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The utilization of solar energy is essential to all living things since the beginning of time. In addition to being a constant source of energy, solar energy (SE) can also be used to generate heat and electricity. Recent technology enables to convert the solar energy into electricity by using thermal solar heat. Solar energy is perhaps the most easily accessible and plentiful source of sustainable energy. Copper-based nanofluid has been considered as a method to improve solar collector performance by absorbing incoming solar energy directly. The goal of this research is to explore theoretically the Agrawal axisymmetric flow induced by Cu-water nanofluid over a moving permeable disk caused by solar energy. Moreover, the impacts of Maxwell velocity and Smoluchowski temperature slip are incorporated to discuss the fine points of nanofluid flow and characteristics of heat transfer. The primary partial differential equations are transformed to similarity equations by employing similarity variables and then utilizing bvp4c to resolve the set of equations numerically. The current numerical approach can produce double solutions by providing suitable initial guesses. In addition, the results revealed that the impact of solar collector efficiency enhances significantly due to nanoparticle volume fraction. The suction parameter delays the boundary layer separation. Moreover, stability analysis is performed and is found that the upper solution is stable and physically trustworthy while the lower one is unstable. [ABSTRACT FROM AUTHOR]

The present study looks at the heat transfer and the unsteady thin film flow of Al2O3 water nanofluid past an inclined stretching sheet having a buoyancy force effect. The boundary value problem solver (bvp4c) package in Matlab is utilized in solving the converted set of ordinary differential equations (ODEs). The multi-shape Al2O3 nanoparticles' impact with respect to the flow as well as heat transfer characteristics are studied and visually displayed for certain governing parameter values, which include the mixed convection, inclination angle, magnetic, slip, and Biot number. Thus, the skin friction coefficient and the local Nusselt number are also determined. Here, the platelet shape of Al2O3 nanoparticles possesses a high heat transfer and flow rate based on the outcomes. In addition, increasing the slip and magnetic parameters improves the temperature, whereas increasing the buoyancy and inclination angle parameters has reverse effects. The results also show that increasing the unsteadiness parameter and the magnetic parameter reduces the film thickness. [ABSTRACT FROM AUTHOR]

Recent advancements in nanotechnology have created a tremendous platform for the development of the improved performance of ultrahigh coolants known as nanofluids for several industrial and engineering technologies. The present research peruses an inspection of irreversibility analysis of mixed convective flow near a stagnation point provoked by ternary hybrid nanoparticles through a vertical heated flat plate with the Hall effects. Water conveying alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) nanoparticles experiencing convectively heated as appropriate in the engineering or industry are investigated. The leading equations are non-dimensionalized using relevant similarity variables and then numerically cracked via utilizing the bvp4c solver. The impressions of different pertinent parameters on the axial velocity, transverse velocity and temperature profile along with heat transfer and drag force are discussed carefully. Double solutions are observed in the opposing flow; however, a single solution is obtained for the assisting flow. Also, the results indicate that due to nanofluid, the velocity boundary layer thicknesses decrease and the thermal boundary layer width upsurges. Further, the flow and the characteristics of heat transfer can be controlled using a magnetic field. [ABSTRACT FROM AUTHOR]

In the last 20 years, mathematics teaching and learning encounters quite a big problem, especially at the tertiary level. The main concern always surrounds the students’ achievement in the subject matter. Students’ performance in mathematics at first year is reflected by the students’ mathematical background prior to the admittance into the university. The study examined 165 first year students in the Faculty of Engineering Technology (FTK) who took the Mathematics Competency test upon entering the university at the beginning of their first semester. A test consisted of 40 fundamental mathematical questions which students have learned them before. From the result, 84% of these students failed this test. However, looking at their Sijil Pelajaran Malaysia (SPM) mathematics result during Form Five (12th grade) in school, the majority did quite well in that exam. These students also took a first year mathematics course which is Technical Mathematics at the same semester. At the end of the semester, the result of their Technical Mathematics course seemed to be quite good. The performance of these three mathematics results was being compared and studied.

In this paper, a numerical simulation of heat pipe heat exchanger (HPHE) is computed by using CFD solver program i.e. AcuSolve. Two idealized model of HPHE are created with different variant of entry’s dimension set to be case 1 and case 2. The geometry of HPHE is designed in SolidWorks and imported to AcuSolve to simulate the fluid flow numerically. The design of HPHE is the key to provide a heat exchanger system to work proficient as expected. Finally, the result is used to optimize and improving heat recovery systems of the increasing demand for energy efficiency in industry.

In this paper, the effect of aligned magnetic field towards the flow and heat transfer of the upper-convected Maxwell (UCM) fluid over a stretching/shrinking sheet is numerically studied. The governing partial differential equations are reduced into a system of ordinary differential equations using a similarity transformation, which are then solved numerically using the shooting method. The skin friction and heat transfer coefficients, the velocity, as well as the temperature profiles of the fluid are presented and discussed. Results indicate that an increase in the aligned angle strengthens the applied magnetic field which decrease the velocity and increase the temperature profiles of the fluid. This implies that an increase in the aligned angle increases the skin friction coefficient and decreases the heat transfer coefficients.

The use of hybrid nanoparticles to increase heat transfer is a favorable area of research, and therefore, numerous scientists, researchers, and scholars have expressed their appreciation for and interest in this field. Determining the dynamic role of nanofluids in the cooling of microscopic electronic gadgets, such as microchips and related devices, is also one of the fundamental tasks. With such interesting and useful applications of hybrid nanofluids in mind, the main objective is to deal with the analysis of the unsteady flow towards a shrinking sheet in a water-based hybrid ferrite nanoparticle in porous media, with heat sink/source effects. Moreover, the impact of these parameters on heat and mass transfers is also reported. Numerical results are obtained using MATLAB software. Non-unique solutions are determined for a certain shrinking strength, in addition to the unsteadiness parameter. The mass transfer and friction factor increase for the first solution due to the hybrid nanoparticles, but the heat transfer rate shows the opposite effect. [ABSTRACT FROM AUTHOR]

The mixed convection flow with thermal characteristics of a water-based Cu-Al2O3 hybrid nanofluid towards a vertical and permeable wedge was numerically and statistically analyzed in this study. The governing model was constructed using physical and theoretical assumptions, which were then reduced to a set of ordinary differential equations (ODEs) using similarity transformation. The steady flow solutions were computed using the Matlab software bvp4c. All possible solutions were presented in the graphs of skin friction coefficient and thermal rate. The numerical results show that the flow and thermal progresses are developed by enhancing the controlling parameters (wedge parameter, volumetric concentration of nanoparticles, and suction parameter). Moreover, the response surface methodology (RSM) with analysis of variance (ANOVA) was employed for the statistical evaluation and conducted using the fit general linear model in the Minitab software. From the standpoint of statistical analysis, the wedge parameter and volumetric nanoparticle concentration have a considerable impact on all responses; however, the suction parameter effect is only substantial for a single response. [ABSTRACT FROM AUTHOR]

Conventional liquids have poor thermal conductivity, thus limiting their use in engineering. Therefore, scientists and researchers have created nanofluids, which consist of nanoparticles dispersed in a base fluid, to improve heat transfer properties in various fields, such as electronics, medicine, and molten metals. In this study, we examine the micropolar nanofluid flow in a stagnation region of a stretching/shrinking sheet by employing the modified Buongiorno nanofluid model. The nanofluid consists of magnetite (Fe3O4) nanoparticles. The similarity equations are solved numerically using MATLAB software. The solution is unique for the shrinking strength λ ≥ − 1 . Two solutions are found for the limited range of λ when λ c < λ < − 1 . The solutions terminate at λ = λ c in the shrinking region. The rise in micropolar parameter K contributes to the increment in the skin friction coefficient Re x 1 / 2 C f and the couple stress Re x M w , but the Nusselt number Re x − 1 / 2 N u x and the Sherwood number Re x − 1 / 2 S h x decrease. These physical quantities intensify with the rise in the magnetic parameter M. Finally, we investigated the stability of the solutions over time. This work contributes to the dual solution and time stability analysis of the current problem. In addition, critical values of the main physical parameters are also presented. These critical values are usually known as the separation values from laminar to turbulent boundary layer flows. In this case, once the critical value is achieved, the process for the specific product can be planned according to the desired output to optimize the productivity. [ABSTRACT FROM AUTHOR]

This study examines the Blasius flow with Cu-Al2O3 hybrid nanoparticles over a moving plate. Additionally, the effects of viscous dissipation and radiation are considered. Similarity transformation is employed to convert the respective model into similarity equations. The results are generated by using bvp4c in MATLAB. Findings reveal that two solutions are attained when both the free stream and the plate move in opposite directions. Moreover, the domains of the velocity ratio parameter are extended when suction is available. Besides, the upsurge of radiation and hybrid nanoparticles lead to the heat transfer enhancement. The rise in radiation heat energy incorporated in radiation parameter leads to the development of fluid temperature as well as the thermal boundary layer. Meanwhile, hybrid nanoparticles offer good thermal characteristics because of synergistic effects. However, the effects reduce with the rise in Eckert number. The first solution is stable and acceptable based on the temporal stability analysis. Furthermore, the critical/separation values of the physical parameters are also reported. With these findings, the optimized productivity will be achieved as well as the processes on certain products can be planned according to the desire output. This significant preliminary study provides future insight to the engineers and scientist on the real applications. [ABSTRACT FROM AUTHOR]

The field of magnetohydrodynamics (MHD) encompasses a wide range of physical objects due to their stabilising effects. Thus, this study concerns the numerical investigation of the radiative non-Newtonian fluid flow past a shrinking sheet in the presence of an aligned magnetic field. By adopting proper similarity transformations, the governing partial derivatives of multivariable differential equations are converted to similarity equations of a particular form. The numerical results are obtained by using the bvp4c technique. According to the findings, increases in the suction parameter resulted in higher values of the skin friction and heat transfer rate. The same pattern emerges as the aligned angle and magnetic parameter are considered. On the other hand, the inclusion of the Bingham number, the Reiner--Philippoff fluid, and the thermal radiation parameters deteriorate the heat transfer performance, evidently. The dual solutions are established, which results in a stability analysis that upholds the validity of the first solution. [ABSTRACT FROM AUTHOR]

The proficiency of hybrid nanofluid from Cu-Al2O3/water formation as the heat transfer coolant is numerically analyzed using the powerful and user-friendly interface bvp4c in the Matlab software. For that purpose, the Cu-Al2O3/water nanofluid flow between two parallel plates is examined where the lower plate can be deformed while the upper plate moves towards/away from the lower plate. Other considerable factors are the wall mass suction/injection and the magnetic field that applied on the lower plate. The reduced ordinary (similarity) differential equations are solved using the bvp4c application. The validation of this novel model is conducted by comparing a few of numerical values for the reduced case of viscous fluid. The results imply the potency of this heat transfer fluid which can enhance the heat transfer performance for both upper and lower plates approximately by 7.10% and 4.11%, respectively. An increase of squeezing parameter deteriorates the heat transfer coefficient by 4.28% (upper) and 5.35% (lower), accordingly. The rise of suction strength inflates the heat transfer at the lower plate while the presence of the magnetic field shows a reverse result. [ABSTRACT FROM AUTHOR]

This study investigates the unsteady flow of Al2O3‐Cu/water hybrid nanofluid on a stagnation point of a permeable rigid surface. The similarity equations are obtained using similarity variables and then solved using the bvp4c solver. The outcomes show that dual solutions exist for the negative unsteadiness and some mass flux parameters. Besides, the heat transfer rate is intensified with the hybrid nanoparticles. Moreover, the increasing of the mass flux parameter tends to increase the heat transfer rate and the skin friction on the surface. Also, the reduction of the skin friction coefficient is observed, and a higher heat transfer rate is achieved for smaller values of the unsteadiness parameter. Finally, by a temporal stability analysis, it is found that the first solution is stable and reliable as time evolves. [ABSTRACT FROM AUTHOR]

This paper examines the behaviour of a hybrid nanofluid flow towards a stagnation point on a stretching or shrinking surface with second-order slip and melting heat transfer effects. Copper (Cu) and alumina (Al2O3) are considered as the hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in MATLAB software through the bvp4c solver to obtain the numerical solutions. The results reveal that two solutions are possible for the shrinking case (λ < 0) , where the bifurcation of the solutions occurs in this region. Moreover, the heat transfer rate and the skin friction coefficient enhance with the rise of the melting parameter. Meanwhile, these quantities decrease for a smaller second-order slip parameter. The temporal stability analysis shows that only one of the two solutions is stable as time evolves. [ABSTRACT FROM AUTHOR]

AbstractThe fundamental goal of this study is to scrutinize the flow and the heat transfer performance of Reiner-Philippoff hybrid ferrofluid (magnetic nanofluid) magnetite-cobalt ferrite/water, magnetite/water, and cobalt ferrite/water with radiation effect past a permeable stretching/shrinking sheet. Different variations of Bingham number, Reiner-Philippoff parameter, and radiation effect are examined to estimate the thermal progress across the fluid at the boundary layer when the sheet is shrunk and stretched. The governing fluid flow model is remodeled into a nonlinear set of ordinary differential equations via transformation of similarity. The new transformed system is numerically solved aided by MATLAB's bvp4c solver. Within a certain set of physical parameters, two distinct solutions can be generated. Hybrid ferrofluid has been shown to have an improved heat transfer performance when the sheet is shrunk compared to mono ferrofluids. The laminar state of the flow can be maintained efficiently when a hybrid ferrofluid is considered. The radiation parameter can be used to enhance the thermal progress except when the sheet is shrunk. The first solution has been shown to be stable by stability analysis. [ABSTRACT FROM AUTHOR]