Abstract In this article, we extend the notion of double Laplace transformation to triple and fourth order. We first develop theory for the extended Laplace transformations and then exploit it for analytical solution of fractional order partial differential equations (FOPDEs) in three dimensions. The fractional derivatives have been taken in the Caputo sense. As a particular example, we consider a fractional order three dimensional homogeneous heat equation and apply the extended notion for its analytical solution. We then perform numerical simulations to support and verify our analytical calculations. We use Fox-function theory to present the derived solution in compact form.
The performance and thermal properties of convective-radiative rectangular and moving exponential porous fins with variable thermal conductivity together with internal heat generation are investigated. The second law of thermodynamics is used to investigate entropy generation in the proposed fins. The model is numerically solved using shooting technique. It is observed that the entropy generation depends on porosity parameter, temperature ratio, temperature distribution, thermal conductivity and fins structure. It is noted that entropy generation for a decay exponential fin is higher than that of a rectangular fin which is greater than that of a growing exponential fin. Moreover, entropy generation decreases as thermal conductivity increases. The results also reveal that entropy generation is maximum at the fin's base and the average entropy production depends on porosity parameters and temperature ratio. It is further reveal that the temperature ratio has a smaller amount of influence on entropy as compared to porosity parameter. It is concluded that when the temperature ratio is increases from 1.1 to 1.9, the entropy generation number is also increase by [Formula: see text] approximately. However, increasing porosity from 1 to 80 gives 14-fold increase in average entropy generation.
This paper deals with a simple mathematical model for the transmission dynamics of a vector-borne disease that incorporates both direct and indirect transmission. The model is analyzed using dynamical systems techniques and it reveals the backward bifurcation to occur for some range of parameters. In such cases, the reproduction number does not describe the necessary elimination effort of disease rather the effort is described by the value of the critical parame ter at the turning point. The model is extended to assess the impact of some control measures, by re-formulating the model as an optimal control problem with density-dependent demographic parameters. The optimality system is derived and solved numerically to investigate that there are cost effective control efforts in reducing the incidence of infectious hosts and vectors.
We study the efficiency of shrinking/stretching radiative fins to improve heat transfer rate. To evaluate the competence of suggested fins, the influence of shrinking/stretching, thermogeometric parameters, surface temperature, convection conduction, radiation conduction, and Peclet number is investigated. The problem is solved numerically using a shooting method. To validate the numerical solution, the results are compared with the solution of a differential transform method. Temperature distribution increases with a rise in convection and radiation conduction parameters when Peclet number, stretching/shrinking, ambience, and surface temperatures are raised. The temperature of the fin’s tip increases as ambient temperature, Peclet number, and surface temperature increase, and decreases for enhanced radiation and convection conduction parameters. Radiation and convection cause the efficiency of the fin to increase for shrinking and decrease for stretching, which shows an important role in heat transfer analysis in mechanical engineering. The formulated model is also studied analytically, and the result is compared to numerical solution, which shows qualitatively good agreement.
In this paper, we consider the SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model by taking into account both standard and bilinear incidence rates of fractional order. First, the nonnegative solution of the SEIR model of fractional order is presented. Then, the multi-step generalized differential transform method (MSGDTM) is employed to compute an approximation to the solution of the model of fractional order. Finally, the obtained results are compared with those obtained by the fourth-order Runge-Kutta method and non-standard finite difference (NSFD) method in the integer case.
Abstract Main concern of current research is to develop a novel mathematical model for stagnation-point flow of magnetohydrodynamic (MHD) Prandtl–Eyring fluid over a stretchable cylinder. The thermal radiation and convective boundary condition are also incorporated. The modeled partial differential equations (PDEs) with associative boundary conditions are deduced into coupled non-linear ordinary differential equations (ODEs) by utilizing proper similarity transformations. The deduced dimensionless set of ODEs are solved numerically via shooting method. Behavior of controlling parameters on the fluid velocity, temperature fields as well as skin friction and Nusselt number are highlighted through graphs. Outcome declared that dimensionless fluid temperature boosts up for both the radiation parameter and Biot number. It is also revealed that the magnitude of both heat transfer rate and skin friction enhance for higher estimation of curvature parameter. Furthermore, comparative analysis between present and previous reports are provided for some specific cases to verify the obtained results.
This article presents some new exact solutions corresponding to unsteady magnetohydrodynamic flow of generalized Jeffrey fluid in a rectangular duct, filled with a porous medium oscillating parallel to its length. The exact solutions are established by means of the double finite Fourier sine transform and discrete Laplace transform. The series solution of velocity field, associated shear stress, and volume flow rate in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.
'/%3e%3cpath fill='%23fff' d='m8.751-17.959 10.11 11.373L3.997-9.844l13.94-6.1-7.692 13.129z'/%3e%3c/svg%3e)
'%3e%3cpath fill='%23012169' d='M0 0v30h60V0z'/%3e%3cpath stroke='%23fff' stroke-width='6' d='m0 0 60 30m0-30L0 30'/%3e%3cpath stroke='%23C8102E' stroke-width='4' d='m0 0 60 30m0-30L0 30' clip-path='url(%23b)'/%3e%3cpath stroke='%23fff' stroke-width='10' d='M30 0v30M0 15h60'/%3e%3cpath stroke='%23C8102E' stroke-width='6' d='M30 0v30M0 15h60'/%3e%3c/g%3e%3c/svg%3e)
'/%3e%3cuse xlink:href='%23a' transform='rotate(60)'/%3e%3ccircle r='17' fill='%23000095'/%3e%3ccircle r='15' fill='%23fff'/%3e%3c/svg%3e)