Abstract: Abstract The heat and mass transfer of rotating Casson nanofluid flow is incorporated in the present study. Influence of magnetic field, nonlinear thermal radiation, viscous dissipation and Joule heating effects are taken into the account. A set of nonlinear ordinary differential equations are obtained from the governing partial differential equations with the aid of suitable similarity transformations. The resultant equations are solved for the numerical solution using Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique. The impact of several existing physical parameter on velocity, temperature and nanofluid concentration profiles are analyzed through graphs and tables in detail. It is found that, velocity component decreases and temperature component increases for rotating parameter.

Abstract: Abstract An analysis of this paper is examined, two-dimensional, laminar with heat and mass transfer of natural convective nanofluid flow past a semi-infinite vertical plate surface with velocity and thermal slip effects are studied theoretically. The coupled governing partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller Box Method (KBM). The influences of the emerging parameters i.e. Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Buoyancy ratio parameter (N), Lewis number (Le), Prandtl number (Pr), Velocity slip factor (Sf) and Thermal slip factor (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. The major sources of nanoparticle migration in Nanofluids are Thermophoresis and Brownian motion. A suitable agreement with existing published literature is made and an excellent agreement is observed for the limiting case and also validation of solutions with a Nakamura tridiagonal method has been included. It is observed that nanoparticle concentrations on surface decreases with an increase in slip parameter. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

Abstract: Abstract The laminar boundary layer MHD three-dimensional mixed convective flow of Maxwell nanofluid towards a bidirectional stretching sheet with non-linear radiation is analyzed. A constant magnetic field is implemented normal to the fluid flow direction. A numerical technique of Runge-Kutta-Fehlberg (RFK45) is utilized to obtain the numerical solution of the dimensionless coupled ODEs with associated boundary conditions. The various pertinent dimensionless parameters on the flow are examined with the help of graphs and tables. Results shows that, nonlinear thermal radiation is more influential o on temperature profile when compared to linear thermal radiation.

Abstract: Abstract In this work, we aim to apply a reliable analytic algorithm based on homotopy perturbation Sumudu transform method (HPSTM) to examine the nonlinear time-fractional coupled Burger’s equations. The approximate analytical solution and some numerical examples show the accuracy and efficiency of the proposed method, which is simple and accurate in comparison to the Adomain decomposition method (ADM), homotopy perturbation method (HPM) and generalized differential transform method (GDTM).

Abstract: Abstract This research is devoted to the peristaltic flow of Eyring-Powell nanofluid in an asymmetric channel. Robins-type (convective) boundary conditions are employed in the presence of mixed convection and magnetic field. The basic equations of Eyring-Powell nanofluid are modeled in wave frame of reference. Long wavelength and low Reynolds number approach is utilized. Numerical solution of the governing problem is computed and analyzed. The effects of various parameters of interest on the velocity, pressure rise, concentration and temperature are discussed and illustrated graphically. Brownian motion parameter and thermophoresis parameter facilitates the increase in temperature of fluid. Biot numbers serve to reduce the temperature at channel walls.

Abstract: Abstract A hybrid method of Sumudu transforms and homotopy perturbation method (HPM) is used to solve nonlinear partial differential equation. Here the nonlinear terms are handled with He’s polynomial to obtain the series solution. But, for the authenticity of the obtained solution, the condition of convergence and uniqueness of the solution is derived. The facts are obtained in reference to convergence and error analysis of this solution. Finally, the established fact is supported by finding solution of two well known equations Newell-Whitehead Segel and Fisher’s equation

Abstract: Abstract In the present paper, the flow of an incompressible, electrically conducting dusty fluid over a stretching sheet is considered. The Cattaneo- Christov heat flux theory is employed to control the thermal boundary layer. The flow equations are transformed into nonlinear ordinary differential equations (NODEs) and which are solved with help of Runge-Kutta 4th order method. Flow equations are examined with respect to boundary conditions namely prescribed wall temperature (PWT) and prescribed heat flux (PHF) cases. In general PWT and PHF boundary conditions are very useful in the industrial as well as manufacturing up and down processes. Impact of the emerging parameters on the dimensionless velocity and temperature as well as friction coefficient and local Nusselt number are examined. We also validated my results with already available literature. It is found that the heat transfer rate of the flow in PWT case is higher than that of PHF case. These results can help us to conclude that for higher heating processes (Heating industries) PWT case and lesser heating processes (Cooling industries) PHF boundary condition is useful.

Abstract: Abstract The steady operation of a turbocharged diesel direct injection (TDI) engine featuring a variable speed ratio mechanism linking the turbocharger shaft to the crankshaft is modelled in the present study. Key parameters of the variable speed ratio mechanism are range of speed ratios, efficiency and inertia, in addition to the ability to control relative speed and flow of power. The device receives energy from, or delivers energy to, the crankshaft or the turbocharger. In addition to the pistons of the internal combustion engine (ICE), also the turbocharger thus contributes to the total mechanical power output of the engine. The energy supply from the crankshaft is mostly needed during sharp accelerations to avoid turbo-lag, and to boost torque at low speeds. At low speeds, the maximum torque is drastically improved, radically expanding the load range. Additionally, moving closer to the points of operation of a balanced turbocharger, it is also possible to improve both the efficiency η, defined as the ratio of the piston crankshaft power to the fuel flow power, and the total efficiency η*, defined as the ratio of piston crankshaft power augmented of the power from the turbocharger shaft to the fuel flow power, even if of a minimal extent. The energy supply to the crankshaft is possible mostly at high speeds and high loads, where otherwise the turbine could have been waste gated, and during decelerations. The use of the energy at the turbine otherwise waste gated translates in improvements of the total fuel conversion efficiency η* more than the efficiency η. Much smaller improvements are obtained for the maximum torque, yet again moving closer to the points of operation of a balanced turbocharger. Adopting a much larger turbocharger (target displacement x speed 30% larger than a conventional turbocharger), better torque outputs and fuel conversion efficiencies η* and η are possible at every speed vs. the engine with a smaller, balanced turbocharger. This result motivates further studies of the mechanism that may considerably benefit traditional powertrains based on diesel engines.

Abstract: Abstract An analysis of this paper is examined, two-dimensional, laminar with heat transfer on natural convective flow in an electro-conductive polymer on the external surface of a vertical plate under radial magnetic field and slip effects is considered. The coupled governing partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller Box Method (KBM). The computed results for the velocity and temperature profiles as well as heat transfer and skin-friction coefficient have been depicted and discussed in detail through graphs for various parametric conditions. Increasing thermal slip strongly decreases skin friction and Nusselt number. Skin friction is also depressed with increasing magnetic body force parameter. Increasing momentum slip is observed to decrease skin friction. The model is relevant to the simulation of magnetic polymer materials processing.

Abstract: Abstract In this study, the peristaltic flow of a Casson fluid in a channel is considered in the presence of an applied magnetic field. Flow is considered in the moving frame of reference with constant velocity along the wave. The developed mathematical model is presented by a set of partial differential equations. A numerical algorithm based on finite element method is implemented to evaluate the numerical solution of the governing partial differential equations in the stream-vorticity formulation. The obtained results are independent of low Reynolds number and long wavelength assumptions, so the effects of non-zero moderate Reynolds number are presented. The expression for the pressure is also calculated implicitly and discussed through graphs. Computed solutions are presented in the form of contours of streamlines and vorticity. Velocity profile and pressure distribution for variation of different involved parameters are also presented through graphs. The investigation shows that the strength of circulation for stream function increases by increasing the Reynolds and Hartmann numbers. Enhancement in longitudinal velocity is noted by increasing the Reynolds number and Casson parameter while increasing Hartmann number reduces the longitudinal velocity. Comparison of the present results with the available results in literature is also included and found in good agreement.

Abstract: Abstract Systematic construction of fractional ordinary differential equations [FODEs] has gained much attention nowadays research because dimensional homogeneity plays a major role in mathematical modeling. In order to keep up the dimension of the physical quantities, we need some auxiliary parameters. When we utilize auxiliary parameters, the FODE turns out to be more intricate. One of such kind of model is non-homogeneous fractional second order RLC circuit. To solve this kind of complicated FODEs, we need proficient modern analytical method. In this paper, we use two different methods, one is modern and the other is traditional, namely generalized differential transform Method (GDTM) and Laplace transform method (LTM) to obtain the analytical solution of non-homogeneous fractional second order RLC circuit. We present the solution in terms of convergent series. Though GDTM and LTM are capable to produce the exact solution of fractional RLC circuit, great strength of GDTM over LTM is that differential transform of initial conditions occupy the coefficients of first two terms in series solution so that we arrive exact solution with few iterations and also, it does not allow the noise terms while computing the coefficients. Due to this, GDTM takes less time to converge than LTM and it has been demonstrated. Furthermost, we discuss the characteristics of non-homogeneous fractional second order RLC circuit through numerical illustrations.

Abstract: Abstract In present work, nonlinear fractional partial differential equations namely transport equation and Fokker-Planck equation involving local fractional differential operators, are investigated by means of the local fractional homotopy perturbation Sumudu transform method. The proposed method is a coupling of homotopy perturbation method with local fractional Sumudu transform and is used to describe the non-differentiable problems. Numerical simulation results are projected to show the efficiency of the proposed technique.

Abstract: Abstract An analysis illustrating the flow of an Ostwald-de-Waele liquid film on an unsteady stretching sheet under the influence of thermocapillary force, magnetic field and viscous dissipation is carried out. In this study, thermal conductivity is assumed to be a function of fluid temperature. Numerical solutions for the partial differential equations governing the flow are obtained by employing the elegant Runge-Kutta-Fehlberg method for certain representative values of controlling parameters, such as thermocapillarity number, magnetic field parameter, etc. Film thickness is calculated for various values of flow parameters. Film thickness of shear thinning fluids is found to be smaller than that of a Newtonian fluid and a converse trend holds true for shear thickening fluids. Thicker films are noticed for increasing values of thermocapillarity number. In the presence of thermocapillary force, an initial decrease in the velocity of a shear thinning fluid occurs before fluid velocity experiences a significant increase towards the free surface. Stronger magnetic field strengths are seen to increase the free surface velocity. Themocapillary force on temperature in a shear thinning fluid is more prominent.

Abstract: Abstract In this paper, first order linear homogeneous difference equation is evaluated in fuzzy environment. Difference equations become more notable when it is studied in conjunction with fuzzy theory. Hence, here amelioration of these equations is demonstrated by three different tactics of incorporating fuzzy numbers.Subsequently, the existence and stability analysis of the attained solutions of fuzzy difference equations (FDEs) are then discussed under different cases of impreciseness. In addition, considering triangular and generalized triangular fuzzy numbers, numerical experiments are illustrated and efficient solutions are depicted, graphically and in tabular form.

Abstract: Abstract Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Abstract: Abstract Mathematical model for an adiabatic tubular chemical reactor which processes an irreversible exothermic chemical reaction has been considered. For steady state solution for an adiabatic tubular chemical reactor, the model can be reduced to ordinary differential equation with a parameter in the boundary conditions. Again the ordinary differential equation has been converted into a Hammerstein integral equation which can be solved numerically. B-spline wavelet method has been developed to approximate the solution of Hammerstein integral equation. This method reduces the integral equation to a system of algebraic equations. The numerical results obtained by the present method have been compared with the available results.

Abstract: Abstract This research peruses the characteristics of heat and mass transfern of a special non-Newtonian third-grade fluid over a porous convectively-heated shrinking sheet filled with nanoparticles. The Buongiorno model is used for the special non-Newtonian third-grade fluid that includes both the Brownian motion and the thermophoresis effects with non-linear radiation. The nonlinear system of ordinary differential equations are obtained using a suitable transformation. The converted system of equations are then numerically solved using shooting method. The numerically-obtained results for the skin friction, local Nusselt number and the local Sherwood number as well as velocity profile, temperature distribution and concentration of nanoparticle are illustrated for different physical parameters through graphs and tables. On the behalf of the whole studies, final conclusions are made and it is observed that multiple solutions are achieved for certain values of the suction parameter. Further, the non-Newtonian parameter reduces the velocity of the fluid and increases the temperature and the concentration profiles for the first solution while the reverse trend is seen for the second solution. Finally, a comparative analysis is made through previous studies in limiting cases and shown good correlation.

Abstract: Abstract In this paper, we propose an efficient method to solve linear and nonlinear singular initial value problems of Lane-Emden type equations by combining Laplace transformation and homotopy perturbation methods. The method is based upon Laplace transform, polynomial series and perturbation technique. Several examples, including some well-known Lane-Emden problems, are presented to show the ability and accuracy of the modify method.

Abstract: Abstract A steady incompressible chemically reacting fluid between two disks under the influence of cross-diffusion, Hall and ion-slip effects is studied by assuming the lower disk is rotating and the upper disk is stationary. The system of nonlinear differential equations representing velocity, temperature and concentration is solved numerically using spectral quasi-linearisation method. The effects of chemical reaction, Hall current and ion-slip, Dufour and Soret on velocity, temperature and concentration distributions are studied. The stress, rate of heat and mass transfers are discussed for various parameters and the results are displayed in the tabular form. It is found that increasing Hall parameter decreases the temperature and concentration, and the opposite trend observed when ion-slip parameter increased. The concentration reduces with the enhance of the chemical reaction parameter and Soret number.

Abstract: Abstract We introduce new numerical techniques for solving nonlinear unsteady Burgers equation. The numerical technique involves discretization of all variables except the time variable which converts nonlinear PDE into nonlinear ODE system. Stability of the nonlinear system is verified using Lyapunov’s stability criteria. Implicit stiff solvers backward differentiation formula of order one, two and three are used to solve the nonlinear ODE system. Four test problems are included to show the applicability of introduced numerical techniques. Numerical solutions so obtained are compared with solutions of existing schemes in literature. The proposed numerical schemes are found to be simple, accurate, fast, practical and superior to some existing methods.

Abstract: Abstract This paper emphasizes the thermo-diffusion and viscous dissipation effects on double diffusive natural convection heat and mass transfer characteristics of non-Newtonian power-law fluid over a vertical cone embedded in a non-Darcy porous medium with variable heat and mass flux conditions. The Ostwald–de Waele power-law model is employed to describe the behavior of non-Newtonian fluid. Local non-similarity procedure is applied to transform the set of non-dimensional partial differential equations into set of ordinary differential equations and then the resulting system of equations are solved numerically by Runge-Kutta fourth order method together with a shooting technique. The influence of pertinent parameters on temperature and concentration, heat and mass transfer rates are analyzed in opposing and aiding buoyancy cases through graphical representation and explored in detail.

Abstract: Abstract In the present work, the problem of Hiemenz flow through a porous medium of a incompressible non-Newtonian Rivlin-Ericksen fluid with heat transfer is presented and newly developed analytic method, namely the homotopy analysis method (HAM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This flow impinges normal to a plane wall with heat transfer. It has been attempted to show capabilities and wide-range applications of the homotopy analysis method in comparison with the numerical method in solving this problem. Also the convergence of the obtained HAM solution is discussed explicitly. Our reports consist of the effect of the porosity of the medium and the characteristics of the Non-Newtonian fluid on both the flow and heat.

Abstract: Abstract The infra-sound spectra recorded inside homes located even several kilometres far from wind turbine installations is characterized by large pressure fluctuation in the low frequency range. There is a significant body of literature suggesting inaudible sounds at low frequency are sensed by humans and affect the wellbeing through different mechanisms. These mechanisms include amplitude modulation of heard sounds, stimulating subconscious pathways, causing endolymphatic hydrops, and possibly potentiating noise-induced hearing loss. We suggest the study of infra-sound active cancellation and mitigation to address the low frequency noise issues. Loudspeakers generate pressure wave components of same amplitude and frequency but opposite phase of the recorded infra sound. They also produce pressure wave components within the audible range reducing the perception of the infra-sound to minimize the sensing of the residual infra sound.

Abstract: Abstract In this paper, a plankton-fish interaction model is proposed and analyzed with the help of delay differential equations. Firstly, the elementary dynamical properties of the system in the absence of time delay is discussed. Then, we have established the existence of local Hopf-bifurcation as the time delay crosses its threshold value. The explicit results for stability and direction of the bifurcating periodic solution are derived by using normal form theory and center manifold arguments. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using the global Hopf-bifurcation result of [38] for functional differential equations, we establish the global existence of periodic solutions. The outcomes of the system are validated through numerical simulations in the concluding section.

Abstract: Abstract In present study, some sufficient conditions for the exponential stability of impulsive delay differential equations are obtained by introducing weight function in the norm and applying the concept of Lyapunov functions and Razumikhin techniques. The function ψ plays the role of weight and hence increases the rate of convergence towards stability. The obtained results are demonstrated with examples.

Abstract: Abstract In quest to contain and subsequently eradication Human Immunodeficiency virus (HIV) in the society, mathematical modelling remains an important research tool. In this paper, we formulated a mathematical model to study the effects of cortisol on immune response to HIV capturing the roles played by dendritic cells, T helper cells, regulatory T cells and cytotoxic T cells in the virus replication dynamics. The primary source of concentration of cortisol in this work is through psychological stress. Numerical experiments are performed to examine the effect of cortisol on selective inhibition of antigen presentation activities and up-regulation of naive cytotoxic T cells activation in the case of acute and persistent stressful conditions.

Abstract: Abstract In this paper, the influence of mixed convection in a porous square enclosure under the effect of radiation is numerically examined. The top and bottom walls are maintained at uniform temperature θc while some portion of the vertical walls is partially heated with temperature θh and rest of the vertical walls are thermally insulated, with θh > θc. The non-dimensional governing equations are solved by MAC (Marker and Cell) method. The effect of various parameters (thermal Grashof number, Darcy number, Prandtl number, Reynolds number) on flow patterns and heat transfer has been presented.

Abstract: This paper developed a method called "modified exponential cubic B-Spline differential quadrature (mExp-DQM) for space discretization together with a time integration algorithm" for the numerical computation of hyperbolic telegraph equation in $(2+1)$ dimension. The mExp-DQM is a new differential quadrature method based on modified exponential cubic B-splines as basis which reduces the problem into an amenable system of ordinary differential equations. The resulting system is solved using a time integration algorithm. The stability of the method is also studied by computing the eigenvalues of the coefficients matrices, it is found that the scheme is conditionally stable. The accuracy of the method is illustrated by computing the error between analytical solutions and numerical solutions is measured by using $L_2$ and $L_{\infty}$ error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes.

Abstract: Abstract The present study is proposed to investigate the effects of various lengths and different locations of the heater on the left sidewall in a square lid-driven porous cavity filled with nanofluid. A higher temperature is maintained on the left wall where three different lengths and three different locations of the heat source are considered for the analysis. The right wall is kept at a lower temperature while the top and bottom walls, and the remaining portions of the heated wall are adiabatic. The governing equations are solved by finite volume method. The results show that among the different lengths of the heat source, an enhancement in the heat transfer rate is observed only for the length LH = 1/3 of the heat source. In the case of location of the heat source, the overall heat transfer rate is increased when the heat source is located at the top of the hot wall. For Ri = 1 and 0.01, a better heat transfer rate is obtained when the heat source is placed at the top of the hot wall whereas for Ri = 100, it occurs when the heating portion is at the middle of the hot wall. As the solid volume fraction increases, the viscosity of the fluid is increased, which causes a reduction in the flow intensity. An addition of nanoparticles in the base fluid enhances the overall heat transfer rate significantly for all Da considered. The permeability of the porous medium plays a major role in convection of nanofluid than porosity. A high heat transfer rate (57.26%) is attained for Da = 10−1 and χ = 0.06.