The present research work explores the effects of suction/injection and viscous dissipation on entropy generation in the boundary layer flow of a hybrid nanofluid (Cu–Al₂O₃–H₂O) over a nonlinear radially stretching porous disk. The energy dissipation function is added in the energy equation in order to incorporate the effects of viscous dissipation. The Tiwari and Das model is used in this work. The flow, heat transfer, and entropy generation analysis have been performed using a modified form of the Maxwell Garnett (MG) and Brinkman nanofluid model for effective thermal conductivity and dynamic viscosity, respectively. Suitable transformations are utilized to obtain a set of self-similar ordinary differential equations. Numerical solutions are obtained using shooting and bvp4c Matlab solver. The comparison of solutions shows excellent agreement. To examine the effects of principal flow parameters like suction/injection, the Eckert number, and solid volume fraction, different graphs are plotted and discussed. It is concluded that entropy generation inside the boundary layer of a hybrid nanofluid is high compared to a convectional nanofluid.

Heat transfer and entropy generation in a hybrid nanoliquid flow caused by an elastic curved surface is investigated in the present article. To examine the effects of frictional heating on entropy generation, the energy dissipation function is included in the energy equation. The Tiwari and Dass model for nanofluid is used by taking water as a base fluid. A new class of nanofluid (hybrid nanofluid) with two kinds of nanoparticles, Copper (Cu) and Aluminum oxide (Al₂O₃), is considered. Curvilinear coordinates are used in the mathematical formulation due to the curved nature of the solid boundary. By utilizing similarity transformations, the modelled partial differential equations are converted into ordinary differential equations. Shooting and the Runge-Kutta-Fehlberg method (FRKM) have been used to solve the transformed set of non-linear differential equations. The expression for entropy generation is derived in curvilinear coordinates and computed by using the numerical results obtained from dimensionless momentum and energy equations. Comparisons of our numerical results and those published in the previous literature demonstrate excellent agreements, validating our numerical simulation. In addition, we have also conducted parametric studies and find that entropy generation and temperature suppress with increasing values of dimensionless radius of curvature. Furthermore, it is found that less entropy is generated in regular nanofluid as compare to hybrid nanofluid. To examine the influences of a set of embedding physical parameters on quantities of interest, different graphs are plotted and discussed.

The primary objective of the present work is to study the effects of heat transfer and entropy production in a nanofluid flow over a curved surface. The influences of Lorentz force and magnetic heating caused by the applied uniform magnetic field and energy dissipation by virtue of frictional heating are considered in the problem formulation. The effects of variable thermal conductivity are also encountered in the present model. The dimensional governing equations are reduced to dimensionless form by introducing the similarity transformations. The dimensionless equations are solved numerically by using the Chebyshev–Gauss–Lobatto spectral method (CGLSM). The rate of increase/increase in the local Nusselt number and skin friction coefficient are estimated by using a linear regression model. The expression for dimensionless entropy production is computed by employing the solutions obtained from dimensionless momentum and energy equations. Various graphs are plotted in order to examine the effects of physical flow parameters on velocity, temperature, and entropy production. The increase in skin friction coefficient with magnetic parameter is high for nanofluid containing copper nanoparticles as compared to silver nanoparticles. The analysis reveals that velocity, temperature, and entropy generation decrease with the rising value of dimensionless radius of curvature. Comparative analysis also reveals that the entropy generation during the flow of nanofluid containing copper nanoparticles is greater than that of containing silver nanoparticles.

The main purpose of this numerical investigation is to estimate energetically the thermo-magnetohydrodynamic (MHD) irreversibility arising in Stokes’ second problem by successfully applying the first and second thermodynamic laws to the unsteady MHD free convection flow of an electrically conducting dissipative fluid. This fluid flow is assumed to originate periodically in time over a vertical oscillatory plate which is heated with uniformly distributed temperature and flowing in the presence of viscous dissipation and Ohmic heating effects. Moreover, the mathematical model governing the studied flow is formulated in the form of dimensional partial differential equations (PDEs), which are transformed into non-dimensional ones with the help of appropriate mathematical transformations. The expressions of entropy generation and the Bejan number are also derived formally from the velocity and temperature fields. Mathematically, the resulting momentum and energy conservation equations are solved accurately by utilizing a novel hybrid numerical procedure called the Gear-Generalized Differential Quadrature Method (GGDQM). Furthermore, the velocity and temperature fields obtained numerically by the GGDQM are exploited thereafter for computing the entropy generation and Bejan number. Finally, the impacts of the various emerging flow parameters are emphasized and discussed in detail with the help of tabular and graphical illustrations. Our principal result is that the entropy generation is maximum near the oscillating boundary. In addition, this thermodynamic quantity can rise with increasing values of the Eckert number and the Prandtl number, whereas it can be reduced by increasing the magnetic parameter and the temperature difference parameter.