A finite difference numerical simulation scrutiny is executed to evaluate the combined impacts of heat generation, buoyancy forces, viscous dissipation and Joule heating in unsteady hydro-magnetic mixed convective chemically reactive and radiative Casson fluid flowing along an exponentially accelerating permeable vertical plate engrossed in a porous media by considering ramp surface concentration and temperature. The dimensionless non-linear coupled PDEs describing the flow model are dealt numerically by adopting the competent implicit Crank-Nicolson finite difference procedure. The variance of velocity, temperature, and concentration distributions are exposed via graphical representations due to the dissimilarity of the flow restrained parameters. Computational outcomes of the skin-friction, Nusselt and the Sherwood numbers are portrayed in the tabular pattern. The final outcomes of the research exposed that the impacts of thermal radiation, viscous dissipation, and heat production parameters enlarges the temperature and velocity distributions. The fluid motion deflates for growing Casson parameter and magnetic field intensity. The rising chemical reaction parameter suppresses the concentration and velocity distributions. Very importantly it is distinguished that fluid momentum, temperature, and concentration are quicker in the instance of isothermal plate temperature than ramp wall temperature. This kind of research may find specific industrial and medical utilizations such as glass manufacturing, crude oil purification, lubrication, paper production, blood transport study in cardiovascular design, etc.

As a novel fluid of functional material, magnetohydrodynamic (MHD) micropolar fluid has the special properties of light, heat, magnetic and so on. It is of highly practical significance. The characteristics of flow, heat and mass transfer in MHD micropolar nanofluid boundary layer past a stretching plate are investigated based on the micropolar fluid theory in the present numerical work. In the presence of magnetic field, viscous dissipation and the cross-diffusion caused by Dufour effect and Soret effect are considered. First order slip velocity condition is employed. Mathematical models are built based on the assumptions. Collocation spectral method (CSM) via matrix multiplication is adopted to solve the two-dimensional dimensionless nonlinear partial governing equations. The program codes based on CSM is developed, validated and employed. The coupled effects of microrotation, Dufour effect, Soret effect, magnetic field as well as first order slip velocity boundary condition on the flow, heat and mass transfer are revealed. Besides, the variation trends of local Nusselt number and Sherwood number are analyzed in detail. The numerical results indicate that the fluid flow can be suppressed obviously in the consideration n of slip condition and magnetic field. As slip parameter δ and magnetic parameter M rise, the velocity in the boundary layer becomes lower gradually; further, both temperature and concentration increase. On the other hand, the opposite trend can be noticed with the effect of material parameter K. Moreover, Ec and Df augment the temperature; while, Sr leads to an upsurge in concentration. The temperature rises by about 79.73% with Dufour effect and Sh enlarges by a factor of about 38.15% with Soret effect. The concentration boundary layer decreases by about 37.50% is when K=5.0.

The scrutinization of entropy optimization in the various flow mechanisms of non-Newtonian fluids with heat transfer has been incredibly enhanced. Through the investigation of irreversibility sources in the steady flow of a non-Newtonian Willaimson fluid, an analysis of entropy generation is carried out in this current work. The current study has an essential aspect of investigating the heat transfer mechanism with flow phenomenon by considering convective-radiative boundary conditions. A horizontal MHD channel is assumed with two parallel plates to develop a mathematical model for the flow phenomenon by considering the variable viscosity of the fluid. The contribution of physical impacts of thermal radiation, Joule heating, and viscous dissipation is interpolated in the constitutive energy equation. The complete flow of the current analysis is established in the form of ordinary differential equations which further take the form of the dimensionless system through the contribution of the similarity variables. A graphical scrutinization of the physical features of the flow phenomenon in relation to the pertinent parameters is proposed. This study reveals that the higher magnitude of radiation parameter and Brinkman number dominates the system\'s entropy. Moreover, the temperature distribution experiences an increasing mechanism with improved conduction-radiation parameter at the lower plate.

This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler-Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number.

Non-Newtonian fluids are essential in situations where heat and mass transfer are involved. Heat and mass transfer processes increase efficiency when nanoparticles (0.01≤φ≤0.03) are added to these fluids. The present study implements a computational approach to investigate the behavior of non-Newtonian nanofluids on the surface of an upright cone. Viscous dissipation (0.3≤Ec≤0.9) and magnetohydrodynamics (MHD) (1≤M≤3) are also taken into account. Furthermore, we explore how microorganisms impact the fluid\'s mass and heat transfer. The physical model\'s governing equations are transformed into ordinary differential equations (ODEs) using a similarity transformation to make the analysis easier. The ODEs are solved numerically using the Bvp4c solver in MATLAB. The momentum, thermal, concentration, and microbe diffusion profiles are graphically represented in the current research. MHD (1≤M≤3) effects improve the diffusion of microbes, resulting in increased heat and mass transfer rates of 18 % and 19 %, respectively, based on our results. Furthermore, a comparison of our findings with existing literature demonstrates promising agreement.

In this investigation , the consequence of viscous dissipation on the unstable magneto porous convective transport by a micropolar binary fluid due to an inclined surface with viscous dissipation and thermal radiation is examined. Viscous dissipation plays a noteworthy role in industrial applications. The governing PDEs are converted to combined ODEs with the Boussinesq approximation using a similarity analysis. The obtained non-linear ODEs are resolved using the shooting method with \"ODE45 MATLAB\" coding assistance. The numerical outcomes are revealed graphically for various dimensionless parameters and numbers, including temperature, concentration, velocity, and micro-rotation. The temperature, micro-rotation, and velocity fields escalate with increasing Eckert numbers. The radiation parameter and variable viscosity parameter increase the flow rate of the fluid. Increasing radiation parameters, suction parameters, and Prandtl numbers lessen the fluid temperature. The buoyancy parameters have symmetrical impacts on the velocity and microrotation of fluid particles in the cooling and heating modes. Improving Eckert number, inclined angle, Schmidt number, Prandtl number, and magnetic parameter reduces skin friction. The heat transmission rate escalates in quantity due to larger Prandtl number values. Rising Prandtl, Eckert, and Schmidt numbers accelerate the mass transfer rate. The current research result is compared to previously published article\'s result with good agreement.

Transforming growth factor (TGF)-β1 is a multifunctional cytokine that plays important roles in health and disease. Previous studies have revealed that TGFβ1 activation, signaling, and downstream cell responses including epithelial-mesenchymal transition (EMT) and apoptosis are regulated by the elasticity or stiffness of the extracellular matrix. However, tissues within the body are not purely elastic, rather they are viscoelastic. How matrix viscoelasticity impacts cell fate decisions downstream of TGFβ1 remains unknown. Here, we synthesized polyacrylamide hydrogels that mimic the viscoelastic properties of breast tumor tissue. We found that increasing matrix viscous dissipation reduces TGFβ1-induced cell spreading, F-actin stress fiber formation, and EMT-associated gene expression changes, and promotes TGFβ1-induced apoptosis in mammary epithelial cells. Furthermore, TGFβ1-induced expression of integrin linked kinase (ILK) and colocalization of ILK with vinculin at cell adhesions is attenuated in mammary epithelial cells cultured on viscoelastic substrata in comparison to cells cultured on nearly elastic substrata. Overexpression of ILK promotes TGFβ1-induced EMT and reduces apoptosis in cells cultured on viscoelastic substrata, suggesting that ILK plays an important role in regulating cell fate downstream of TGFβ1 in response to matrix viscoelasticity.

This work aimed to numerically investigate the dynamic and thermal behavior of a fully developed, laminar, gaseous flow in a microchannel featuring a rhombic cross-section. Due to new fabrication techniques, microducts with rhombic cross-sections have recently received more attention. The momentum and energy balance equations were solved by using a commercial CDF code and assuming the slip and the H2 boundary conditions. The temperature jump between the wall and the adjacent fluid was also taken into account. The accuracy of the numerical results was checked by using the data available in the literature in terms of velocity profiles in the slip flow regime and the Nusselt number in the continuum flow regime. To also investigate the geometry effects on the fluid behavior, several values of the side angle of the rhombus were considered. The numerical results revealed that the rarefaction degree and geometrical properties significantly affected the Nusselt number.

Present study is dedicated to analyze the closed form solution of nanofluid flow over a stretching/shrinking sheet with dual availability. Flow is developed through two-dimensional boundary layer theory. Appropriate tensor is used to generate the continuity, energy, and momentum equations. Converted governing partial differential equations (PDEs) into dimensionless non-linear ordinary differential equations (ODEs) by adoption of favorable similarity variables. The dimensionless ODEs of energy and momentum produced a dual nature solution in closed form under certain conditions. To deal with the nanofluid, the Koo-Kleinstreuer and Li (KKL) model is used, and the equations are solved using well-known software Maple. The effect of porosity Φ, suction/injection fw, stretching/shrinking λ, and magnetic effect M on skin friction, velocity, temperature, and streamlines are well explored and showcased. The results for the stable solutions have been showed that the upper branch\'s fluid velocity is increasing as the magnetic parameter M rises whereas the lower branch\'s fluid velocity is decreasing as M rises. Additionally, the CuO-nanofluid\'s velocity is impacted by the volume fraction of nanoparticles, with an increase in volume fraction causing a decrease in velocity. On both the lower and upper branches, the temperature profile is seen to improve as the Biot number increases. On the other hand, as the magnetic parameter varies and the magnetic field increases, the local Nusselt number against suction/injection decreases, as well as the rate of heat transfer in the upper branch decreases.

This study is confined to the numerical evaluation of variable density and magnetohydrodynamics influence on Williamson Sakiadis flow in a porous space. In this study, Joule heating, dissipation, heat generation effect on optically dense gray fluid is encountered. The inclined moving surface as flow geometry is considered to induce the fluid flow. A proposed phenomenon is given a mathematical structure in partial differential equations form. These partial differential equations are then made dimensionless using dimensionless variables. The obtained dimensionless model in partial differential equations is then changed to ordinary differential equations via stream function formulation. A set of transformed equations has been solved with bvp4c solver. The numerical fallout of velocity field, temperature field, skin friction, and heat transfer rate are illustrated in graphs and tables with flow parametric variations. Conclusion is drawn that mounting values of density variation parameter confirm the reduction in velocity field and augmentation in temperature of the fluid. When Williamson fluid parameter enhances, both fluid velocity and temperature are rising correspondingly. Growing magnitudes of the magnetic number, radiation parameter, heat generation, and Eckert number rise the temperature of the fluid. A rise in a porous medium parameter weakens the fluid velocity. Skin friction is reducing as radiation parameter and density variation parameter are increased. The present solutions are compared to those that have already been published in order to validate the current model. The comparison leads to the conclusion that the two outcomes are in excellent agreement, endorsing the veracity of the current answers.