Importance of Darcy-Forchheimer relation in chemically reactive radiating flow towards convectively heated surface

Computational analysis of Darcy-Forchheimer relation, reduced gravity, and external applied magnetic field influence on radiative fluid flow and heat transfer past a sphere: Finite difference method

The study of radiation, Darcy-Forchheimer relation, and reduced gravity, effects on magnetohydrodynamic flow across a solid sphere immersed in porous material, is the focus of the current work. Coupled and nonlinear partial differential governing equations, are established to model the studied configuration. By using appropriate scaling variables, the resultant set of governing equations is converted to its dimensionless form. Based on these established equations, a numerical algorithm is written based on the finite element approach to solve the considered problem. A verification of the validity of the proposed model is done by comparing with already published results. Furthermore, to check the precision of solutions, a grid independence test has been accomplished. The unknown variables, such as fluid velocity and temperature, and their gradients are evaluated. This investigation's main objective is to demonstrate how the Darcy-Forchheimer law and reduced gravity due to density difference affect the natural convective heat transfer across a solid sphere immersed in a porous medium. Results show that the flow intensity decreases with the magnetic field parameter, local inertial coefficient, Prandtl number, and porosity parameter and becomes more important by increasing the reduced gravity and radiation parameters. In addition, the temperature increases with the inertial coefficient, porosity parameter, Prandtl number, radiation parameter, and magnetic field parameter and get declined with the reduced gravity parameter.

Significance of Chemical Reaction and Lorentz Force on Third-Grade Fluid Flow and Heat Transfer with Darcy–Forchheimer Law over an Inclined Exponentially Stretching Sheet Embedded in a Porous Medium

The combined impact of a linear chemical reaction and Lorentz force on heat and mass transfer in a third-grade fluid with the Darcy–Forchheimer relation over an inclined, exponentially stretching surface embedded in a porous medium is investigated. The proposed process is mathematically expressed in terms of nonlinear and coupled partial differential equations, with the symmetry of the conditions normal to the surface. To solve the mathematical model of the proposed phenomenon, the partial differential equations are first reduced to ordinary differential equations; then, MATLAB built-in Numerical Solver bvp4c is used to obtain the numerical results of these equations. The influence of all the pertinent parameters that appeared in the flow model on the unknown material properties of interest is depicted in the forms of tables and graphs. The physical attitude of the unknown variables is discussed with physical reasoning. From the numerical solutions, it is inferred that, as Lorentz force parameter is increased, the velocity of the fluid decreases, but fluid temperature and mass concentration increase. Thisis due to the fact that Lorentz force retards the motion of fluid, and the increasing resistive force causes the rise in the temperature of the fluid. It is also noted that, owing to an increasein the magnitude of chemical reaction parameter , the velocity profile and the mass concentration decline as well, but the fluid temperature increases in a reasonable manner. It is noted that, by augmenting the values of the local inertial coefficient and the permeability parameter , the velocity field decreases, the temperature field increases, and mass concentration also increases with reasonable difference. Increasing values of Prandtl number results in a decrease in the profiles of velocity and temperature. All the numerical results are computed at the angle of inclination . The current results are compared with the available results in the existing literature for thisspecial case, and there is good agreement between them that shows the validation of the present study. All the numerical results show asymptotic behavior by satisfying the given boundary conditions.

Exploring the features for flow of Oldroyd-B liquid film subjected to rotating disk with homogeneous/heterogeneous processes

BACKGROUND AND OBJECTIVE

In the working principle of magnetic devices, the thin film substances are the verified efficient ingredients. Several fields of physics and chemistry has taken advanced studies for the features and utilization of thin film for various aspects. Here, we extracted the features of thin film analysis for time-dependent Oldroyd-B liquid. More specifically, our emphasis is to explore transportation rate of mass/heat by considering mass/energy fluxes. Furthermore, space/temperature dependent heat source/sink are considered. Radiation aspects are taken into account for mathematical modeling of Oldroyd-B liquid. Additionally, Oldroyd-B liquid features are elaborated considering Dufour/Soret aspects. Moreover, the heated surface by convection and chemical aspects remained under consideration while designing the physical model.

METHOD

Feasible variables are employed to achieve nonlinear structure. Computational analysis of such a nonlinear structure is too easy. Therefore, we have engaged numerical technique (bvp4c technique) to solve nonlinear system.

RESULTS

Thickness of liquid film boosts for larger rotation whereas it dwindles against magnetic parameter. Liquid concentration intensifies for Soret number. Transportation rate of mass for larger rotation parameter.

CONCLUSION

Velocity components (Radial, axial, azimuthal) rises via higher ω. Velocity of liquid increase for greater (β₂) while reverse trend is detected for (β₁). Temperature of liquid dwindles for heat sink (A* < 0, B* < 0) parameters while (θ(η)) rises for (A* > 0, B* > 0).

Eyring-Powell nanofluid flow with nonlinear mixed convection: Entropy generation minimization

BACKGROUND

Entropy is the amount of energy which is lost during any irreversible process. Here our main focus is that how can we reduce this energy loss to enhance the capability of our system. Blood is an example of Eyring-Powell fluid. Many strategies are used to rise the capacity of heat transport. Heat transport can be enhanced by intensifying the materials thermal conductivity through nanoparticles. Thermal conductivity of the material can be enhanced by adding nanoparticles in base fluid. The objective of this work is to discuss entropy generation in MHD Eyring-Powell nanofluid flow. The flow is generated by a linear stretchable surface. Current analysis includes the effects of viscous dissipation, nonlinear mixed convection and Joule heating. Nanoparticles analyzed the consequences of Brownian motion and thermophoresis effects.

METHOD

The boundary layer flow equations are solved for series solutions by applying homotopic technique.

RESULTS AND CONCLUSION

Graphical results of involved quantities like entropy generation, velocity, concentration and thermal fields are presented. Skin friction, Sherwood and Nusselt number are numerically scrutinized.

Modeling and computational analysis of hybrid class nanomaterials subject to entropy generation

BACKGROUND AND OBJECTIVE

Nanoliquids are dilute suspensions of nanoparticles with at least one of their principal dimensions smaller than 100 nm. Form literature, nanoliquids have been found to possess increased thermos-physical characteristics like thermal diffusivity, thermal conductivity, convective heat transport coefficients and viscosity associated to those of continuous phase liquids foe example oil, ethylene glycol and water. Nanoliquids have novel characteristics that make them possibly beneficial in numerous applications in heat transport like fuel cells, microelectronics, hybrid-powered engines, pharmaceutical processes, domestic refrigerator, engine cooling thermal management, chiller and heat exchanger. The above applications of nanofluids/hybrid nanofluids insist the researchers and engineers to develop new methodologies and technique in the field of heat transport. Therefore, we have considered mixed convective flow hybrid nanomaterial over a convectively heated surface of disk. Flow nature is discussed due to stretchable rotating surface of disk. Applied magnetic field is accounted. Ohmic heating and dissipation effects are utilized in the modeling of energy expression. Total entropy rate is calculated.

METHODS

Suitable transformation leads to ordinary differential equations. Shooting method is implemented for numerical outcomes. Comparative analysis is made for the present result with published ones.

RESULTS

The effects of key parameters like magnetic parameter, mixed convection variable and Eckert and Biot numbers on the dimensionless velocity, surface drag force, temperature, (heat transfer rate) Nusselt number and entropy rate are discussed in detail and presented graphically. Furthermore, the outcomes demonstrate that velocity of liquid particles decline against magnetic parameter. Temperature and associated layer upsurge versus magnetic parameter and Eckert number. Skin friction coefficient (drag force) improves through higher values of stretching and magnetic variables. Heat transfer rate is more for higher Eckert number and magnetic parameter. Entropy rate is also enhances against Eckert number and Brickman number.

CONCLUSIONS

Magnitude of surface drag force increases for higher values of stretching and magnetic variables. Magnitude of heat transfer rate is more when magnetic variable and Eckert number attain the maximum values. Brinkman number is used to decrease the entropy rate. Furthermore, velocity and temperature show contrast behavior versus magnetic parameter i.e., velocity of fluid particles decreases.