Thermal enhancement in Falkner-Skan flow of the nanofluid by considering molecular diameter and freezing temperature.

The analysis of nanofluids heat transfer over a wedge is very important due to their wider applications in applied thermal engineering, chemical engineering and biomedical engineering etc. Therefore, aim of the study is to explore the heat transport in nanofluid over a wedge (Falkner Skan flow) under viscous dissipation and thermal radiation over a wedge. The proper model formulation is carried out via similarity relations and empirical correlations of the nanofluids. After successful model transformation, numerical scheme (RK technique along with shooting technique) applied and furnished the results over the desired domain under varying effects of preemenant flow parameters. The results revealed that the velocity rises for opposing ([Formula: see text]) and assisting ([Formula: see text]) flows against [Formula: see text] and significant contribution of Ec and imposed thermal radiations (Rd number) observed in thermal performance of the nanofluid. The temperature declines by strengthen [Formula: see text] and optimum decrement is noted for opposing flow. Finally, a comparison is provided for various values of [Formula: see text] ([Formula: see text]) with previously published work under certain restrictions and found an excellent agreement.

Robust model selection using the out-of-bag bootstrap in linear regression.

Outlying observations have a large influence on the linear model selection process. In this article, we present a novel approach to robust model selection in linear regression to accommodate the situations where outliers are present in the data. The model selection criterion is based on two components, the robust conditional expected prediction loss, and a robust goodness-of-fit with a penalty term. We estimate the conditional expected prediction loss by using the out-of-bag stratified bootstrap approach. In the presence of outliers, the stratified bootstrap ensures that we obtain bootstrap samples that are similar to the original sample data. Furthermore, to control the undue effect of outliers, we use the robust MM-estimator and a bounded loss function in the proposed criterion. Specifically, we observe that instead of minimizing the penalized loss function or the conditional expected prediction loss separately, it is better to minimize them simultaneously. The simulation and real-data based studies confirm the consistent and satisfactory behavior of our bootstrap model selection procedure in the presence of response outliers and covariate outliers.

Role of socioeconomic and parental involvement factors on children foundational learning skills based on MICS (2017-2018) data Punjab, Pakistan.

Developing countries lack studies investigated the socioeconomic and parental role on students' learning skills. This study is helpful to detect bottlenecks in the foundational learning skills (reading skills and numeracy skills) in the education system of Pakistan. Reading skills of children are found better who had no functional disabilities. Mothers with higher education had a significant positive contribution toward children learning skills. Children deprived of books for reading in appropriate language had a negative impact on their reading skills. Rich children had predominantly higher possibilities of good learning skills than poor children. Parents who had not attended children's school to discuss child progress had a significantly negative effect on children's numeracy skills. Overall parental involvement in some forms had insignificantly improved children reading and numeracy skills in Punjab, Pakistan.

Global analysis of a time fractional order spatio-temporal SIR model.

We deal in this paper with a diffusive SIR epidemic model described by reaction-diffusion equations involving a fractional derivative. The existence and uniqueness of the solution are shown, next to the boundedness of the solution. Further, it has been shown that the global behavior of the solution is governed by the value of [Formula: see text], which is known in epidemiology by the basic reproduction number. Indeed, using the Lyapunov direct method it has been proved that the disease will extinct for [Formula: see text] for any value of the diffusion constants. For [Formula: see text], the disease will persist and the unique positive equilibrium is globally stable. Some numerical illustrations have been used to confirm our theoretical results.

Free convection flow of second grade dusty fluid between two parallel plates using Fick's and Fourier's laws: a fractional model.

The paper aims to investigate the channel flow of second grade visco-elastic fluid generated due to an oscillating wall. The effect of heat and mass transfer has been taken into account. The phenomenon has been modelled in terms of PDEs. The constitutive equations are fractionalized by using the definition of the Caputo fractional operator with Fick's and Fourier's Laws. The system of fractional PDEs is non-dimensionalized by using appropriate dimensionless variables. The closed-form solutions of thermal and concentration boundary layers are obtained by using the Laplace and finite Fourier-Sine transforms, while the momentum equation is solved by a numerical approach by Zakian using [Formula: see text]. Furthermore, the parametric influence of various embedded physical parameters on momentum, temperature, and concentration distributions is depicted through various graphs. It is observed that the fractional approach is more convenient and realistic as compared to the classical approach. It is worth noting that the increasing values of [Formula: see text], [Formula: see text] and [Formula: see text] retard the boundary layer profile. For instance, this behaviour of [Formula: see text] is significant where boundary control is necessary. That is, in the case of resonance, the physical solution may be obtained by adding the effect of MHD. The Reynolds number is useful in characterising the transport properties of a fluid or a particle travelling through a fluid. The Reynolds number is one of the main controlling parameters in all viscous flow. It determines whether the fluid flow is laminar or turbulent. The evolution of the rate of heat, mass transfer, and skin friction on the left plate with various physical parameters are presented in tables. These quantities are of high interest for engineers. Keeping in mind the effect of various parameters on these engineering quantities, they make their feasibility reports.

Thermal decomposition of propylene oxide with different activation energy and Reynolds number in a multicomponent tubular reactor containing a cooling jacket.

In this article, we are focusing on heat and mass transfer through a Multicomponent tubular reactor containing a cooling jacket by thermal decomposition of propylene oxide in water. The chemical reaction is an irreversible, 1st order reaction and an exothermic reaction that yields propylene glycol with enthalpy = -84,666 J/mol. The constant rate of the reaction is followed by the Arrhenius equation in which the activation energy is taken on a trial basis in the range from 75,000 to 80,000 J/mol with a fixed frequency factor. For the fluid to flow, the Reynolds number is kept in the range from 100 to 1000. The three partial differential equations of mass, momentum, and energy are coupled to study heat and mass transfer in a tubular reactor by using the chemistry interface in COMSOL Multiphysics 5.4. The initial concentration of propylene oxide is tested in the range from 2 to 3% and the thermal conductivity of the mixture is tested in the range 0.599-0.799. It was found that the amount deactivated of the compound decreases with an increase in Reynolds number. Propylene oxide is decomposed at about 99.8% at Re = 100 at lower activation energy and gives the total maximum enthalpy change in the tubular reactor. Observing the relationship between Sherwood numbers to Nusselt numbers, it was deducted that the convective heat transfer is opposite to convective mass transfer for high Reynolds numbers.

Impact of freezing temperature (Tfr) of Al2O3 and molecular diameter (H2O)d on thermal enhancement in magnetized and radiative nanofluid with mixed convection.

The dynamics of nanofluid by considering the role of imposed Lorentz forces, thermal radiations and velocity slip effects over a vertically convectively heated surface is a topic of huge interest. Therefore, the said study is conducted for Al2O3-H2O nanofluid. Mathematical modelling of the problem is done via nanofluid effective correlations comprising the influences of freezing temperature, molecular diameter and similarity transformations. The results for multiple parameters are plotted and provide comprehensive discussion. From the analysis, it is examined that Al2O3-H2O nanofluid motion drops by strengthening Lorentz forces. The temperature in the nanofluid (Al2O3-H2O) is improved by inducing viscous dissipation effects (Ec number), surface convection (Biot number) and thermal radiations (Rd). Moreover, the shear stresses at the surface decreased due to higher magnetic field effects and rises due to velocity slip. A significant rise in Local Nusselt number is observed due to thermal radiations and Biot effects. Finally, enhanced heat transport mechanism in Al2O3-H2O is examined than a conventional liquid. Therefore, nanofluids are better for industrial applications and the uses of conventional liquids are limited due to low thermal conductivity.

Fractional model of MHD blood flow in a cylindrical tube containing magnetic particles.

In recent years, the use of magnetic particles for biomedicine and clinical therapies has gained considerable attention. Unique features of magnetic particles have made it possible to apply them in medical techniques. These techniques not only provide minimal invasive diagnostic tools but also transport medicine within the cell. In recent years, MRI, drug supply to infected tissue, Hyperthermia are more enhanced by the use of magnetic particles. The present study aims to observe heat and mass transport through blood flow containing magnetic particles in a cylindrical tube. Furthermore, the magnetic field is applied vertically to blood flow direction. The Caputo time fractional derivative is used to model the problem. The obtained partial fractional derivatives are solved using Laplace transform and finite Hankel transform. Furthermore, the effect of various physical parameters of our interest has also been observed through various graphs. It has been noticed that the motion of blood and magnetic particles is decelerated when the particle mass parameter and the magnetic parameter are increased. These findings are important for medicine delivery and blood pressure regulation.

Influence of a Darcy-Forchheimer porous medium on the flow of a radiative magnetized rotating hybrid nanofluid over a shrinking surface.

In this paper, the heat transfer properties in the three-dimensional (3D) magnetized with the Darcy-Forchheimer flow over a shrinking surface of the [Formula: see text] water hybrid nanofluid with radiation effect were studied. Valid linear similarity variables convert the partial differential equations (PDEs) into the ordinary differential equations (ODEs). With the help of the shootlib function in the Maple software, the generalized model in the form of ODEs is numerically solved by the shooting method. Shooting method can produce non-unique solutions when correct initial assumptions are suggested. The findings are found to have two solutions, thereby contributing to the introduction of a stability analysis that validates the attainability of first solution. Stability analysis is performed by employing if bvp4c method in MATLAB software. The results show limitless values of dual solutions at many calculated parameters allowing the turning points and essential values to not exist. Results reveal that the presence of dual solutions relies on the values of the porosity, coefficient of inertia, magnetic, and suction parameters for the specific values of the other applied parameters. Moreover, it has been noted that dual solutions exist in the ranges of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] whereas no solution exists in the ranges of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Further, a reduction in the rate of heat transfer is noticed with a rise in the parameter of the copper solid volume fraction.