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This paper investigates the magnetic blood flow in an inclined multi-stenosed artery under the influence of a uniformly distributed magnetic field and an oscillating pressure gradient. The blood is modelled using the non-Newtonian Casson fluid model. The governing fractional differential equations are expressed by using the fractional Caputo Fabrizio derivative without singular kernel. Exact analytical solutions are obtained by using the Laplace and finite Hankel transforms for both velocities. The velocities of blood flow and magnetic particles are graphically presented. It shows that the velocity increases with respect to the Reynolds number and the Casson parameter. Meanwhile, the velocity decreases as the Hartmann number increases. These results are useful for the diagnosis and treatment of certain medical problems.

A current ideal control issue in the region of financial aspects has numerical properties that do not fall into the standard optimal control problem detailing. In our concern, the state condition at the final time, y(T ) = z, is free and obscure, and furthermore, the integrand is a piecewise consistent capacity of the obscure esteem y(T ). This is not a standard optimal control problem and cannot be settled utilizing Pontryagin’s minimum principle with the standard limit conditions at the final time. In the standard issue, a free final state y(T ) yields an important limit condition p(T ) = 0, where p(t) is the costate. Since the integrand is a component of y(T ), the new fundamental condition is that y(T ) yield is equivalent to a specific necessary consistent capacity of z. We present a continuous approximation of the piecewise consistent integrand function through hyperbolic tangent approach and tackle a case utilizing a C++ shooting method. The limiting free y(T ) value is computed in an external circle emphasis through the golden section method.

This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo–Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo–Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo–Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo–Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological analysis and medical diagnosis.

This study aimed to develop a mathematical model of an unsteady Burgers’ fluid in a circular cylinder with a trapezoidal pressure waveform described by an infinite Fourier series. An analytical solution was obtained for the governing equation using the Bessel transform method together with similarity arguments. The validity of the solution was verified using a numerical inversion method based on Stehfest’s method. Limiting cases were considered to examine the fluid flow performance of different fluids. Our results show that the Newtonian and Oldroyd-B fluids performed similar velocity time variation for the trapezoidal waveform of oscillating motion, whereas the velocity time variation was different for Maxwell and Burger’s fluids. Moreover, it is evident that the material constant of a Burgers’ fluid is another important factor that affects flow performance in an oscillating flow.

Background and Objective Arterial diseases would lead to several serious disorders in the cardiovascular system such as atherosclerosis. These disorders are mainly caused by the presence of fatty deposits, cholesterol and lipoproteins inside blood vessel. This paper deals with the analysis of non-Newtonian magnetic blood flow in an inclined stenosed artery. Methods The Casson fluid was used to model the blood that flows under the influences of uniformly distributed magnetic field and oscillating pressure gradient. The governing fractional differential equations were expressed using the Caputo Fabrizio fractional derivative without singular kernel. Results The analytical solutions of velocities for non-Newtonian model were then calculated by means of Laplace and finite Hankel transforms. These velocities were then presented graphically. The result shows that the velocity increases with respect to Reynolds number and Casson parameter, while decreases when Hartmann number increases. Conclusions Casson blood was treated as the non-Newtonian fluid. The MHD blood flow was accelerated by pressure gradient. These findings are beneficial for studying atherosclerosis therapy, the diagnosis and therapeutic treatment of some medical problems.

In the present paper, an unsteady motion of fluid flow in a pulsating pipe is studied to determine the effect of non-sinusoidal waveforms on the heat transfer performance. Three non-sinusoidal waveforms, namely sawtooth, square and triangular waveforms have been considered. Explicit analytical expressions for a periodic laminar flow describing the flow and heat transfer at small and large times with sawtooth and square pressure waveforms have been derived using Bessel transform technique. The heat transfer performance of periodic flow at sawtooth and square pressure waveforms has been compared with the published result for triangular waveform [1] . The temperature performance for a triangular waveform pressure is very different from the sawtooth and square pressure waveforms.

The flow of an oscillating motion of viscoelastic fluid in a capillary tube is modelled to determine a sinusoidal waveform effect on the heat transfer performance. Analytical technique based on finite Hankel transformation, incorporating Laplace transformation and combined with confluent hypergeometric function (Kummer’s function) is implemented in time and space with the constitutive model for the viscoelastic fluid. Explicit analytical expressions for the steady, permanent and transient solutions for both the velocity and temperature fields describing the flow at small and large times have been derived. The results are displayed graphically, and the influence of the Prandtl number Pr and transient amplitude $$B_{1}$$ is discussed.

In this paper, an analytical study of squeezing unsteady nanofluid flow between two parallel plates is carried out. The effects of thermal radiation and heat generation/absorption along the temperature profile were observed. The homotopy perturbation method (HPM) was used to solve the two-dimensional nonlinear momentum and energy equations. The results found in this study are being compared with the result obtained using the RK4 technique with shooting scheme. The results obtained fascinatingly agree with the numerical solutions. Keywords: Nanofluid, Squeezing flow, Nonlinear equations, Homotopy perturbation method (HPM), Runge-Kutta scheme (RK4)

In this paper, a revised optimal homotopy asymptotic method (OHAM) is applied to derive an explicit analytical solution of the Falkner-Skan wedge flow problem. The comparisons between the present study with the numerical solutions using (fourth order Runge-Kutta) scheme and with analytical solution using HPM-Padé of order [4/4] and order [13/13] show that the revised form of OHAM is an extremely effective analytical technique.

In this paper, the third grade non-Newtonian MHD blood flow in the porous arteries subjected to the periodic pressure gradient was studied using the Caputo-Fabrizio (NFDt ) time fractional order derivative. The time fractional model was solved by taking the Laplace and the finite Hankel transforms. Results were compared with those reported in the previous studies and good agreement was found. The Mathematica software was used to simulate the velocity profile and the Bessel functions with zero order and first order of first kind. The correlations between the flow velocity and the third grade non-Newtonian fluid parameter, the magnetic field and the porosity were negative. Nevertheless, the flow velocity increased with respect to the Womersely number.

This paper contains introduction, materials and methods, results and discussions, conclusions and references. Based on the title mentioned, high volatility of the price of natural rubber nowadays will give the significant risk to the producers, traders, consumers, and others parties involved in the production of natural rubber. To help them in making decisions, forecasting is needed to predict the price of natural rubber. The main objective of the research is to forecast the upcoming price of natural rubber by using the reliable statistical method. The data are gathered from Malaysia Rubber Board which the data are from January 2000 until December 2015. In this research, average monthly price of Standard Malaysia Rubber 20 (SMR20) will be forecast by using Box-Jenkins approach. Time series plot is used to determine the pattern of the data. The data have trend pattern which indicates the data is non-stationary data and the data need to be transformed. By using the Box-Jenkins method, the best fit model for the time series data is ARIMA (1, 1, 0) which this model satisfy all the criteria needed. Hence, ARIMA (1, 1, 0) is the best fitted model and the model will be used to forecast the average monthly price of Standard Malaysia Rubber 20 (SMR20) for twelve months ahead.

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

The palm oil industry has been an important component of the national economy especially the agriculture sector. The aim of this study is to identify the pattern of import of palm oil products, to model the time series using Box-Jenkins model and to forecast the monthly import of palm oil products. The method approach is included in the statistical test for verifying the equivalence model and statistical measurement of three models, namely Autoregressive (AR) model, Moving Average (MA) model and Autoregressive Moving Average (ARMA) model. The model identification of all product import palm oil is different in which the AR(1) was found to be the best model for product import palm oil while MA(3) was found to be the best model for products import palm kernel oil. For the palm kernel, MA(4) was found to be the best model. The results forecast for the next four months for products import palm oil, palm kernel oil and palm kernel showed the most significant decrease compared to the actual data.

This work is to examine theoretically unsteady flow of viscoelastic fluid in a circular cylinder and to investigate the existence of steady solutions. We consider the flow is solely due to pressure gradient in following three forms: (i) sinusoidal; (ii) square; (iii) constant. Based on the pressure gradient described, three flow situations are solved and the exact analytical solutions are given in terms of Bessel functions. In all the three problems, it is found that the variation of the unsteady and steady solution mainly depends for small time, while for large time the two solutions are identical.

Oscillating motion of Oldroyd-B flow in a capillary tube at a triangular sine and cosine pressure waveform is considered. An analytical solution of velocity field is obtained for an oscillating laminar flow, which can be used to determine the existence of trapezoidal waveform effect on the flow. When both triangular sine and cosine components are dominate, the oscillating flow can result in significant trapezoidal waveform performance. The dimensionless oscillating frequency, amplitude, and fluid material parameters, are primary factors affecting the flow performance of an oscillating flow in a capillary tube.

A new analytical algorithm based on modified homotopy perturbation transform method is employed for solving the transient flow of third grade fluid in a porous channel generated by an oscillating upper wall. This method incorporates the He’s polynomial into the HPM, combined with Laplace transform. Comparison with HPM and OHAM analytical solutions reveals that the proposed algorithm is highly accurate. This proves the validity and great potential of the proposed algorithm as a new kind of powerful analytical tool for transient nonlinear problems. Graphs representing the solutions are discussed, and appropriate conclusions are drawn.

An analytical solution of mixed convection flow of viscoelastic fluid in a channel with walls transpiration is obtained by optimal homotopy asymptotic method. Comparison with previous recorded result through reduction in pertinent parameters unveils the presented optimal series solution is correct. The result valid for non-transpiration walls for the values from the pertinent flow parameters could be derived as a special case from the present analysis. The results show that the proposed method is effective and has a distinct advantage over usual approximation methods in that the approximate solution obtained here is valid not only for weakly nonlinear equations, but also for strongly nonlinear ones. Second order approximation is needed for velocity while only first order temperature is needed to obtain desired results.

In this work, the unidirectional flow of an incompressible electrically conducting third-grade fluid past a vertical transpiration wall through a porous medium with time-dependent periodic motion is presented. The nonlinear partial differential equations are transformed to ordinary differential equation by means of symmetry reductions. The reduced equation is then solved analytically for steady-state and time-dependent transient parts. The time series of the transient flow velocity for different pertinent parameters are examined through plots. During the course of computation, it was observed that the time-dependent transient and steady-state solutions agree very well at large value of time when the ratio is related to fluid parameters γ ∗ γ > 1 .