic model. The flow is presumed to transfer over a geometry horizontal circular cylinder (HCC). The thermal boundary condition is set to be constant wall temperature (CWT). The governing equations which based on Navier Stokes equations are first transformed to the less complex form by utilizing a non-dimensionless and a non-similarity variable. The resulting equations were obtained in the partial differential equations (PDEs) and at the lower stagnation point case, the model is reduced to the ordinary differential equations (ODEs). The Keller-box method (KBM) is applied to solved the final equations. The validation process is performed by direct comparing with the established output in literature and found to be in a very strong agreement. This process is valid since the present model can be reduced to the previous model at the limiting case where the identical equations were obtained. The results of the present model are then computed and presented in tabular form and also illustrated in graphical form. It is noticed that the viscoelastic parameter and Brinkman Parameter significantly affected the fluid flow characteristics

Flow Analysis of Brinkman-Viscoelastic Fluid in Boundary Layer Region of Horizontal Circular Cylinder

This paper examines the flow of Brinkman-viscoelastic fluid in the boundary layer re-gion. The flow over a Horizontal Circular Cylinder (HCC) is investigated theoretically. The proposed model’s governing equations, which are partial differential equations (PDEs), are transformed to their simplest form by using the appropriate non-dimen-sional variables and non-similarity transformation. The numerical computations for the obtained equations are then computed using the Keller-box method (KBM) which is programmed in MATLAB R2019a software. The velocity distribution results, together with the coefficient of skin friction are presented. A comparison study with previously published results is carried out to ensure that the current findings are accurate. It is discovered that the presence of the Brinkman and viscoelastic parameters influences the velocity behaviour of fluid, with a tendency to decrease the velocity distribution of fluid. Furthermore, both parameters have the potential to decrease the skin friction coefficient. The output can be used as a starting point for complex flow problems that occur frequently in engineering applications

Impact of align magnetic field on viscous flow with combined convective transport

The present study focuses on the solution of the magnetic field that affected the flow of viscous fluid under combined convective transport. Flow is assumed to be moving over a stretching sheet with the Newtonian heating as the thermal condition. The mathematical model for present problem was derived from law of conservation of mass, the first law of thermodynamics and Navier Stokes equation. The formulation of the model is started by reducing the equations which were in partial differential equations to ordinary differential equation using the appropriate similarity transformations. The transformed equations were then solved by employing the finite difference scheme, known as Keller-Box method. The validation process is performed and found to be in excellent agreement with the existing results in the literature. The magnetic field that aligned 30° towards the flow boosted the value of skin friction up to 32.57% and 4.82% for Nusselt number compared to the magnetic field that acted transverse to the flow field (90°)

Generalized Mathematical Model of Brinkman Fluid with Viscoelastic Properties: Case over a Sphere Embedded in Porous Media

The process of heat transfer that involves non-Newtonian fluids in porous regions has attracted considerable attention due to its practical application. A mathematical model is proposed for monitoring fluid flow properties and heat transmission in order to optimize the final output. Thus, this attempt aims to demonstrate the behavior of fluid flow in porous regions, using the Brinkman viscoelastic model for combined convective transport over a sphere embedded in porous medium. The governing partial differential equations (PDEs) of the proposed model are transformed into a set of less complex equations by applying the non-dimensional variables and non-similarity transformation, before they are numerically solved via the Keller-Box method (KBM) with the help of MATLAB software. In order to validate the model for the present issue, numerical values from current and earlier reports are compared in a particular case. The studied parameters such as combined convection, Brinkman and viscoelastic are analyzed to obtain the velocity and temperature distribution. Graphs are used to illustrate the variation in local skin friction and the Nusselt number. The results of this study showcase that when the viscoelastic and Brinkman parameters are enlarged, the fluid velocity drops and the temperature increases, while the combined convection parameter reacts in an opposite manner. Additionally, as the Brinkman and combined convection parameters are increased, the physical magnitudes of skin friction and Nusselt number are increased across the sphere. Of all the parameters reported in this study, the viscoelastic parameter could delay the separation of boundary layers, while the Brinkman and combined convection parameters show no effect on the flow separation. The results obtained can be used as a foundation for other complex boundary layer issues, particularly in the engineering field. The findings also can help researchers to gain a better understanding of heat transfer analysis and fluid flow properties