Academic literature on the topic 'MATLAB "fsolve" solver'

In this paper, a new bio-nano-transport model is presented. The effects of first- and second-order velocity slips, thermal slip, mass slip, and gyro-tactic (torque-responsive) microorganism slip of bioconvective nanofluid flow from a moving plate under blowing phenomenon are numerically examined. The flow model is expressed by partial differential equations which are converted to a similar boundary value problem by similarity transformations. The boundary value problem is converted to a system of nonlinear equations which are then solved by a Matlab nonlinear equation solver fsolve integrated with a Matlab ODE solver ode15s. The effects of selected control parameters (first order slip, second order slip, thermal slip, microorganism slip, blowing, nanofluid parameters) on the non-dimensional velocity, temperature, nanoparticle volume fraction, density of motile micro-organism, skin friction coefficient, heat transfer rate, mass flux of nanoparticles and mass flux of microorganisms are analyzed. Our analysis reveals that a higher blowing parameter enhances micro-organism propulsion, flow velocity and nano-particle concentration, and increases the associated boundary layer thicknesses. A higher wall slip parameter enhances mass transfer and accelerates the flow. The MATLAB computations have been rigorously validated with the second-order accurate finite difference Nakamura tri-diagonal method. The current study is relevant to microbial fuel cell technologies which combine nanofluid transport, bioconvection phenomena and furthermore can be applied in nano-biomaterials sheet processing systems.

This article focuses on finding the numerical solution of the nonlinear time–fractional partial integro–differential equation. For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative, nonlinear, and integro–differential terms; and by collocation points, we transform the problem to a system of nonlinear equations. This nonlinear system can be solved by the fsolve command in Matlab. The method’s stability and convergence have been studied. Also included are five numerical examples to demonstrate the veracity of the suggested strategy.

For intelligent distribution system including Distributed Generations, we take the generator and load static characteristic into account and propose a flexible power flow algorithm for distribution network including second-order items. First, this algorithm modifies the distribution network power flow equations including second-order items in order to meet the static characteristic of generator and load. Moreover, we use the fsolve function of MATLAB to solve the power flow equations. This algorithm makes full use of the characteristic of high accuracy of the distribution network flow equations including second-order items and good convergence of the fsolve function. Compared with conventional distribution power flow algorithm, it does not need to set the trend flexible node type of each one. Not only the voltage amplitude, phase information of each node and the system frequency information can be calculated, as well as the actual power of generator and loads. The result of the algorithm is more in line with the practical electric power system engineering. Improved IEEE33 node system is chosen to verify the correctness of the algorithm.

In this paper, Euler polynomials were utilized to formulate a collocation method for approximating Lane-Emden equations. The approximation formulations were initialized producing truncation function. The residual functions were constructed by using the truncation function. The collocation points were substituted into the residual function to form system of equations and were solved by Matlab application fsolve or Newton-Raphson methods. The results were tabulated and compared with the Herodt (2004) results for absolute error. It was observed that the Euler polynomial is very accurate and converges faster producing zero error as compared. The study recommended in solving Lane-Emden and higher order equations.

This paper describes a steady state model of a multiple effect evaporator system for simulation and control purposes. The model includes overall as well as component mass balance equations, energy balance equations and heat transfer rate equations for area calculations for all the effects. Each effect in the process is represented by a number of variables which are related by the energy and material balance equations for the feed, product and vapor flow for backward, mixed and split feed. For simulation 'fsolve' solver in MATLAB source code is used. The optimality of three sequences i.e. backward, mixed and splitting feed is studied by varying the various input parameters.

A numerical investigation has been performed to analyze an unsteady magnetohydrodynamic gravity-driven flow of a Newtonian hybrid nanofluid (Cu-Al2O3/H2O) along an impermeable vertical plate with linearly accelerated temperature and concentration. The Hall current, nanoparticle volume fraction, inclined magnetic field, and Soret effect on water-based Cu-Al2O3 hybrid nanofluid are incorporated into the flow model. The model's governing nonlinear partial differential equations are formulated and transformed into a non-dimensional form by introducing suitable variables and parameters. The finite difference method is implemented via the MATLAB solver fsolve to resolve the model equations numerically. The evolution of the primary and secondary velocities, temperature, and species concentration profiles is discussed via graphical illustration. Furthermore, a comparative analysis is performed on the coefficient of skin friction, rate of heat, and mass transport for hybrid nanofluid and nanofluid through tabular values. The novelty of the investigation reveals that a deceleration in the primary velocity and acceleration in the secondary velocity with the increasing magnetic field inclination parameter exists. The rising value of Cu nanoparticle volume fraction augments the primary, secondary skin friction coefficients, and the heat and mass transport rates at the plate. The Dufour number stimulates a reduction in the heat transport rate, while an enhancement occurs with the Soret number. The present investigation demonstrates that the heat transfer rate for water-based Cu-Al2O3 hybrid nanofluid is higher than that for water-based Cu nanofluid. The current research can be implemented to augment the efficiency of the cooling mechanism of heat exchangers, solar collectors, nuclear reactors, and many more.