Numerical Treatment for the flow of Casson Fluid and heat transfer Model Over an Unsteady Stretching Surface in the Presence Of Internal Heat Generation/Absorption and Thermal Radiation

Several important industrial and engineering problems are very difficult to solve analytically since they are high nonlinear. The Chebyshev spectral collocation method possesses an ability to predict the solution behavior for a system of high nonlinear ordinary differential equations. This method which is based on differentiated Chebyshev polynomials is introduced to obtain an approximate solution to the system of ordinary differential equations which physically describe the flow and heat transfer problem of an unsteady Casson fluid model taking into consideration both heat generation and radiation effects in the temperature equation. Based on the spectral collocation method, the obtained solution is introduced numerically to various parameter values

On the solutions of the heat, wave and Laplace equations with nonlocal conditions

In this paper, we present a new approach to solve nonlocal initial- boundary value problems for heat, wave and Laplace equations subject to initial, final and nonlocal boundary conditions of integral type. We first transform the given nonlocal initial-boundary value problems of integral type and then apply the method of separation of variables

On Approximate Solutions for Fractional Logistic Differential Equation

A new approximate formula of the fractional derivatives is derived. The proposed formula is based on the generalized Laguerre polynomials. Global approximations to functions defined on a semi-infinite interval are constructed. The fractional derivatives are presented in terms of Caputo sense. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. The new spectral Laguerre collocation method is presented for solving fractional Logistic differential equation (FLDE). The properties of Laguerre polynomials approximation are used to reduce FLDE to solve a system of algebraic equations which is solved using a suitable numerical method. Numerical results are provided to confirm the theoretical results and the efficiency of the proposed method

Numerical Study of Thermal Radiation Phenomenon and Its Influence on Amelioration of the Heat Transfer Mechanism through MHD Non-Newtonian Casson Model

The present study’s main focus is regarding the physical properties of a two-dimensional (2D) magneto-hydrodynamic boundary layer non-Newtonian Casson fluid flow that moves due to an exponentially expanding surface with a mixed convection heat transfer mechanism. In the hydrodynamic flow and heat transmission process, the combined impact of thermal radiation and magnetic field influence is explored. The internal heat generation owing to the fluid motion or a very fluid viscosity is not taken into account. The Chebyshev spectral method (CSM) is employed in this work due to its ability, accuracy, and ease of obtaining the solution for non-linear system of ordinary differential equations (ODEs). This method is an approximate method that can usually obtain the solution in a series form. The mixed convection impact is incorporated in our problem. The results are graphed to help comprehend the many physical parameters that arise in the problem. Graphical results uncover that the speed liquid stream is lessened when reinforcing both the Casson boundary and the Hartmann number, while converse attributes are applied for the Grashof number and the radiation boundary. Finally, a comparison of our current results with previously published work on several particular situations of the problem reveals that they are in excellent agreement

Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples

Jacobi Spectral Collocation Technique for Time-Fractional Inverse Heat Equations

In this paper, we introduce a numerical solution for the time-fractional inverse heat equations. We focus on obtaining the unknown source term along with the unknown temperature function based on an additional condition given in an integral form. The proposed scheme is based on a spectral collocation approach to obtain the two independent variables. Our approach is accurate, efficient, and feasible for the model problem under consideration. The proposed Jacobi spectral collocation method yields an exponential rate of convergence with a relatively small number of degrees of freedom. Finally, a series of numerical examples are provided to demonstrate the efficiency and flexibility of the numerical scheme

Prevalence and molecular characterization of hepatitis D virus in Saudi Arabia: A single-center study

Background/Aims: Hepatitis D virus (HDV) is a defective RNA virus that is dependent on hepatitis B surface antigen (HBsAg) for transmission and replication. HDV significance arises from the possibility of poor prognosis of hepatitis B virus (HBV) infection. In Saudi Arabia, HDV prevalence varied from 8 to 32% before the HBV vaccination program and ranged from 0 to 14.7% after the vaccination program was started. The last study, performed in 2004, showed a prevalence of 8.6% in hospital-based HBV cases and 3.3% in healthy donors. The aim of this study was to investigate the prevalence and molecular characterization of HDV in chronic hepatitis B (CHB) patients at the King Abdulaziz University Hospital in Jeddah, Saudi Arabia by molecular and serological techniques. To the best of our knowledge, this is the first study to detect HDV at the molecular level in Saudi Arabia. Patients and Methods: The study included samples from 182 CHB patients from Jeddah; 13 samples with HBsAg negative were excluded. Samples were tested for HDV-Ab, viral RNA by reverse transcriptase–polymerase chain reaction (RT-PCR) in the HDV L-Ag region and sequence analysis. Results: The mean age of the participants was 44.36 years; 75.1% of the participants were Saudi nationals, 58% were males. Nine samples were positive for HDV-Ab and four were borderline; all were subjected to RT-PCR amplification. Three of the positive HDV-Ab cases and 1 borderline case were positive by RT-PCR. All the positive cases had HBV genotype D, and the positive RT-PCR cases were positive for HBV DNA. One of the HDV viremic samples was of genotype 1 by sequencing. The prevalence of HDV in the study was 7.7%, which was lower in Saudis (6.3%) than in non-Saudis (11.9%). Conclusion: HDV coinfection does not seem to have an effect on the clinical status of the recruited CHB cases in this study. More studies are needed to investigate the genetic diversity in other areas such as the southern parts of the Kingdom