Viscous dissipation and hall effects on MHD radiative Brinkman type EO-based heat consuming MoS2 nanofluid past a rotating plate in porous medium

Hydromagnetic nanofluid flow due to a stretching or shrinking sheet with viscous dissipation and chemical reaction effects

This study examines the flow and heat transfer of a finite thin layer of a hybrid nanofluid across an unstable stretching surface with varying thermal conductivity and viscous dissipation effects. A hybrid nanofluid model is considered to comprise two different types of nanoparticles, Go and Ag , with kerosene oil used as a base fluid. To study the phenomenon of thermal conduction, a modified version of Fourier’s law model is adopted because in the power-law model, the thermal conductivity depends on the velocity gradient. A system of nonlinear ordinary differential equations is obtained by considering the similarity transformations over the obtained rheological system of partial differential equations which is then tackled by a well-known numerical approach, i.e., the bvp4c MATLAB technique. The rheological impacts of the power-law index, solid volume fraction, film thickness, Eckert number, and modified Prandtl number on temperature and velocity fields are graphically discussed and illustrated. In the presence of nanoparticles, the temperature of the working fluid is enhanced and the power-law index has an inverse relation with the velocity of the hybrid nanofluid.

We investigate the convective heat and mass transfer in a magnetohydrodynamic nanofluid flow through a porous medium over a stretching sheet subject to heat generation, thermal radiation, viscous dissipation and chemical reaction effects. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. Two types of nanofluids, namely Cu-water and Al2O3-water are studied. The physical problem is modeled using systems of nonlinear differential equations which have been solved numerically using the spectral relaxation method. Comparing the results with those previously published results in the literature shows excellent agreement. The impact of porosity, heat generation, thermal radiation, magnetic field, viscous dissipation and chemical reaction on the flow field is evaluated and explained.

The upper–lower solution method for the coupled system of first order nonlinear PDEs

The current work presents a theoretical investigation on the bioconvective electromagnetohydrodynamic (EMHD) hybrid nanofluid flow over a stretching surface considering viscous dissipation, chemical reaction, and stratification effects. The highly nonlinear system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs) with the aid of effectual similarity transformations. The transmuted ODEs are then treated numerically using bvp4c (a finite difference-based built-in numerical procedure) in MATLAB. It is observed that an increase in the electric field parameter augments the velocity profile. It is also noted that the Nusselt number is a decreasing function of the thermal stratification parameter. Further, the influence of nanoparticle volume fraction of carbon nanotubes ( 0.01 ≤ ϕ 1 ≤ 0.09 ) , the nanoparticle volume fraction of magnetite nanoparticles ( 0.01 ≤ ϕ 2 ≤ 0.09 ) , Hartmann number ( 0.4 ≤ M ≤ 2 ) , and electric field parameter ( 0.1 ≤ E ≤ 0.5 ) on the drag coefficient has been statistically scrutinized utilizing the four-factor response surface methodology. The highest drag coefficient is experienced for smaller values of Hartmann number and larger values of electric field parameter. The current work finds application in cancer therapy, bio-microsystems, biomedical imaging, and therapeutic drug delivery.

Joule heating and viscous dissipation effects on the behavior of the boundary layer flow of a micropolar nanofluid over a stretching vertical Riga plate (electro magnetize plate) are considered. The flow is disturbed by an external electric magnetic field. The problem is formulated mathematically by nonlinear system of partial differential equations (PDEs). By using suitable variables transformations, this system is transformed onto a system of nonlinear ordinary differential equations (ODEs). The Parametric NDsolve package of the commercial software Mathematica is used to solve the obtained ODEs as well as the considered numerical results for different physical parameters with appropriate boundary conditions. Novel results are obtained by studying the stream lines flow around the plate in two and three dimensions. Moreover, the effects of the pertinent parameters on the skin friction coefficient, couple stress, local Nusselt, and Sherwood number are discussed. Special cases of the obtained results show excellent agreements with previous works. The results showed that as the magnetic field parameter increases the velocity of the boundary layer adjacent to the stretching sheet decreases. Also, for a productive chemical reaction near the sheet surface, the angular velocity decreases but opposite trend is observed far from the sheet surface. The importance of this study comes from its significant applications in many scientific fields, such as nuclear reactors, industry, medicine, and geophysics.

In this article, a sub-optimal controller based on Extended State-Dependent Differential Riccati Equation (ESDDRE) is suggested for a class of time-delay nonlinear Partial Differential Equation (PDE) systems. At first, an extended pseudo linearisation presentation for parameterisation form using State-Dependent Coefficients (SDC) is proposed. In this presentation, all the time-delay parts are placed in system matrices as well as in input vectors. By defining a cost function and a Hamiltonian related to the PDE systems, the sub-optimal control law regarded on the ESDDRE is obtained. The stability of the closed-loop system based on the ESDDRE control approach is ensured by using a proper Lyapunov function and also Poincaré inequality. Numerical simulation results for three time-delay nonlinear PDE systems illustrate the appropriate performance of the proposed control approach.

SummaryThis paper designs an interval observer for switched nonlinear partial differential equation (PDE) systems. Initially, persistent dwell‐time switching rules are used to model switched PDE systems with fast and slow switching phenomena. Next, for unobservable systems caused by uncertainties, the interval observer for the target PDE systems is proposed by utilizing unknown but bounded information of the initial states, boundary conditions, external disturbances, and measurement noises. Subsequently, by utilizing the estimated state's upper and lower bounds, an interval observer‐based control strategy is devised to stabilize the studied systems, and sufficient conditions to ensure the stability of the target systems and the observation error dynamics are provided. Furthermore, the designed interval observer is employed to detect sensor failures in the presence of various uncertainties. Finally, two examples, including the lithium‐ion battery's temperature estimation and fault detection, are utilized to demonstrate the effectiveness of the obtained methods.

This article studied a numerical estimation of the double-diffusive peristaltic flow of a non-Newtonian Sisko nanofluid through a porous medium inside a horizontal symmetric flexible channel under the impact of Joule heating, nonlinear thermal radiation, viscous dissipation, and heat generation/absorption in presence of heat and mass convection, considering effects of the Brownian motion and the thermophoresis coefficients. On the other hand, the long wave approximation was used to transform the nonlinear system of partial differential equations into a nonlinear system of ordinary differential equations which were later solved numerically using the fourth-order Runge–Kutta method with shooting technique using MATLAB package program code. The effects of all physical parameters resulting from this study on the distributions of velocity, temperature, solutal concentration, and nanoparticles volume fraction inside the fluid were studied in addition to a study of the pressure gradients using the 2D and 3D graphs that were made for studying the impact of some parameters on the behavior of the streamlines graphically within the channel with a mention of their physical meaning. Finally, some of the results of this study showed that the effect of Darcy number Da and the magnetic field parameter M is opposite to the effect of the rotation parameter Omega on the velocity distribution whereas, the two parameters nonlinear thermal radiation R and the ratio temperature {theta }_{w} works on a decrease in the temperature distribution and an increase in both the solutal concentration distribution, and the nanoparticle's volume fraction. Finally, the impact of the rotation parameter Omega on the distribution of pressure gradients was positive, but the effect of both Darcy number Da and the magnetic field parameter M on the same distribution was negative. The results obtained have been compared with the previous results obtained that agreement if the new parameters were neglected and indicate the phenomenon's importance in diverse fields.

This study investigates the heat transfer dissipation on stagnation point flow over a slippery stretching/shrinking cylinder in a copper nanofluid by considering the effect of viscous dissipation. A system of nonlinear partial differential equations is modelled and transformed into ordinary differential equations using similarity transformations. The governing equations with the corresponding boundary conditions are analysed numerically using a bvp4c solver in MATLAB. The solutions are found to be dependent on the Eckert number and slip parameters. The results are represented by the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. Dual solutions are observed for the shrinking cylinder in the presence of Eckert number. Velocity profile and skin friction coefficient consistently increase while temperature profile increases initially and then decreases with the increase of slip parameter for both first and second solutions. Moreover, the presence of copper nanoparticles reduces the thermal boundary layer thickness. This research can be enhanced by using hybrid nanofluids to further improve the heat transfer.

Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.

Investigation of nanofluid flows under various conditions is becoming fascinating research due to its numerous applications in many science and engineering fields such as solar energy, geothermal energy, water purification, glass blowing, enhanced oil recovery, petroleum production and food processing. For the present requirements in thermal energy applications, this mathematical model is considered to explore the diffusion and heat source effects on the flow of conductive Casson and Maxwell nanofluids in a porous medium on an elongating sheet with a chemical reaction. Further, the effects of viscous dissipation and thermal radiation are also examined. Moreover, the entropy generation is analyzed since this approach is employed in solar energy exchangers. The governing equations and the corresponding boundary conditions are constructed. This system of partial differential equations (PDEs) is changed into a system of nonlinear ordinary differential equations (ODEs) with the help of a suitable transformation and then solved numerically by the bvp5c MATLAB package. The influences of the physical parameters on the flow phenomena are discussed and presented through figures and tables. This analysis explains that the Casson fluid flow has a higher velocity field than the Maxwell fluid flow. The Nusselt number becomes higher as the Dufour numbers increase. It has also been noticed that increasing the Brinkmann number improves the entropy and, an increase in radiation enriches the temperature profile. The concentration of the fluid is decreased for the increasing values of the higher-order chemical reaction parameter. Furthermore, comparisons of the current results were conducted for limiting examples of the problem and found to be in good agreement with existing results in the literature.

In this paper, the effects of viscous dissipation on natural convection flow along a uniformly heated vertical wavy surface with heat generation have been investigated. The governing boundary layer equations are first transformed into a non-dimensional form using suitable set of dimensionless variables. The resulting nonlinear systems of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the Keller-box method. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the velocity as well as the temperature profiles are shown graphically and in tabular form for different values of physical parameters namely, viscous dissipation parameter Vd, heat generation parameter Q and Prandtl number Pr.

A numerical study was carried out to examine the magnetohydrodynamic (MHD) flow of micropolar fluid on a shrinking surface in the presence of both Joule heating and viscous dissipation effects. The governing system of non-linear ordinary differential equations (ODEs) was obtained from the system of partial differential equations (PDEs) by employing exponential transformations. The resultant equations were transformed into initial value problems (IVPs) by shooting technique and then solved by the Runge–Kutta (RK) method. The effects of different parameters on velocity, angular velocity, temperature profiles, skin friction coefficient, and Nusselt number were obtained and demonstrated graphically. We observed that multiple solutions occurred in certain assortments of the parameters for suction on a surface. The stability analysis of solutions was performed, and we noted that the first solution was stable while the remaining two solutions were not. The results also showed that the velocity of the fluid increased as the non-Newtonian parameter rose in all solutions. Furthermore, it was detected that the temperature of fluid rose at higher values of the Eckert number in all solutions.

Simulation of magnetic dipole and dual stratification in radiative flow of ferromagnetic Maxwell fluid