Entropy Optimization in Magnetohydrodynamic Flow of Third-Grade Nanofluid with Viscous Dissipation and Chemical Reaction

Darcy–Forchheimer Relation Influence on MHD Dissipative Third-Grade Fluid Flow and Heat Transfer in Porous Medium with Joule Heating Effects: A Numerical Approach

The current investigations are carried out to study the influence of the Darcy–Forchheimer relation on third-grade fluid flow and heat transfer over an angled exponentially stretching sheet embedded in a porous medium. In the current study, the applied magnetic field, Joule heating, thermaldiffusion, viscous dissipation, and diffusion-thermo effects are incorporated. The proposed model in terms of partial differential equations is transformed into ordinary differential equations using suitable similarity transformation. The reduced model is then solved numerically with the help of MATLAB built-in function bvp4c.The numerical solutions for velocity profile, temperature profile, and mass concentration under the effects of pertinent parameters involved in the model are determined and portrayed in graphical form. The graphical effects of the skin friction coefficient, the Nusselt number, and the Sherwood number are also shown. From the displayed results, we conclude that when the Joule heating parameter is enlarged, the velocity and the temperature of the fluid are increased. We observed that while enhancing the viscous dissipation parameter (Eckert number) the fluid’s velocity and temperature increase but decreases the mass concentration. By increasing the values of the thermal-diffusion parameter, the velocity distribution, the temperature field, and the mass concentration increase. When the diffusion–thermo parameter rises, the velocity field and the temperature distribution increase, and the reverse scenario is seen in the mass concentration. The results of the current study are compared with already published results, and a good agreement is noted to validate the current study.

Evaluation of entropy generation in cubic autocatalytic unsteady squeezing flow of nanofluid between two parallel plates

BACKGROUND

Nanomaterials have advanced behaviors that make them possibly beneficial in various applications in mass and heat transports such as engine cooling, pharmaceutical processes, fuel cells, engine cooling and domestic refrigerator etc. Therefore here we deliberated the entropy generation in unsteady magnetohydrodynamic squeezing flow of viscous nanomaterials between two parallel plates. The upper plate is squeezing towards lower plate. The lower plate exhibits porous character. Energy attributes are discussed through heat flux, dissipation and Joule heating. Furthermore the irreversibility analysis with cubic autocatalysis chemical reaction is also accounted.

METHODS

Nonlinear differential systems are converted to ordinary differential system by transformations. For convergent series solution the given system are solved by homotopy analysis method (HAM).

RESULTS

Characteristics of various interesting variables on velocity, Bejan number, concentration, entropy optimization and temperature are deliberated through graphs. Gradient of velocity (C_fx) and Nusselt number (Nu_x) are numerically computed against various physical variables. Entropy generation and Bejan number both quantitatively enhance versus radiation parameter. For larger squeezing parameter the velocity and temperature field are increased.

CONCLUSIONS

The obtained results show that for larger squeezing parameter the velocity field boosts up. Velocity have opposite impact For larger magnetic and porosity parameters. Temperature is decreased for higher values of radiation parameter and Prandtl number. Temperature and concentration have same outcome for thermophoresis parameter. Entropy generation and Bejan number both quantitatively enhance versus radiation parameter, while reverse is hold for Brinkman number.