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Exploration related to chemical processes in nanomaterial flows contains astonishing features. Nanoparticles have unique physical and chemical properties, so they are continuously used in almost every field of nanotechnology and nanoscience. The motive behind this article is to investigate the Cross nanofluid model along with its chemical processes via auto catalysts, inclined magnetic field phenomena, heat generation, Brownian movement, and thermophoresis phenomena over a symmetric shrinking (stretching) wedge. The transport of heat via nonuniform heat sources/sinks, the impact of thermophoretic diffusion, and Brownian motion are considered. The Buongiorno nanofluid model is used to investigate the impact of nanofluids on fluid flow. Modeled PDEs are transformed into ODEs by utilizing similarity variables and handling dimensionless ODEs numerically with the adoption of MATLAB's developed bvp4c technique. This software performs a finite difference method that uses the collocation method with a three-stage LobattoIIIA strategy. Obtained outcomes are strictly for the case of a symmetric wedge. The velocity field lessens due to amplification in the magneto field variable. Fluid temperature is amplified through the enhancement of Brownian diffusion and the concentration field improves under magnification in a homogeneous reaction effect. [ABSTRACT FROM AUTHOR]

Highlights: What are the main findings? The problem of 2-D Prandtl nanofluid past a moving wedge is investigated in detail; Tri-hybrid nanoparticles are considered here; Heat and mass transmission evaluations are conducted in the presence of endothermic/exothermic chemical reactions; The moving wedge is considered; What is the implication of the main finding? LobattoIIIA scheme is implemented for the numerical solution of modeled PDEs. Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick's second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter α brings about a decrement in fluid velocity and augmentation in thermal conductivity ϵ , thermal radiation R d , thermophoresis parameter N t and endothermic/exothermic reaction Ω , and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature. [ABSTRACT FROM AUTHOR]

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%. [ABSTRACT FROM AUTHOR]

Here, modeling and computations are performed to explore the impact of variable molecular diffusivity, nonlinear thermal radiation, convective boundary conditions, momentum slip, and variable molecular diffusivity on Prandtl fluid past a stretching sheet. By using the compatible transformation, the partial differential equations regarding momentum, energy, and concentration are reformed into ordinary differential equations and furthermore, these equations are handled numerically via the shooting method. The behavior of intricate parameters that emerge during numerical simulation is displayed in the form of tables and graphs. These outcomes are supplemented with the information for the heat transfer rate and surface drag coefficients. It is perceived that an uplift in the temperature profile occurs by virtue of augmentation in the temperature convection parameter, and furthermore, mass fraction field escalates owing to an amplification in the chemical reaction coefficient. [ABSTRACT FROM AUTHOR]

• Cross non-Newtonian tetra hybridity bio-nanofluid flowing along stenosed artery with convective heat transport is analyzed. • Impacts like heat source/sink, viscous dissipation, Joules heating as well as nonlinear thermal radiation are probed. • Numerical treatment with the utilization of MATLAB builtin bvp4c scheme is introduced. • Temperature within the arteries is intensified by the advantage of a thermal radiation and viscous dissipation. Researchers around the planet are attempted to explore the influence of various non-Newtonian fluids with the mono and dihybrid nanoparticles in the status of blood flowing arteries to investigate the heat transference aspect for the cure of various diseases. Current examination is created to investigate the effect of extended novel tetra hybrid Tiwari and Das nanofluid model on blood flow arteries with consideration of Cross non-Newtonian fluid model. Heat transference assessment has been taken with the insertion of impacts like heat source/sink, viscous dissipation, Joules heating as well as nonlinear thermal radiation. PDE are designed to investigate the momentum of blood flowing and temperature analysis. The governing PDE are converted into ODE with the application of similarity conversions and furthermore managed these ODE numerically with the utilization of MATLAB builtin bvp4c scheme. The obtained outcomes are studied numerically as well as graphically in the case of diverse dimensionless variables ranges between 0.5 ≤ M ≤ 2 , 0.1 ≤ W e ≤ 4 , 0.1 ≤ n ≤ 1.5 , 0.1 ≤ γ ≤ 2 , 0.5 ≤ R d ≤ 2 , 19 ≤ P r ≤ 22 , 0.1 ≤ θ w ≤ 1.5 , 0.1 ≤ E c ≤ 2.1 , 0.5 ≤ U ≤ 2 , 0.5 ≤ W ≤ 2 versus velocity, temperature, wall frictional factor and heat transition rate. From obtained outcomes it is reflected that the surface drag phenomenon weakens by the boost of a Weissenberg number and an increment variation in magneto force provides a resistance against the fluid flow. Temperature within the arteries intensifies by the advantage of a thermal radiation and viscous dissipation. [ABSTRACT FROM AUTHOR]

• Flow problem of Reiner-Philippoff fluid with A A 7072 , A A 7075 , Ti 6 Al 4 V , Ti 5 Al 2.5 S n is analyzed. • Cattaneo-Christov heat flux and Forchheimer velocity are considered. • Variable heat source (sink) and thermal radiative heat flux is taken into consideration. • Numerical treatment is accomplished in collaboration with the Galerkin finite element method. • The heat transfer rate magnifies extra in tetra hybridity nanofluid in disparity to tri and di hybridity nanofluid. Scientists across the world have tried to explore the effect of non-Newtonian fluids moving over a symmetric stretchable sheet with the presence of diverse influences revealed in this study due to its tremendous applications in various engineering and industrialized sectors like aerodynamics extrusion of plastic surfaces, condensation procedure of metal symmetric plate in a refrigeration immersion, and extrusion of a polymeric surface from a dye. Proposed model Reiner-Philippoff fluids flowing related to a symmetric stretch surface with the inclusion of effects like Forchheimer velocity, thermal radiative, and Cattaneo Christov heat fluxing are considered in the momentum and temperature equation. Novel tetra hybrid nanoparticles are considered to check the thermo physical behaviour of the proposed model. The showed PDEs are transformed into ODEs with the utilization of symmetric and self-similarity variables and further attempted numerically with the assistance of the Galerkin finite element methodology (G-FEM). The obtained findings are scrutinized in the form of figures and tables. Findings From obtained outcomes, it is perceived that the heat transfer Nusselt magnifies extra in the instance of tetra hybrid nanofluids (THNFs) in disparity to tri and di hybrid nanoparticles. Darcy Forcheeimer effect Fr diminishes the fluid velocity and the temperature outline amplifies owed to amplification in thermal radiative variable Rd. The insertion of nanoparticles supports in the stabilizating of a nanofluid's flow and provides the symmetric of the structure. Error in heat transfer Nusselt number diminishes by the virtue of magnification in Rd and the heat deliverance phenomenon magnifies as a consequence of enlargement in the thermal relaxation constraint. Practical application of the proposed model Due to its particle use in manufacturing and engineering for shells that expand and contract, like stretchable (shrinkable) packaging, bundle wrapping, hot roll, sheet material extrusion, wire roll, glass fiber manufacturing, metallic packags, and aluminum bottles manufacturing, parabolic tough surface collectors, cooling of thermal reactors, polymer production, etc., the examination of two-dimensional flowing over an extending shallow has attracted attention. The proposed model outcomes are utilized in order the enhance heat transfer of the various liquids by utilizing tetra hybrid nanoparticles and effects like nonlinear based thermal radiation, Cattaneo-Christov heat flux and heat source/sink phenomenon. Novelty The effort is novel in its sagacity that no nanofluid model has been developed yet to examine the effect of tetra hybrid nanoparticles on liquid moving over any sort of surface. [ABSTRACT FROM AUTHOR]

The communication aims to analyze the conduct of rotating Prandtl nanofluid with the inclusion of effects like MHD, variable species diffusivity, nonlinear warm radiation, convective limit conditions, velocity slip and chemical reaction on fluid moving along a stretchable surface. Buongiorno model is implemented in orde to catch the Brownian movement and thermophoresis impacts by the presence of nanofluids. The effect of viscous dissemination and Joule heating is used in the current review. Using suitable similarity variables, the governing differential conditions with respect to momentum, energy, and concentration are improved into customary, ordinary differential equations and these equations numerically with the shooting technique. The ranges of different dimensionless parameters used in our study are Prandtl fluid parameter 0 ≤ α ≤ 3.5, elastic parameter 1 ≤ β ≤ 7, thermal radiation 1 ≤ Rd ≤ 2, temperature ratio parameter 1 ≤ θ w ≤ 1.6, Eckart number 0.3 ≤ Ec ≤ 0.7, velocity slip parameter 0 ≤ γ 1 ≤ 1, thermophoresis parameter 0.1 ≤ Nt ≤ 4, Brownian motion parameter 0.1 ≤ Nb ≤ 1.5, Prandtl number 1.7 ≤ Pr ≤ −2.6, magnetic parameter 0.1 ≤ M ≤ 0.8, chemical reaction parameter 0.2 ≤ δ ≤ 1, convection parameter 0.3 ≤ γ 2 ≤ 1.1, rotational parameter 0.1 ≤ λ ≤ 0.7, Schmidt number 0.1 ≤ Sc ≤ 0.7, variable species diffusivity 0.1 ≤ ϵ ≤ 0.5 which shows up during mathematical arrangement are shown as tables and charts. These results are enhanced with the data for the heat transfer rate and skin friction coefficients. It is seen that the temperature profile enhanced on account of an increase in temperature convection boundary and mass fraction field raises due to an improvement in species diffusivity parameter. [ABSTRACT FROM AUTHOR]

The primary concern of writing this article is to study the rheological properties of the micropolar non‐Newtonian nanofluid flowing through the porous medium along with magnetic field effects. In it, the outer boundary of the sheet is heated by applying an external heat source. The insertion of aluminum oxide nanoparticles in water turned it into a nanofluid. Together with the viscous dissipation phenomena, adding a magnetic field has another effect known as a Joule heating impact that is considered in the energy equation. To investigate the impact of viscosity and thermal conductivity on flow patterns, we considered the Koo‐Kleinstreuer‐Li model. A generalized Proudman‐Johnson equation is obtained by using similarity transformation on Navier‐Stokes equations. The well‐known classical shooting method is used to get the numerical solution to the said problem. Graphical results are portrayed for variant rheological parameters lke power law index, Reynolds number, volume fraction, Prandtl number, expansion ratio, and Hartmann number on the velocity and temperature of nanofluids. [ABSTRACT FROM AUTHOR]

Objective: To determine the accuracy of intraoperative radionuclide scintigraphy for detection of sentinel lymph node (SLN), using 99mTc-Nanocolloids, in patients with early breast carcinoma. Study Design: Cross sectional analytical study. Place and Duration of Study: Nuclear Medical Centre, Armed Forces Institute of Pathology, Rawalpindi and department of Surgery, Pak Emirates Military Hospital, Rawalpindi, from Jul 2012 to Jun 2013. Patients and Methods: After fulfilling the inclusion and exclusion criteria and taking written informed consent, 67 patients of carcinoma breast were enrolled in the study. Each patient was injected with 37 MBq of 99mTc-Nanocolloids, via sub areolar, peri-tumoural route, pre-operatively. SLNs were identified using handheld gamma probe followed by excision biopsy. Patients, then, underwent modified radical mastectomy with dissection of axillary lymph nodes (ALN) and the samples were sent for histopathology. Results: Out of 67 patients, 28 to 77 years of age (mean ± SD of 49.61 ± 11.572 years), 17.9% (12) patients had T1tumour while 82.1% (55) had T2 tumour (mean ± SD of 3.48 cm ± 1.050 cm). Histopathology revealed no metastasis in SLNs as well as ALN of 55.2% (37) patients while 40.3% (27) patients were positive for both. However, in 4.5% (3) patients SLNs were negative for metastasis with positive ALN. Diagnostic accuracy was calculated to be 95.5%, sensitivity 90%, false negative rate 4.5% and negative predictive value 92.5%. Conclusion: Intraoperative radionuclide scintigraphy, using 99mTc-Nanocolloids and handheld gamma probe is a reasonably accurate technique for localization of SLNs in early breast carcinoma. [ABSTRACT FROM AUTHOR]

Solar energy is the basic source of renewable energy, and it is being used for controlling global pollution/warming. As the Cross nanofluid is very useful for cooling solar devices, in this paper analysis of the global warming effect is investigated by incorporating the nonlinear thermal radiation over the exponentially extendable surface because it plays a major role related to solar energy absorption of nanofluid. Furthermore, the mathematical modeling of Cross nanofluid involving magnetic effect and diffusion is discussed by using the fact of chemical reaction. Chemical reaction finds astonishing applications in pollution studies, chemical processing equipment, and polymer production. As a result of this study, it is noticed that more magnetized conducting fluid controls the motion of fluids for both cases of shear thinning and shear thickening. Brownian motion parameter Nb affects the rate of the random motion of nanoparticles. Increased Nb temperature also increases due to these random movements of nanoparticles. That is the reason why pollutant nanoparticles spread in air as a result of global warming increase. [ABSTRACT FROM AUTHOR]

A mathematical model is created to analyze the impact of Thompson and Troian slip boundaries over a contracting/expanding surface sustaining nanofluid-containing carbon nanotubes along a stagnation point flow. Both multi-wall (MWCNTs) and single-wall (SWCNTs) carbon nanotubes are taken into consideration, with water serving as the base liquid. The flow is obtained due to the stretching or contracting of the surface. The thermal radiation, activation energy, buoyancy impacts, and chemical processes called quartic autocatalysis are additionally added to the original mathematical model. The MATLAB-constructed bvp4c function involving the three-stage Lobatto IIIa formula for the numerical results of dimensionless velocity, concentration, and temperature profiles are used. By contrasting it against a published paper in this limited instance, it is determined whether the suggested mathematical model is legitimate. In this sense, a remarkable consensus is achieved. Graphical representations are used to depict the behavior of many non-dimensional flow variables, such as the slip velocity parameter, the inertia coefficient, the porosity parameter, and the solid volume fraction. Surface drag force computations are reported to examine the effects at the permeable stretching surface. It has been shown that increasing the slip velocity factor increases the fluid streaming velocity while decreasing the surface drag force. If the endothermic/exothermic coefficient increases, the local thermal transfer efficiency falls. For nanofluids, the changing viscosity factor increases axial velocity while decreasing temperature distribution. Additionally, the solid volumetric fraction improves the temperature distributions by lowering the concentration profile and speed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 Ec 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. [ABSTRACT FROM AUTHOR]

Objective: To assess live donor nephrectomy for development of hypertension. Study Design: Retrospective observational study. Place and Duration of Study: The study was conducted at Armed Forces Institute of Urology (AFIU) Rawalpindi, from May 2016 to May 2020. Methodology: All consenting kidney donors for live renal transplant were introduced with the process. Baseline blood pressure at time of workup of donation and annually afterwards after transplant on follow up examinations using retrospective data analysis of donor's workup and follow up was used. Comparison of 1,2,3 and 4-year occurrence of hypertension among (normotensive) donors with 1,2,3 and 4-year of donation using estimates from Framingham Hypertension Risk Score. Results: A total of 79 donors with a completed annual follow-up rate of up to100 % during a 4-year period. The average age at donation was 33.96 ± 10.23 SD years; 50 donors (63.4%) were women. Overall 27% (22 out of 79) of all live donors developed post donation hypertension who were normotensive at the time of donation. Almost 2/3rd of the patients developing hypertension were females. There was a significant increase in blood pressure measurements each year after donation. Increased BMI of the patient was a risk factor for post donation development of hypertension. The donors who continue being normotensive 1-year post donation yielded an analogous risk to that fit Framingham populace. Conclusion: Live organ kidney givers are at augmented risk of development of hypertension post kidney donation. The study ascertains the potential significance of following donors and handling risk factors aggressively to avert hypertension and to increase donor survival. [ABSTRACT FROM AUTHOR]