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The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applications in medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In this paper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of a Prandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation and an induced magnetic field. The equations for the current flow scenario are developed, incorporating relevant assumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and double diffusion on public health is of particular interest. For instance, infrared radiation techniques have been used to treat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones to enhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governing equations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB. The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticle volume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared with the findings of limiting situations for verification. [ABSTRACT FROM AUTHOR]

Darcy-Forchheimer model has been used to consider the mathematical and statistical aspects of Prandtl nanofluid flow on a stretched curvy geometry, with homogenic-heterogenic reactions, nonlinear radiation, exponential heat, Joule heating, velocity slip, and convective heat conditions. An account of entropy significance has been given to boost the applicability of the study. The 4-5th ordered numerical tool, Runge-Kutta-Fehlberg, has been employed to establish the plots for the considered flow. ANOVA and Taguchi optimisation technique is used to obtain the optimal condition in enhancing the heat transfer rate for modelled mathematical problem. Here, the study reveals that the increasing homo-heterogenic strength parameters foster the concentration profile. The study also found that the thermal curves are positively affected by the radiation parameter and the temperature differential parameter. In addition to this, graphical portraits of isotherms and streamlines have been given to characterise the flow and heat pattern. Taguchi method reveal that first level of Prandtl number, magnetic parameter, Weissenberg number, heat source parameter and third level of curvature parameter, produce maximum Nusselt number. Heat source parameter has large contribution of about 49.45% among the other parameters and Prandtl number has the least contribution of about 1.4% for optimisation. [ABSTRACT FROM AUTHOR]

Current study examined the magnetohydrodynamic (MHD) Prandtl nanofluid of a thermal double‐diffusive flow through an exponentially vertical surface in association with heat generation, and thermophoresis effect. The novelty of this study is due to the analysis of Prandtl nanofluid model with Soret mechanism and chemically responding fluids. This suggested model is beneficial since it can significantly advance the domains of thermal and industrial engineering. The fluid flow phenomenon is characterized by nonlinear coupled differential equations involving two or more independent variables. A suitable numerical technique is used to handle the set of governing equations along with a stability and convergence analysis. According to recent study, the fluid velocity increases since all the parameters are set to higher levels. For the various parametric values, isotherms and streamlines have been explored. This suggested model is beneficial since it can significantly advance the domains of thermal and industrial engineering. For instance, thermal radiation is crucial in designing sophisticated energy‐transformed systems that operate at high temperatures. On the other hand, the phenomenon of Soret is useful in separating isotopes in chemical engineering. An important findings of the current investigations can be treated as, radiative heat encourages fluid temperature distribution since it is the measure of the electromagnetic element radiates from the fluid particle that convert it into thermal radiation. These studies have several applications in the manufacturing and biomedical fields, petrochemical industries, automobiles, medical sciences, and various production processes in industries. [ABSTRACT FROM AUTHOR]

The use of renewable energy sources is leading the charge to solve the world's energy problems, and non-Newtonian nanofluid dynamics play a significant role in applications such as expanding solar sheets, which are examined in this paper, along with the impacts of activation energy and solar radiation. We solve physical flow issues using partial differential equations and models like Casson, Williamson, and Prandtl. To get numerical solutions, we first apply a transformation to make these equations ordinary differential equations, and then we use the MATLAB-integrated bvp4c methodology. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. In addition to numerical and tabular studies of the skin friction coefficient, Sherwood number, and local Nusselt number, important components of the flow field are graphically shown and analyzed. Consistent with previous research, this work adds important new information to the continuing conversation in this area. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. Comparing the Casson nanofluid to the Williamson and Prandtl nanofluids, it is found that the former has a lower velocity. Compared to Casson and Williamson nanofluid, Prandtl nanofluid advanced in heat flux more quickly. The transfer of heat rates are 25.87 % , 33.61 % and 40.52 % at R d = 0.5 , R d = 1.0 , and R d = 1.5 , respectively. The heat transfer rate is increased by 6.91 % as the value of Rd rises from 1.0 to 1.5. This study is further strengthened by a comparative analysis with previous research, which is complemented by an extensive table of comparisons for a full evaluation. [ABSTRACT FROM AUTHOR]

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applications in medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In this paper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of a Prandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation and an induced magnetic field. The equations for the current flow scenario are developed, incorporating relevant assumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and double diffusion on public health is of particular interest. For instance, infrared radiation techniques have been used to treat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones to enhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governing equations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB. The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticle volume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared with the findings of limiting situations for verification. [ABSTRACT FROM AUTHOR]

The aim of this study is to explore the effects of radiative-induced magneto-Prandtl nanofluid on peristaltic waves, in conjunction with viscous dissipation and double-diffusivity convection caused by slip boundaries over an asymmetric channel, using the long wavelength and low but finite Reynold number approximation. The application of thermal radiation and double diffusion is significant in medical research, particularly for treating skin-related ailments through the use of infrared radiation technique. Additionally, infrared radiation can be utilized for medical treatment to restore thermal regulation homeostasis. This study integrates peristaltic motion theory, heat flux using linear approximation, and thermal radiation to analyze the flow problem which incorporates the situation with small temperature difference. The mathematical framework is based on partial differential equations that are further calculated through Numerical Solutions. The numerical solution is calculated using built-in command in the software Mathematica 11 and MATLAB. The impact of various physical parameters on the temperature profile, pressure rise, velocity profile, solute (species) concentration of thermal radiation is illustrated graphically. The significant finding of the study is that the heat radiation effect on blood circulation enhances the temperature which may help to destroy the cancer tissues in drug distribution. [ABSTRACT FROM AUTHOR]

Entropy generation in nanofluid flows is a complex phenomenon influenced by various factors, including the presence of nanoparticles, temperature gradients, and other effects such as magnetic fields and heat generation. Minimizing entropy generation is crucial for improving the efficiency of nanofluid-based heat transfer systems. In this study, we analyze the irreversibility in cubic autocatalytic Prandtl nanofluid flow by a porous stretchable sheet. To model the nanofluid flow, we consider the effects of Darcy-Forchheimer, thermophoresis, and Brownian motion. Additionally, we account for the impacts of magnetic fields, heat generation, and radiation. Under the implementation of second thermodynamics approach, the entropy generation mechanism is evaluated. Under the certain flow assumptions, the mathematical model is constructed for which numerical treatment is followed via the Runge-Kutta-Fehlberg method (RKF-45) implemented in the Mathematica package. The novel-interpreted outcomes are physically observed in view of flow parameters. Numerical studies are conducted to examine engineering quantities. The results show that fluid velocity decreases with higher magnetic and Forchheimer variables. Temperature increases with greater radiation and heat generation parameters. Concentration and temperature fields are enhanced with higher estimations of the thermophoresis variable. Entropy increases with advanced magnetic variables and the Brinkman number, while the opposite effect is observed for the Bejan number. [ABSTRACT FROM AUTHOR]

The focus of this study is to examine cross-diffusion effects on radiative and reactive Prandtl nanofluid due to a convectively heated stretching surface. The present flow problem is considered under the assumption that the external magnetic field is applied to study the nanofluid behavior and thermal radiation considered, for a complete understanding of magnetohydrodynamics of the flow. The governing system of the nonlinear partial differential equations of the flow problem is remodeled with suitable similarity invariants and obtained the system of nonlinear ordinary differential equations. The transformed ODEs with their modified boundary conditions deal with the employment of the Runge-Kutta technique using computation shooting schema with MATLAB software. The consequence of numerous leading parameters on the fluid velocity, temperature, concentration, and engineering quantities profiles are discoursed and presented through graphical illustration. Moreover, the current work is also equated with the available work for limiting cases. It is found that the external magnetic field diminishes the motion of fluid and improvement in heat transfer. Concentration performance improvises on cross diffusion, thermophoresis, and Brownian motion impacts. [ABSTRACT FROM AUTHOR]

The two-dimensional boundary layer flow of a Prandtl nanofluid was explored in the presence of an aligned magnetic field over an inclined stretching/shrinking sheet in a non-Darcy permeable medium. To transform the PDEs of the leading equations into ODEs, a coupled boundary value problem was formed and suitable similarity functions were used. To obtain numerical answers, an efficient code for the Runge–Kutta technique with a shooting tool was constructed with a MATLAB script. This procedure is widely used for the solution of such problems as it is efficient and cost-effective with a fifth-order accuracy. The significance of immersed parameters on the velocity, temperature, concentration, and bioconvection is shown through figures. Furthermore, the physical parameters of the skin friction coefficient and the Nusselt numbers are demonstrated in tables. The declining behavior of the flow velocity against the porosity parameter K p and the local inertia co-efficient F r is shown, and the both parameters of the Darcy resistance and Darcy–Forchheimer resistance are responsible for slowing the fluid speed. The increasing values of the Schmidt number S c decrease the concentration of the nano entities. [ABSTRACT FROM AUTHOR]

In this paper, the boundary layer analysis of three-dimensional Prandtl nanofluid flow over a convectively heated sheet in a porous material is addressed. Nonlinear radiation and high-order chemical reaction analysis are featured in this work. Nonlinear differential equations representing flow expressions are numerically solved by shooting technique. Features of Brownian motion and thermophoresis accounting for nanoparticle diffusion are taken into account. Then, a complete discussion of the influences of the flow regime on several thermofluidic parameters is presented. The outcome of the present study is that velocity field lines are grown due to the strengthening of Prandtl fluid numbers β 1 and β 2 while a reverse trend takes place for temperature profile. Furthermore, it is shown that when the magnetic strength is improved, the skin friction coefficient and heat transfer rate triggers considerable evolution. The obtained results of this model closely match with those available in the literature as a limiting situation. [ABSTRACT FROM AUTHOR]

The present contribution determines the impacts of viscous dissipation and Ohmic heating with magnetic coating on Prandtl nanofluid flow driven by an unsteady bidirectionally moveable surface. Random motion of nanoparticles and thermophoretic diffusion are elaborated through a two-phase nanofluid model. The novelty of the investigation is fortified by prescribed heat flux and prescribed mass flux mechanisms. The appropriate combination of variables leads to a system of strong nonlinear ordinary differential equations. The formulated nonlinear system is then tackled by an efficient numerical scheme, namely, the Keller-Box method. Nanoliquidtemperature and mass-concentration distributions are conferred through various plots with the impacts of miscellaneous-arising parameters. The rates of heat and mass transferences are also discussed through tables. The thermal states of the nanomaterial and mass concentration are reduced for incremental amounts of the unsteady factor, ratio parameter, elastic parameter, and Prandtl fluid parameter. Moreover, escalating amounts of the Brownian parameter, Eckert number, magnetic factor, and thermophoresis parameter enhances the temperature of the nanoliquid. An error analysis is also presented to predict the efficiency of the method used for the computational work. [ABSTRACT FROM AUTHOR]