Cattano Christov double diffusion model for third grade nanofluid flow over a stretching Riga plate with entropy generation analysis

In this work, entropy generation analysis of an air-cooled natural draft wire-and-tube condenser commonly used in the domestic refrigerator is carried out to investigate geometrical and operating parameters. The Bejan number formulation is used for the analysis because of its ability to relate the heat transfer to pressure drop entropy generation. The analysis also incorporates thermoeconomics by combining the second law of thermodynamics with economic principles. The analytical study is carried out by varying geometrical parameters of the condenser such as tube outer diameter, wire diameter, number of wire pairs, number of tube rows, tube pitch, wire pitch and refrigerant (R134a) properties such as mass velocity, saturation temperature and dryness fraction. The behaviour of entropy generation due to heat transfer and pressure drop, Bejan number and thermoeconomic variables such as relative cost difference and exergoeconomic factor are analysed. These results are used in obtaining the values of condenser dimensions leading to better performance.

In this work, entropy generation is optimized through the application of the second law of thermodynamics. The slip mechanisms, Brownian diffusions, and thermophoresis are elaborated using the tangent hyperbolic nanomaterial model. Magnetohydrodynamic (MHD) fluid is taken into consideration. To characterize the impact of activation energy, a unique model involving the binary chemical reaction is deployed. The effects of mixed convection that is nonlinear in nature, bioconvection, and Joule effect are all taken into consideration. The key partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by utilizing appropriate similarity transformations and then solved numerically with the help of a built-in ‘bvp4c’ technique of MATLAB software. Varied flow parameters’ impacts on the nanoparticle volume concentration, entropy number, microorganism concentration, temperature, and velocity fields are analyzed using graphs. Various flow variables are taken into consideration to calculate the total rate of entropy generation. The obtained results show that concentration irreversibility, Joule effect irreversibility, viscous dissipation, and heat irreversibility all influence the entropy. The numerical outcomes were observed by fixing the physical parameters as 0.1<α<4.0, 0.1<M<1.2, 0.1<Nr<2.2, 0.1<Le<2.2, 0.1<Nb<0.4, 0.1<Nt<1.0, 2.0<⁡Pr⁡<5.0, and 0.1<Lb<2.0, as well as their impact on the momentum, thermal, concentration, and microorganism density profiles. From results, an increasing estimate of the variable representing chemical reaction indicates a decline in the concentration. The higher the chemical reaction variable, Hartmann number, and Weissenberg number, the higher the entropy number, while the Bejan number has a contrary behavior. Subsequently, all the outcomes are plotted in graphs and discussed in detail, when subjected to the involving physical quantities.

A theoretical study of unsteady magnetohydrodynamic boundary layer stagnation point flow, heat and mass transfer of a second grade electrically-conducting nanofluid from a horizontal stretching sheet with thermal slip and second order slip velocity effects is presented. The Buongiorno formulation is employed for nanofluids and in addition the no-flux nanoparticle boundary condition is also considered. The appropriate similarity transformations are applied to convert the governing equations into the system of nonlinear partial differential equations, which is solved by using homotopy analysis method. Entropy generation and Bejan number have also been evaluated for the effects of magnetic parameter, Reynolds number and slip parameter in non-Newtonian (second-grade) time-dependent flow. The computations show that skin friction coefficient and entropy generation number increase with an increment in magnetic parameter whereas Bejan number decreases with it. Local Nusselt number decreases with an increase in the value of Eckert number (viscous dissipation) and thermal slip whereas the converse behaviour is captured for velocity parameter. The work is relevant to magnetohydrodynamic nanomaterials processing.

The main emphasis of the present study is to analyze the novel feature of entropy generation in the flow and heat transfer of Sisko nanofluid over a stretching sheet in the presence of the magnetic field, chemical reaction, and convective boundary conditions. Buongiorno's nanofluid model is used to consider the effect of Brownian diffusion and thermophoresis. The governing Sisko nanofluid flow equations comprising the momentum, nanoparticle volume fraction, and energy are reduced to nonlinear differential equations by utilizing appropriate similarity variables. The numerical solution of nonlinear coupled differential equations is obtained using the finite difference scheme in combination with the quasilinearization technique. The impact of different physical parameters on velocity, nanoparticle volume fraction, and temperature is presented graphically. The variation in entropy generation and Bejan number with different pertinent parameters that characterize the entropy generation phenomenon for the flow of Sisko nanofluid is discussed. The obtained results indicate that the entropy generation enhances with an increase in the magnetic parameter, Brinkman number, and thermal Biot number while reduces with the Sisko material parameter. Moreover, the behavior of mass and heat transfer rates is displayed through the Brownian diffusion parameter and thermophoresis parameter. The analysis of entropy generation minimization has crucial applications in the industrial heat transfer problems, solar heat exchanger, turbomachinery designing, LED‐based spotlights, designing of air‐cooled gas turbine blades, cooling in nuclear fuel rods, rotating reactors, in chillers, air separators, and so forth. Furthermore, entropy generation with MHD flow has applications in MHD generators, nuclear reactors, flow meters, micropumps, power plants, and so forth.

Entropy generation analysis on a heat exchanger with different design and operation factors during transient processes

Analysis of entropy generation in double-diffusive natural convection of nanofluid

Entropy generation and optimal analysis for laminar forced convection in curved rectangular ducts: A numerical study

The main objective of this research is to evaluate the Jeffery-Hamel model and entropy generation on the thermal radiation and magnetohydrodynamic flow of second-grade hybrid nanofluid between convergence and divergence channels in stretching and shrinking walls. We used blood as the base fluid and Cu and Fe3O4 as the nanoparticles in our model. The highly coupled nonlinear Partial differential equations are transformed into ordinary differential equations with the help of self-similarities transformation and solved using MATLAB solver by using the Bvp4c shooting technique. The Homotopy Perturbation Method (HPM) is compared to the Numerical Method (NM), and the results are reliable. The influences of velocity, temperature, entropy generation, and the Bejan number on nondimensional parameters like a magnetic field, the Reynolds number, thermal radiation, Deborah number, magnetic field, and the Brinkman number are discussed through graphs. The skin friction coefficients and heat transfer are also studied and portrayed as graphs and tables. The effect of a magnetic field on the velocity of stretching and shrinking through converging and diverging channels. When increasing the magnetic field, the velocity profile increases. As magnetic field values increase, the temperature profile decreases with the stretching and shrinking of converging channels. Also, the opposite behavior of stretching and shrinking for diverging channels is observed. As the Deborah number grows, the velocity reduces for the converging channel in the stretching and shrinking of the walls. It is observed that the opposite nature of the diverging channel occurs in the stretching and shrinking of the walls. In this model, biomedical applications in surgical procedures, nano-mediated atherosclerosis treatment, and several diseases with drug delivery systems.

Present communication aims to inspect the entropy optimization, heat and mass transport in Darcy-Forchheimer nanofluid flow surrounded by a non-linearly stretching surface. Navier-Stokes model based governing equations for non-Newtonian nanofluids having symmetric components in various terms are considered. Non-linear stretching is assumed to be the driving force whereas influence of thermal radiation, Brownian diffusion, dissipation and thermophoresis is considered. Importantly, entropy optimization is performed using second law of thermodynamics. Governing problems are converted into nonlinear ordinary problems (ODEs) using suitably adjusted transformations. RK-45 based built-in shooting mechanism is used to solve the problems. Final outcomes are plotted graphically. In addition to velocity, temperature, concentration and Bejan number, the stream lines, contour graphs and density graphs have been prepared. For their industrial and engineering importance, results for wall-drag force, heat flux (Nusselt) rate and mass flux (Sherwood) rate are also given in tabular data form. Outputs indicate that velocity reduces for Forchheimer number as well as for the porosity factor. However, a rise is noted in temperature distribution for elevated values of thermal radiation. Entropy optimization shows enhancement for larger values of temperature difference ratio. Skin-friction enhances for all relevant parameters involved in momentum equation.

On account of the significance of entropy generation and bioconvection in biomedical and bioengineering, valuable contributions have been made by scientists in the present decade. The current study explores the impact of entropy generation, bioconvection of microorganisms, and Ohmic heating on the peristaltic transport of Williamson fluid containing molybdenum disulfide and silver nanoparticles through an endoscope with a long wavelength and low Reynolds number assumptions. The second law of thermodynamics is used to examine the entropy generation, and also Ohmic heating effect is used in the system. Between two coaxial tubes, a non-Newtonian Williamson fluid with molybdenum disulfide and silver nanoparticles is considered. The Homotopy perturbation method (HPM) is applied to describe the nonlinear partial differential equations. We were able to arrive at analytical solutions for velocity, nanoparticle concentration, microbes’ density, and temperature. In the end, the impact of distinct physical parameters on temperature, nanoparticle concentration, velocity, microorganism density, entropy generation, Bejan number, and the heat transfer rate was graphically depicted. The significant outcome of the present study is that the impact of the Peclet number enhances the velocity profile. But Peclet number and bioconvection constantly decline the density of motile microorganisms. One more significant outcome is that the Brinkman number declines the entropy generation near the inner tube and in the rest of the part, enhances the entropy generation. Brinkman number enhances the heat transfer rate. These findings have applications in biological sciences, engineering, geothermal energy, and industry, including the construction of microbial fuel cells and bio-convection nanotechnology devices. Microorganisms are beneficial in the degradation of biomaterials, resulting in the production of oxygen and the preservation of human health.

Heat transfer and turbulent flow of Al2O3-water nanofluid within alternating oval cross-section tube are numerically simulated using Eulerian-Eulerian two-phase mixture model. The primary goal of the present study is to investigate the effects of nanoparticles volume fraction, nanoparticles diameter and different inlet velocities on heat transfer, pressure drop and entropy generation characteristics of the alternating oval cross-section tube. For numerical simulation validation, the numerical results were compared with experimental data. Also, constant wall temperature boundary condition was considered on the tube wall. In addition, the comparison of thermal-hydraulic performance and the entropy generation characteristics between alternating oval cross-section tube and circular tube under same fluids were done. The results show that the heat transfer coefficient and pressure drop of alternating oval cross-section tube is more than base tube under same fluids. Also, these two parameters are increased when adding Al2O3 nanoparticle into water fluid, at any inlet velocity for both tubes. Furthermore, compared to the base fluid, the value of the heat transfer enhancement of nanofluid is higher than the increase of friction factor of nanofluid at the same given inlet boundary conditions. The results of entropy generation analysis illustrate that the total entropy generation increase with increasing the nanoparticles volume fraction and decreasing the nanoparticles diameter of nanofluid. The generation of thermal entropy is the main part of irreversibility, and Bejan number with an increase of the nanoparticles diameter slightly increases. Finally, at any given inlet velocity the frictional irreversibility is grown with an increase the nanoparticles volume fraction.

Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation

In recent times, the loss of useful energy and solutions to those energy challenges have a wide scope in different areas of engineering. This work focuses on entropy analysis for unsteady viscoelastic fluids. The momentum boundary layer and thermal boundary layer are described under the effects of a magnetic field in the absence of an induced magnetic field. The study of a fractional model of Maxwell nanofluid by partial differential equation using Caputo time differential operator can well address the memory effect. Using transformations, the fractional ordered partial differential equations (PDEs) are transfigured into dimensionless PDEs. Numerical results for fractional Maxwell nanofluids flow and heat transfer are driven graphically. The Bejan number is obtained following the suggested transformation of dimensionless quantities like entropy generation. A mathematical model of entropy generation, Bejan number, Nusselt number and skin friction are developed for nanofluids. Effects of different physical parameters like Brickman number, Prandtl number, Grashof number and Hartmann number are illustrated graphically by MAPLE. Results depict that the addition of nanoparticles in base-fluid controls the entropy generation that enhances the thermal conductivity and application of magnetic field has strong effects on the heat transfer of fractional Maxwell fluids. An increasing behavior in entropy generation is noticed in the presence of source term and thermal radiation parameter.

This study investigates entropy generation due to the unsteady boundary layer flow of an Oldroyd-B nanofluid past a Riga plate. The velocity, temperature and concentration fields are obtained and the flow equations solved numerically using the spectral collocation method with overlapping grids. The local entropy generation distribution is obtained by solving the entropy generation equation numerically. Sensitivity and convergence analysis is performed to demonstrate the accuracy and convergence of the numerical method. The effect of principal flow parameters on entropy generation is investigated and it is established that entropy generation is directly proportional to the width of the Riga plate, Brinkman number, Prantl number and the Brownian motion parameter. It is further shown that the entropy generation is inversely proportional to the Eckert number and Deborah number in relaxation time. The range of parameter values were obtained from the reported literature. The current study may have applications of physics, including in the design of both cooling and heating devices.

The current study investigates the intrinsic irreversibility phenomenon of a mixed convection and electrically conducting couple stress Casson fluid motion over a thermally stretching sheet. We have considered the combined effect of applied magnetic field, Brownian motion, thermal radiation, permeability, Casson parameter, and the stretching parameter on the entropy generation rate of the model. The first and second laws of thermodynamics have been applied to examine the flow problem. The obtained dimensionless structure of highly nonlinear ordinary differential equations is then solved numerically applying the overlapping grid spectral collocation method. This method has high accuracy and converges fast. The approximate solutions for velocity, temperature and concentration are used to evaluate the rate of entropy generation and some physical parameters of the flow. For engineering interest, we have obtained tabular results for the skin friction coefficient, Nusselt number, and the Sherwood number for pertinent parameters. We found that entropy generation rate is minimized when there is an increase in the applied magnetic field, thermophoresis parameter, Casson parameter, Brownian motion, and the energy variance parameter. Further, the entropy generation rate is increased by enhancing the stretching parameter, permeability parameter, the Biot number, and thermal radiation parameter.