A design of an optimal backstepping fractional order proportional integral derivative (FOPID) controller for handling the trajectory tracking problem of wheeled mobile robots (WMR) is examined in this study. Tuning parameters is a challenging task, to overcome this issue a hybrid meta-heuristic optimization algorithm has been utilized. This evolutionary technique is known as the hybrid whale grey wolf optimizer (HWGO), which benefits from the performances of the two traditional algorithms, the whale optimizer algorithm (WOA) and the grey wolf optimizer (GWO), to obtain the most suitable solution. The efficiency of the HWGO algorithm is compared against those of the original algorithms WOA, GWO, the particle swarm optimizer (PSO), and the hybrid particle swarm grey wolf optimizer (HPSOGWO). The simulation results in MATLAB–Simulink environment revealed the highest efficiency of the suggested HWGO technique compared to the other methods in terms of settling and rise time, overshoot, as well as steady-state error. Finally, a star trajectory is made to illustrate the capability of the mentioned controller.

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau–Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

The present investigation suggests a novel control technique that merge the advantage of the adaptive Neuro-Fuzzy inference system (ANFIS) with the proportional integral derivative (PID) controller, abbreviated as (ANFIS-PID), for dealing with the dynamics of the of wheeled mobile robot (WMR). A comparative study of various meta-heuristic optimization algorithms is made. The results revealed the highest efficiency of the suggested ANFIS-PID technique compared to seven designed PID controllers, in terms of settling and rise time, overshoot, and the integral square error (ISE) as a cost function. Various cases, study (circular path, diamond path, zigzag path) have highlighted the over performance of mentioned controller. Moreover, this hybrid technique is fused with backstepping approach for the kinematic control. A lemniscate and a square trajectory were performed to clarify the capability of the mentioned controller.

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In the present paper, a numerical investigation was performed to assess the effect of the rheological behavior of non-Newtonian fluids on Rayleigh–Bénard thermosolutal convection instabilities within shallow and finite aspect ratio enclosures. Neumann and Dirichlet thermal and solutal boundary condition types were applied on the horizontal walls of the enclosure. Using the Boussinesq approximation, the momentum, energy, and species transport equations were numerically solved using a finite difference method. Performing a nonlinear asymptotic analysis, a bistability convective phenomenon was discovered, which was induced by the combined fluid shear-thinning and aiding thermosolutal convection effects. Therefore, bistability convection was the main focus in the current study using the more practical constitutive Carreau–Yasuda viscosity model, which is valid from zero to infinite shear rates. Also, the combined effects of the rheology parameters and double diffusive bistability convection were studied. For aiding flow, the shear-thinning and the slower diffusing solute effects were counteracting and, as a result, two steady-state finite amplitude solutions were found to exist for the same values of the governing parameters, which indicated and demonstrated evidence for the existence of bistability convective flows. For opposing flows, the shear-thinning effect strengthened subcritical flows, which sustained well below the threshold of Newtonian thermosolutal convection. Thus, bistability convection did not exist for opposing flows, as both the shear-thinning and the slower diffusing component effects favored subcritical convection.

Solar thermal collectors, as well as heat exchangers, are energy systems that have become very popular recently in various research centers around the world. Clean systems used to generate thermal energy for its importance in human life. Most of the studies focused on the impact of various physical factors on the efficiency and performance of these systems in the presence of different structures and problems. The current research is mostly focused on evaluating thermal performance in solar receivers and heat exchangers using forced thermal transfer. Due to its importance in numerous industrial domains, the current study is primarily focused on evaluating thermal performance based on forced thermal transfer in solar receivers and heat exchangers.

Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following past laboratory experiments, the investigations dealt with the particular situation where the solutal and thermal buoyancy forces were equal but acting in opposite direction to favor the possible occurrence of the rest state condition. For this situation, the onset of convection could be either supercritical or subcritical and occurred at given thresholds and following various bifurcation routes. The analytical investigation was based on the parallel flow approximation, which was valid only for a tall porous layer. A numerical linear stability analysis of the diffusive and convective states was performed on the basis of the finite element method. The thresholds of supercritical, RTCsup, and overstable, RTCover, convection were computed. In addition, the stability of the established convective flow, predicted by the parallel flow approximation, was studied numerically to predict the onset of Hopf’s bifurcation, RTCHopf, which marked the transition point from steady toward unsteady convective flows; a route towards the chaos. To support the analytical analyses of the convective flows and the numerical stability methodology and results, nonlinear numerical solutions of the full governing equations were obtained using a second-order finite difference method. Overall, the Soret and Dufour effects were seen to affect significantly the thresholds of stationary, overstable and oscillatory convection. The Hopf bifurcation was marked by secondary convective flows consisting of superposed vertical layers of opposite traveling waves. A good agreement was found between the predictions of the parallel flow approximation, the numerical solution and the linear stability results.

In this study, eight configurations of oval and flat tubes in annular finned-tube thermal devices are examined and compared with the conventional circular tube. The objective is to assess the effect of tube flatness and axis ratio of the oval tube on thermal-flow characteristics of a three-row staggered bank for Re (2600 ≤ Re ≤ 10,200). It has been observed that the thermal exchange rate and Colburn factor increase according to the axis ratio and the flatness, where O1 and F1 provide the highest values. O1 produces the lowest friction factor values of all the oval tubes at all Re, and F4 gives 13.2–18.5% less friction than the other tube forms. In terms of performance evaluation criterion, all of the tested tubes outperformed the conventional circular tube (O5), with O1 and F1 obtaining the highest values. The global performance criterion of O1 has been found to be 9.6–45.9% higher as compared to the other oval tube geometries at lower values of Re, and the global performance criterion increases with the increase in flatness. The F1 tube shape outperforms all the examined tube designs; thus, this tube geometry suggests that it be used in energy systems.