Nonlinear mixed convection flow of a tangent hyperbolic fluid with activation energy

In this communication, the dynamics of a non‐Newtonian tangent hyperbolic fluid with nanoparticles past a nonuniformly thickened stretching surface is discussed. We examine the impact of nonlinear mixed convection flow of a hyperbolic tangent fluid with the Cattaneo‐Christov heat and mass diffusion model past a bidirectional stretching surface. The effects of activation energy and magnetic field are incorporated in the analysis. The variables of transformations are used to change the nonlinear partial differential equations into ordinary differential equations (ODEs). Then, these ODEs are numerically solved using the Matlab routine of the bvp4c algorithm. The derailed analysis of the influences of the governing parameters on velocities along the x‐ and y‐axes, temperature and concentration profiles are presented using tables and figures. The outcomes of these parameters reveal that the velocities along the x‐ and y‐axes are decreased for the values of We increasing but the opposite behavior is observed as the value of $A$ increases. The results also show that the values of $e$ and $Nb$ rise as the temperature profiles increase. Similar influences are observed on the profile of concentration as the values of $F$ and $f$ rise. As the values of $N1$ go from 0.27 to 0.25, the skin‐friction coefficient increases, and similarly, as $Nb$ goes from 0.3 to 0.1, $?\theta \prime (0)$ is enhanced.     

Tangent hyperbolic nanofluid with mixed convection flow: An application of improved Fourier and Fick's diffusion model

This article presents a tangent hyperbolic fluid with the effect of the combination of forced and natural convection flow of nanoparticle past a bidirectional extending surface. Modified Fick's and Fourier's diffusion theories are incorporated into concentration and energy equations, respectively. Convective boundary conditions and second‐order slip flow are taken in the boundary condition. Nonlinear partial differential equations result after boundary layer approximations of the mathematical formulation of the flow problem. Nonlinear high order ordinary differential equations (ODEs) are formed by applying similarity transformation on the nonlinear partial differential equations. The transformed equations are solved with the bvp4c algorithm from Matlab. The numerical solution of ODEs was obtained and the effect of interesting parameters, dimensionless velocity component along x‐ and y‐axis, temperature, and concentration particle, Re_x, Re_y, , and , were presented through tables and graphs and discussed thoroughly. The results indicated that a decrease in velocity along with the y‐axis results from the increasing behavior of S, M, and n. Decrease in both temperature and concentration results in an increase of but their elongation is a result of increase in Bi. An increase in concentration results in decrease of N and S but a decrease in concentration results in the widening of Sc, Nb, and . Furthermore, enlargement of and results in increase of and modules and elongation of both and results in increase of and (Sc and Nb), respectively. A comparison with previously published literature was performed and a good agreement was found.     

Analytical investigation of polar fluid flow with induced magnetic field in concentric annular region

The influence of microrotational velocity on a fully developed laminar, natural convection flow in vertical concentric annuli in the presence of radial magnetic field between two nonconducting vertical concentric annuli is investigated in the present study. The induced magnetic field is generated due to the motion of an electrically conducting fluid in the annulus; the polar fluid has been considered in the present analysis. Transport equations such as momentum, energy, polar fluid, and induced magnetic field are solved analytically for the isothermal case. The effects of the different pertinent parameters of the present model are obtained and analyzed after verification of present methodology. The effects of the Hartmann number, the gap between two cylinders, and vertex viscosity parameters on velocity profiles, induced magnetic field, induced current density, and microrotational velocity profiles are studied. It is observed that the velocity profile and induced magnetic field decrease due to the vertex viscosity parameter; the Hartmann number accelerates the velocity of the microrotation; the induced current density profile decreases for both the Hartmann number and vertex viscosity parameter. The Hartmann number reduces the magnitude of mass flux and skin frictions at the inner and outer cylinder.     

Entropy analysis of nanofluid magnetohydrodynamic convection flow past an inclined surface: A numerical review

A numerical investigation is conducted to review the entropy study of magnetohydrodynamic (MHD) convection nanofluid flow from an inclined surface. In evaluating the thermophoresis and Brownian motion impacts, Buongiorno's model is applied to nanofluid transfer. Using Keller's implicit box technique, the governing partial differential conservation equations and wall and free stream boundary conditions are made into the dimensionless form and solved computationally. For different thermos physical parameter values, the numerical results are discussed both graphically and numerically. Verification of the present code with previous Newtonian responses is also included. To analyze the variability in fluid velocity, temperature, nanoparticle volume fraction, entropy, Bejan number, shear stress rate, wall heat, and mass transfer rates, graphical and tabulated results are reported. The study suggests applications in the manufacturing of nanomaterial fabrication, and so on.     

Magnetohydrodynamic mixed convection in a non-Newtonian third-grade fluid flowing through vertical parallel plates: A semianalytical study of flow and heat transfer

Buoyancy assisted and buoyancy opposed mixed convection of a third-grade fluid, which flows through vertically oriented parallel plates, subjected to uniform and constant wall heat fluxes, under the effect of an externally applied magnetic field, are investigated. The coupled, nonlinear conservation equations of momentum and energy are solved employing the collocation method (CM) and velocity and temperature distributions are solved semianalytically. The results produced by the CM and the results of exact solution are compared for the buoyancy assisted and buoyancy opposed flow of a Newtonian fluid through the vertically oriented parallel plates arrangement without the effect of the externally applied magnetic field. An excellent agreement is exhibited by demonstrating the efficacy of the CM. The effects of the third-grade fluid parameter, Hartmann number, and mixed convection parameter on the dimensionless velocity, temperature, and Nusselt number are studied. The results imply that in the case of buoyancy assisted flow, an increment in the non-Newtonian third-grade fluid parameter causes a decrease in the fluid velocity near the plate walls, which finally causes an increase in the velocity in the central core of the plates. In buoyancy opposed flow, the effect of the same parameter is to oppose the flow reversal near the walls and with higher values of this parameter, it can totally prevent the flow reversal near the walls. The results of the present study can be useful in the fields of flow and heat transfer of various grades of polymers, paints, and food processing.     

Mixed Convection Heat Transfer Analysis in an Enclosure with Two Hot Cylinders: A Lattice Boltzmann Approach

The aim of this work is to study laminar mixed convection heat transfer characteristics within an obstructed enclosure by using the Lattice Boltzmann method. Flow is driven by a top cold lid while other walls are stationary and adiabatic. Hot cylinders are located at different places inside the cavity to explore the best arrangement. Comparison of streamlines, isotherms, average Nusselt number are presented to evaluate the influence of Richardson number and location of cylinders on flow field and heat transfer. Results indicate that heat transfer decreases with a rise of Richardson number for all considered arrays of cylinders. Among them, horizontally‐located cylinders at the top of the cavity have the greatest heat transfer at all Richardson numbers. Horizontally located cylinders at the bottom of the cavity have the lowest heat transfer at Richardson numbers of 0.1 and 1 while the lowest heat transfer rate belongs to cross diagonal located cylinders at a Richardson number of 10.     

Simultaneous effects of viscous and Darcy dissipation on mixed convection flow in an annulus partially filled with porous material: Analytical approach

The effect of thermal dissipation on a steady, fully developed, mixed convection viscous, incompressible fluid in an annulus partially filled with porous materials has been thoroughly examined in this work. Fluid flow begins within the annulus when a pressure gradient is applied abruptly in the flow direction. The fluid flow in the porous zone is characterized by the Brinkmann-extended Darcy model. The fluid is divided into transparent and porous parts by a minimal interface. By matching their velocities and considering the shear stress jump conditions at the interface, the clear fluid and the porous region are connected. Additionally, the viscous dissipation effect is considered while determining the energy equation in the clear fluid zone. However, in the porous area, the Darcy dissipation effects are considered in addition to the viscous dissipation influence. In the model, the results of various fluid parameters in the problem were addressed using line graphs and the homotopy perturbation method. The study found that when the porous region's thickness grows, heat transmission on the annular surface enclosing the clear fluid region increases while it decreases on the border surface close to the porous region. In addition, a thicker porous region requires a greater pressure gradient to propel the flow.