Maximum thermodynamic power coefficient of a wind turbine

According to the centenary Betz‐Joukowsky law, the power extracted from a wind turbine in open flow cannot exceed 16/27 of the wind transported kinetic energy rate. This limit is usually interpreted as an absolute theoretical upper bound for the power coefficient of all wind turbines, but it was derived in the special case of incompressible fluids. Following the same steps of Betz classical derivation, we model the turbine as an actuator disk in a one dimensional fluid flow but consider the general case of a compressible reversible fluid, such as air. In doing so, we are obliged to use not only the laws of mechanics but also and explicitly the laws of thermodynamics. We show that the power coefficient depends on the inlet wind Mach number , and that its maximum value exceeds the Betz‐Joukowsky limit. We have developed a series expansion for the maximum power coefficient in powers of the Mach number that unifies all the cases (compressible and incompressible) in the same simple expression: .     

Significance of the nonlinear radiative flow of micropolar nanoparticles over porous surface with a gyrotactic microorganism,activation energy,and Nield's condition

Current continuation presents the numerical study regarding stretched flow micropolar nanofluid over moving the sheet in the existence of activation energy and microorganisms. Furthermore, nonlinear aspects of thermal radiation are also utilized in the energy equation which results in the energy equation becomes highly nonlinear. This investigation has been performed by using convective Nield boundary conditions. First, useful dimensionless variables are implemented to reduce the partial differential into ordinary ones. Later on, the approximate solution of the transformed physical problem is computed by using the shooting scheme. A detailed physical interpretation of obtained results is also presented for velocity, temperature, motile microorganisms density, and mass concentration profiles. A detailed graphical explanation for each engineering parameter has been discussed for some specified range like , and The theoretical computations based presented here can be more proficient to attain the maximum efficiency of various thermal extrusion systems and microbial fuel cells.     

Instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media

We studied linear and nonlinear instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media. We studied the critical Rayleigh number and traced marginal stability curves at different parameters , , , and . We obtained Takens‐Bogdanov and co‐dimension two bifurcation points. The Newell‐Whitehead multiple scheme was employed to derive amplitude equations at Pitchfork and Hopf bifurcation. At the onset of Pitchfork bifurcation we identified Eckhaus and Zigzag instability regions and studied Nusselt number. The system of coupled Landau Ginzburg equations were derived at the onset of Hopf bifurcation and identified secondary instability regions for fixed parameters, steady state mode shifted to standing and traveling waves as increases.     

Natural convection boundary layer flow of nanofluids around different stations of the sphere and into the plume above the sphere

The main intent of the present study is to investigate the natural convection boundary layer flow of nanofluids around different stations of the sphere and eruption of the fluid from the boundary layer in to the plume above the sphere. It is pertinent to point out that in this study heated sphere is treated as point source. The system of transport boundary layer equations is based on the effects of Brownian motion and thermophoresis. The system of dimensioned boundary layer equations is transformed into nondimensional form. Later, the nondimensional form of the mathematical model is solved numerically by using implicit finite difference method. The solution of the problem depends on a controlling parameters Prandtl number P_r, Lewis number , thermophoresis parameter , and Brownian motion parameter . Particularly, it is observed that for Lewis number , Prandtl number P_r, Brownian motion parameter , and thermophoresis parameter the velocity profile is maximum at station and minimum at station . On the other hand temperature distribution is uniform at each station around the sphere and slightly reduced for . It is also observed that nanoparticles concentration is maximum at station and minimum at station We also established the result that with the increase of skin friction is reduced while the heat and mass flux are increased in the plume region‐III.     

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.     

Barycentric rational interpolation method for numerical investigation of magnetohydrodynamics nanofluid flow and heat transfer in nonparallel plates with thermal radiation

In this study, the problem of heat transfer in the steady two‐dimensional flow of an incompressible viscous magnetohydrodynamics nanofluid from a sink or source between two shrinkable or stretchable plates under the effect of thermal radiation has been studied. The governing differential equations have been solved numerically using a collocation method based on the barycentric rational basis functions. This method employs the derivative operational matrix of the barycentric rational bases and the weights that were introduced by Floater and Hormann. The influence of some embedding parameters, such as the solid volume fraction , the Reynolds number , the Hartmann number , the Prandtl number , the radiation parameter , the stretching‐shrinking parameter, , and the angle of the channel on the temperature distribution and velocity profile has been illustrated by graphs and tables. Numerical results reveal the efficiency and high accuracy of the proposed scheme compared to the previously existing solutions. Furthermore, the implementation of the proposed method is fast and the run time is short.     

Power generation control of a hydrostatic wind turbine implemented by model‐free adaptive control scheme

The hydrostatic wind turbine (HWT) is a type of wind turbine that uses hydrostatic transmission (HST) drivetrain to replace the traditional gearbox drivetrain. Without the fragile and expensive gearbox and power converters, HWT can potentially reduce the maintenance costs owing to the gearbox and power converter failures in wind power system, especially in offshore cases. We design an MFAC torque controller to regulate the pump torque of the HWT and compared with an torque controller. Then we design an MFAC pitch controller to stabilise the rotor speed of HWT and compared with a gain‐scheduling proportional‐integral (PI) controller and a gain‐scheduling PI controller with antiwindup (PIAW). The results indicate that MFAC torque controller provides more effective tracking performance than the controller and that MFAC pitch controller shows better rotor speed stabilisation performance in comparison with the gain‐scheduling PI controller and PIAW.     

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

In this paper, an attempt has been made to analyze the effects of various parameters, such as Soret and Dufour effects, chemical reaction, magnetic field, porosity on the fluid flow, and heat and mass transfer of an unsteady Casson fluid flow past a flat plate. Convective boundary conditions in heat and mass transfer and slip constant on velocity have been taken into account for analysis. The governing equations of the model have been solved numerically using the MATLAB program bvp4c. The impact of various parameters of the model on the velocity, temperature, and concentration profiles has been analyzed through different graphs. To get an insight into the physical quantities of engineering interest, viz, skin friction, Sherwood number, and Nusselt number, their numerical values have been computed for various parameters. The range of the parameters used in numerical computations are , , , , , , and . It has been noticed from the tabulated values that the skin friction gets enhanced with the increase in the thermal and solutal Grashof number, whereas its reverse effects have been observed with an increase in the Biot number. In limiting case, the present study is also compared with the available results in the literature.     

Computation of entropy generation in dissipative transient natural convective viscoelastic flow

Entropy generation is an important aspect of modern thermal polymer processing optimization. Many polymers exhibit strongly non‐Newtonian effects and dissipation effects in thermal processing. Motivated by these aspects in this study, a numerical analysis of the entropy generation with viscous dissipation effect in an unsteady flow of viscoelastic fluid from a vertical cylinder is presented. The Reiner‐Rivlin physical model of grade 2 (second‐grade fluid) is used, which can envisage normal stress variations in polymeric flow‐fields. Viscosity variation is included. The obtained governing equations are resolved using implicit finite difference method of Crank‐Nicolson type with well imposed initial and boundary conditions. Key control parameters are the second‐grade viscoelastic fluid parameter (), viscosity variation parameter (), and viscous dissipation parameter (). Also, group parameter (), Grashof number (Gr), and Prandtl number (Pr) are examined. Numerical solutions are presented for steady‐state flow variables, temperature, time histories of friction, wall heat transfer rate, entropy, and Bejan curves for distinct values of control parameters. The results specify that entropy generation decreases with augmenting values of , , and Gr. The converse trend is noticed with increasing Pr and . Furthermore, the computations reveal that entropy and Bejan lines only occur close to the hot cylinder wall.     

Effect of viscous dissipation on finding dual solutions for mixed convection boundary layer flow for nanofluid

The effect of viscous dissipation on mixed convection boundary layer flow for Ag‐water nanofluid under steady‐state condition has been studied numerically for both the buoyancy assisting and opposing flows over a vertical semi‐infinite flat plate. A new co‐ordinate system has been introduced to transform the governing partial differential equations (PDEs) to facilitate the numerical calculations. Then, the local similarity method has been used for approximating the transformed PDEs to ordinary differential equations. Further, the quasi‐linearization method has been introduced to linearize the nonlinear equations and then numerical integration has been carried out using implicit trapezoidal rule along with the principle of superposition. For higher Pr, the coupled differential equations behave like stiff differential equations. To overcome the situation, orthonormalization process has been introduced. The effects of solid volume fraction of nanoparticles , the mixed convection parameter , Prandtl number , and Eckart number have been analyzed on the heat transfer and flow characteristics. It has been observed that the dual solutions are obtained for buoyancy opposing flow only and the range of dual solutions have become wider with the increases in . Further, nanofluids enhance the heat transfer process as compared to conventional heat transfer fluids . Moreover, the addition of viscous dissipation causes less heat transfer in the boundary.     

A semianalytical technique for MHD peristalsis of pseudoplastic nanofluid with temperature‐dependent viscosity: Application in drug delivery system

An analysis has been implemented to study the influences of nonconstant viscosity and magnetohydrodynamics on pseudoplastic nanofluid through a porous medium. Ohmic dissipation, chemical reaction, and heat generation are taken into consideration. The current problem is debated under the molds of tiny or zero and approximation. Two models of nonconstant viscosity are deliberated. Model (I)—all parameters are nondimensional and have been measured as constants inside the flow. Model (II)—all these stated nondimensional parameters have been considered to differ with the temperature. Comparison among the solutions achieved by utilizing numerical results and multi‐step differential transform method (Ms‐DTM) is displayed in excellent agreement. Attention is dedicated to , ‐, and parameters. The governing equations for each case have been explained by an easy and highly perfect series established seminumerical Ms‐DTM utilizing Mathematica 11, which uses mathematical software package. Nanofluids are active for drug carrying and drug delivery systems because of the control with the velocity of fluid.     

MHD boundary layer of GO–H2O nanoliquid flow upon stretching plate with considering nonlinear thermal ray and Joule heating effect

This essay investigates a steady three‐dimensional laminar boundary layer flow of magnetohydromagnetic radiative of graphene oxide‐water nanofluid over an extensible surface in the attendance of couple stress, thermal ray, and Joule heating impact. Governing equations are solved numerically using the Runge‐Kutta‐Fehlberg 4.5 approach after the transformation of partial differential equations into ordinary differential equations. The main goal of this essay is to check the impacts of variations in the value of numerous parameters on the velocity along x and y‐axis directions () and temperature () profiles, and also on the local skin friction coefficient along x and y‐axis directions in the presence of couple stress (K > 0) and the lack of couple stress (K = 0) and local Nusselt number for the two modes of nonlinear () and linear () thermal ray. The results elucidate that the local Nusselt number for both and modes has a direct connection with radiation parameter (R) and Prandtl number (Pr) and an inverse relation with Eckert number (Ec) and Hartman number (Ha). In addition, the skin friction coefficient has an inverse relation with couple stress (K).     

Numerical simulation of nanoparticle shape and thermal ray on a CuO/C2H6O2–H2O hybrid base nanofluid inside a porous enclosure using Darcy's law

In this study, the physical aspects of magnetohydrodynamic flow and heat transfer of a hybrid base nanofluid in a porous medium under the effect of the shape, thermal radiation, and Lorentz force have been examined using the finite element method. Copper oxide (CuO) of various shapes was dispersed into ethylene glycol 50%‐water 50% (likewise for Fe₃O₄). The Darcy model is chosen because of the porous medium. The effect of changeable, diverse parameters, for example, Hartmann number (Ha), volume fraction (), radiation parameter (), and buoyancy force (Ra), on the streamlines, temperature gradient, and Nusselt number are shown through contours. Outputs show that the Fe₃O₄ nanoparticles have a smaller temperature gradient than that of CuO nanoparticles. The Nusselt number decreases for a larger (Ha) number, but increases for a larger Ra, Rd. The blade shaped nanoparticle has a larger impact on increasing compared with that of other shapes.     

Conjugate heat transfer from a circular cylinder to a power‐law non‐Newtonian fluid

In this paper, conjugate heat transfer from a circular cylinder with a heat source to a non‐Newtonian power‐law fluid is studied. Numerical calculations are carried out in an unconfined computational domain for Reynolds numbers (), power‐law indices (), and Prandtl numbers () with different heat source values. The pressure coefficient, value, and position of maximum temperature inside the cylinder and the local and average Nusselt number are calculated. Also, the effects of Re, Pr, n, and heat source value on the thermal characteristics in the solid cylinder and the fluid around it are studied and discussed.     

Studying the effect of radiation on thin‐film sprayed nanofluid flow with heat transfer

In this paper, we discuss thin‐film nanofluid sprayed in non‐Darcian, magnetohydrodynamic, embedding in a porous medium flow and thermal radiation with heat transfer generation on a stretching cylinder. The spray rate is a function of film size. A comparative study is made for the nanoparticles, namely, copper oxide , alumina oxide (), and iron oxide . The governing continuity, momentum, and energy equations of the nanofluid are reduced using similarity transformation and converted into a system of nonlinear ordinary differential equations, which are solved numerically. Numerical solutions are obtained for the velocity and temperature fields as well as for the skin‐friction coefficient and Nusselt number. The pressure distribution and spray rate are also calculated. The results are presented in graphical forms to study the effects of various parameters.     

Heat transfer enhancement using hybrid nanofluids in spiral plate heat exchangers

A possible way to enhance the rate of heat transfer in the spiral plate heat exchanger (SPHE) is by employing hybrid nanofluids as its working medium. Hence, in the present work, effects of hybrid nanofluids on the thermal performance of SPHE has been investigated numerically. First, a countercurrent SPHE is designed and modeled. Later, simulation of SPHE has been carried out by employing conventional fluid , nanofluids , and hybrid nanofluids to investigate the heat transfer rates. Finally, the performance of SPHE using hybrid nanofluid is compared with that of using water and nanofluids. The heat transfer augmentation of approximately 16%‐27% with hybrid nanofluids of overall 4% nanoparticles volume concentration and 10%‐16% with 2% nanoparticles volume concentration is observed when compared with that of pure water. Therefore, it can be inferred that the application of hybrid nanofluids in SPHE seems to be one of the promising solutions for augmentation of its thermal performance.     

Unconditional nonlinear stability for double‐diffusive convection in a porous medium with temperature‐dependent viscosity and density

In this study, fluid flow in a porous medium is analyzed using a Forchheimer model. The problem of double‐diffusive convection is addressed in such a porous medium. We utilize a higher‐order approximation for viscosity‐temperature and density‐temperature, such that the perturbation equations contain more nonlinear terms. For unconditional stability, nonlinear stability has been achieved for all initial data by utilizing the or norms. It also shows that the theory of is not sufficient for such unconditional stability. Both linear instability and nonlinear energy stability thresholds are tested using three‐dimensional (3D) simlations. If the layer is salted above and salted below then stationary convection is dominant. Thus the critical value of the linear instability thresholds occurs at a real eigenvalue , and our results show that the linear theory produces the actual threshold. Moreover, it is known that with the increase of the salt Rayleigh number, R_c, the onset of convection is more likely to be via oscillatory convection as opposed to steady convection. The 3D simulation results show that as the value of R_c increases, the actual threshold moves towards the nonlinear stability threshold, and the behavior of the perturbation of the solutions becomes more oscillatory.     

Modeling,simulation, and optimization of a microalgae biomass drying process

The aim of the present work was to develop a transient mathematical model focused on microalgae biomass drying, considering two phases: solid (wet biomass) and gas (drying air). Mass and thermal energy balances were written for each phase producing a system of ordinary differential equations (ODE). The solution of the ODE set delivers the temperature and air humidity ratio and biomass profiles with respect to time. The numerical results were directly compared with temperature experimental measurements—for both phases—and with the biomass humidity content. Data from experiment 1 were used to carry out the mathematical model adjustment, whereas data from experiment 2 were used for the experimental validation of the model. The model was adjusted by proposing a new correlation for the mass transfer coefficient and by calibrating the heat transfer coefficient. The transient numerical results were in good quantitative and qualitative agreement with the experimental results, ie, within the experimental error bars. Then the experimentally validated mathematical model was utilized to optimize the following parameters: (i) the electric heater power ( ) and the dry air mass flow rate ( ) and (ii) the convection oven length to width ratio (L/W). The goal was to minimize system energy consumption (objective function). The optimization procedure was subject to the following physical constraints: (i) fixed convection oven total volume and (ii) fixed biomass and drying air contact surface area. For the oven original geometry,  = 3.0 kW and  = 9 g s^?1 were numerically found for minimum energy consumption, so that 36.9% and 43.5% energy consumption decreases were obtained, respectively, in comparison with the measurements of experiment 1. Next, the numerical geometric optimization found (L/W)_opt = 9, with and , which was capable to reach a 51.6% energy consumption reduction in comparison with the original system tested in experiment 1. The novelty of this work consists of the development and experimental validation of a physically based microalgae biomass drying mathematical model, ie, instead of using empirical correlations to predict the drying time and temperature profiles and then minimize system energy consumption. Therefore, the results show that it is reasonable to state that the model could be used to design, control, and optimize drying systems with configurations similar to the one analyzed in this study.     

Study of magnetohydrodynamic convection between two rotating cylinders filled with casson fluid and the viscous dissipation effect

We have studied the forced convection of a viscous incompressible and electrically conducting non‐Newtonian Casson fluid between two rotating cylinders with viscous dissipation effect. An angular velocity and gives to inner and outer cylinders, respectively, and constant heat flux presented on the inner cylinder surface. Also, the outer cylinder is taken as insulated. Here, we have discussed three cases: (i) The inner cylinder is rotating with a constant angular velocity while the outer cylinder is at rest; (ii) Both the cylinders rotate in the identical direction with equal angular velocity; and (iii) Both the cylinders are rotating with equal angular speed but the outer cylinder rotates in the opposite direction of the inner cylinder. The governing equations are solved by numerical techniques using MATLAB Software and the results are obtained graphically.     

Experimental and optimization studies of hydrogen production by steam methane reforming over lanthanum strontium cobalt ferrite supported Ni catalyst

Over the years, research focused has been on the development of active and stable catalysts for hydrogen (H₂) production by steam methane reforming (SMR). However, there is less attention on the individual and interaction effect of key process parameters that influence the catalytic performance of such catalysts and how to optimize them. The main objective of this study is to investigate the individual and interaction effects of key parameters such as methane partial pressure ( (10‐30 kPa), steam partial pressure ( (10‐30 kPa), and reaction temperature (T) (750‐850°C) on H₂ yield and methane (CH₄) conversion during SMR using Box‐Behnken experimental design (BBD) and response surface methodology. The H₂ production was catalyzed using Ni/LSCF prepared by wet impregnation method. The evaluation of the Ni/LSCF using different instrument techniques revealed that the catalyst exhibited excellent physicochemical properties suitable for SMR. Response surface models showing the individual and interaction effect of each of the parameters on the H₂ yield and CH₄ conversion were obtained using the set of data obtained from the BBD matrix. The three parameters were found to have significant effects on the H₂ yield and CH₄ conversion. At the highest desirability of 0.8994, maximum H₂ yield and CH₄ conversion of 89.77% and 89.01%, respectively, were obtained at optimum conditions of 30 kPa, 28.86 kPa, and 850°C for , , and temperature, respectively. The predicted values of the responses from the response surface models were found to be in good agreement with the experimental values. At optimum conditions, the catalyst was found to be stable up to 390 minutes with time on stream. The characterization of the used catalyst using thermogravimetric analysis, scanning electron microscopy, energy‐dispersive X‐ray spectroscopy, and transmission electron microscopy showed some evidence deposition of a small amount of carbon on the catalyst surface.