Fractional analysis of unsteady squeezing flow of Casson fluid via homotopy perturbation method.

The objective of this article is to model and analyze unsteady squeezing flow of fractional MHD Casson fluid through a porous channel. Casson fluid model is significant in understanding the properties of non-Newtonian fluids such as blood flows, printing inks, sauces and toothpaste etc. This study provides important results as unsteady flow of Casson fluid in fractional sense with aforementioned effects has not been captured in existing literature. After applying similarity transformations along with fractional calculus a highly non-linear fractional-order differential equation is obtained. Modeled equation is then solved along with no-slip boundary conditions through a hybrid of Laplace transform with homotopy perturbation algorithm. For validity purposes, solution and errors at various values in fractional domain are compared with existing results. LHPM results are better in terms of accuracy than other available results in literature. Effects of fractional parameter on the velocity profile, skin friction and behaviors of involved fluid parameters is the focal point of this study. Comprehensive, quantitative and graphical analysis is performed for investigating the effects of pertinent fluid parameters on the velocity profile and skin friction. Analysis revealed that fractional parameter depicts similar effect in case of positive and negative squeeze number. Also, skin friction decreases with an increasing fractional parameter. Moreover, in fractional environment Casson parameter has shown similar effect on the velocity profile in case of positive and negative squeeze number.

Quadratic multiple regression model and spectral relaxation approach for carreau nanofluid inclined magnetized dipole along stagnation point geometry.

Researchers across the world have tried to explore the impact of non-Newtonian liquid flowing via an extendable surface with the inclusion of various effects due to its industrial and engineering applications like polymer production, paper production, filament extrusion from a dye, etc. This study investigates the behavior of stagnation point flow of Carreau liquid attached with inclined magnetic effect and spectral relaxation approach is utilized here for the numerical outcome. In this study, a few other vital features are attached like the quadratic multiple regression model for Nusselt number evaluation, passive control of nanoparticles, viscus heating thermophoresis, Brownian motion, and mixed convection, etc. Velocity disbursement visibility is analyzed by placing an inclined magnetic field. Physical model generates collection of partial differential equations (PDEs) and these PDEs are moved into ordinary differential equations by a similarity transformations scheme. Further for numerical process, spectral relaxation method is used. Growth in K causes a reduction in velocity because this parameter K creates the impedance to flowing resulting in confines the movement of liquid in restricted the plate. Direct relation is found between [Formula: see text] and the energy file. In the case of S > 1, physically it is a representation of Joule and viscous dissipations. This article is novel in its sense that the influence of oblique magnetic force and second order velocity slippage on Carreau nano liquid and its numerical computation with help of the spectral relaxation method has never been done before. Furthermore, the quadratic multiple regression model has been employed to find the heat transition rate in the status of the Nusselt number.

Experimental and TDDFT materials simulation of thermal characteristics and entropy optimized of Williamson Cu-methanol and Al2O3-methanol nanofluid flowing through solar collector.

Current investigation emphasizes the evaluation of entropy in a porous medium of Williamson nanofluid (WNF) flow past an exponentially extending horizontal plate featuring Parabolic Trough Solar Collector (PTSC). Two kinds of nanofluids such as copper-methanol (Cu-MeOH) and alumina-methanol (Al2O3-MeOH) were tested, discussed and plotted graphically. The fabricated nanoparticles are studied using different techniques, including TDDFT/DMOl3 method as simulated and SEM measurements as an experimental method. The centroid lengths of the dimer are 3.02 Å, 3.27 Å, and 2.49 Å for (Cu-MeOH), (Al2O3-MeOH), and (Cu-MeOH-αAl-MOH), respectively. Adequate similarity transformations were applied to convert the partial differential equation (PDEs) into nonlinear ordinary differential equations (ODEs) with the corresponding boundary constraints. An enhancement in Brinkmann and Reynolds numbers increases the overall system entropy. WNF parameter enhances the heat rate in PTSC. The thermal efficiency gets elevated for Cu-MeOH than that of Al2O3-MeOH among 0.8% at least and 6.6% in maximum for varying parametric values.

Impact of Maxwell velocity slip and Smoluchowski temperature slip on CNTs with modified Fourier theory: Reiner-Philippoff model.

The present article presents a novel idea regarding the implementation of Tiwari and Das model on Reiner-Philippoff fluid (RPF) model by considering blood as a base fluid. The Cattaneo-Christov model and thermal radiative flow have been employed to study heat transfer analysis. Tiwari and Das model consider nanoparticles volume fraction for heat transfer enhancement instead of the Buongiorno model which heavily relies on thermophoresis and Brownian diffusion effects for heat transfer analysis. Maxwell velocity and Temperature slip boundary conditions have been employed at the surface of the sheet. By utilizing the suitable transformations, the modeled PDEs (partial-differential equations) are renewed in ODEs (ordinary-differential equations) and treated these equations numerically with the aid of bvp4c technique in MATLAB software. To check the reliability of the proposed scheme a comparison with available literature has been made. Other than Buongiorno nanofluid model no attempt has been made in literature to study the impact of nanoparticles on Reiner-Philippoff fluid model past a stretchable surface. This article fills this gap available in the existing literature by considering novel ideas like the implementation of carbon nanotubes, CCHF, and thermal radiation effects on Reiner-Philippoff fluid past a slippery expandable sheet. Momentum, as well as temperature slip boundary conditions, are never studied and considered before for the case of Reiner-Philippoff fluid past a slippery expandable sheet. In the light of physical effects used in this model, it is observed that heat transfer rate escalates as a result of magnification in thermal radiation parameter which is 18.5% and skin friction coefficient diminishes by the virtue of amplification in the velocity slip parameter and maximum decrement is 67.9%.

An obscure cause of leg edema, non-Hodgkin's lymphoma.

A 25-year-old female having asymptomatic edema of unilateral leg was provisionally diagnosed as a case of psoas abscess. Later, she turned out to be a case of non-Hodgkin's lymphoma. This presentation is contrary to usual age and mode of presentation of non-Hodgkin's lymphoma.