Nik Mohd Asri Nik Long

Unsteady Stagnation Point Flow and Heat Transfer over a Stretching/Shrinking Sheet with Suction or Injection

The unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction/injection is studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using a similarity transformation and solved numerically. Both stretching and shrinking cases are considered. Results for the skin friction coefficient, local Nusselt number, velocity, and temperature profiles are presented for different values of the governing parameters. It is found that the dual solutions exist for the shrinking case, whereas the solution is unique for the stretching case. Numerical results show that the range of dual solutions increases with mass suction and decreases with mass injection.

General analytical solution for stress intensity factor of a hypocycloid hole with many cusps in an infinite plate

In this article, the problem for the determination of the displacement functions and the stress intensity factors (SIFs) around a boundary of a hypocycloid hole with cusps in an infinite elastic plate subject to normal and shear stresses are presented. A hole with cusps (hypocycloid) is mapped onto a unit circle and the modified complex potential is used for solving the relevant boundary value problems. An analytical solution for the SIF of a hypocycloid hole is obtained. For a special case, our results agree with others.

Computation of Energy Release Rates for a Nearly Circular Crack

This paper deals with a nearly circular crack, Ω in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, Ω and it is then transformed into a similar equation over a circular region, 𝐷, using conformal mapping. Appropriate collocation points are chosen on the region 𝐷 to reduce the hypersingular integral equation into a system of linear equations with (2𝑁

Mode Stresses for the Interaction between an Inclined Crack and a Curved Crack in Plane Elasticity

The interaction between the inclined and curved cracks is studied. Using the complex variable function method, the formulation in hypersingular integral equations is obtained. The curved length coordinate method and suitable quadrature rule are used to solve the integral equations numerically for the unknown function, which are later used to evaluate the stress intensity factor. There are four cases of the mode stresses; Mode I, Mode II, Mode III, and Mix Mode are presented as the numerical examples.

Polynomial Spline Approach for Double Integrals with Algebraic Singularity

In this note, cubature formulas are constructed to evaluate the double integrals on the rectangle with algebraic singularity by replacing the density function f(x,y) with the S?(P) modified spline function interpolation of type (0,2). Rate of convergence are obtained in the classes of function f(x,y) C2,?(D).

Modified Homotopy Perturbation Method for Fredholm–Volterra Integro-Differential Equation

In this paper, consider a linear Fredholm–Volterro integro-differential equation (FVIDE) of the third kind has derivative of order m where m is positive integer. This type of integral has been solved by using modified homotopy perturbation method (HPM) to get approximate solutions. In this modification, selective functions and unknown parameters are introduced to help us obtain only two-step iterations. This proposed method could avoid common problems such as complex and long calculations. It is found that modified HPM is a semi-analytical method and easy to apply for solving FVIDE. Numerical examples are given to present the efficiency and reliability of the propose method.

On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

We develop the Newton-Kantorovich method to solve the system of nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.

Construction of cubature formula for double integration with algebraic singularity by spline polynomial

In this note, singular integration problems of the form H_α(h) = _Ω^{∫∫ h(x,y)}/_|x̅-x̅₀_|^2-^α dA, 0 ≤ α ≤ 1, where Ω = [a₁, a₂] × [b₁, b₂], x̅ = (x, y) ∈ Ω and fixed point x̅₀ = (x₀, y₀) ∈ Ω, is considered. The density function h(x, y) is assumed given, continuous and smooth on the rectangle Ω and belong to the class of functions C^2,α(Ω). Cubature formula for double integrals with algebraic singularity on a rectangle is constructed using the modified spline function S_Ω(P) of type (0, 2). Highly accurate numerical results for the proposed method is given for both tested density function h(x, y) as linear, quadratic and absolute value functions. The results are in line with the theoretical findings.

An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals

The approximate solutions for the semibounded Hadamard type hypersingular integrals (HSIs) for smooth density function are investigated. The automatic quadrature schemes (AQSs) are constructed by approximating the density function using the third and fourth kinds of Chebyshev polynomials. Error estimates for the semibounded solutions are obtained in the class of . Numerical results for the obtained quadrature schemes revealed that the proposed methods are highly accurate when the density function is any polynomial or rational functions. The results are in line with the theoretical findings.

Mixed Convection Boundary Layers with Prescribed Temperature in the Unsteady Stagnation Point Flow toward a Stretching Vertical Sheet

Mixed convection boundary layer caused by time-dependent velocity and the surface temperature in the two-dimensional unsteady stagnation point flow of an in-compressible viscous fluid over a stretching vertical sheet is studied. The transformed nonlinear boundary layer equations are solved numerically using the shooting technique in cooperation with Runge-Kutta-Fehlberg (RKF) method. Different step sizes are used ranging from 0.0001 to 1. Numerical results for the skin friction coefficient and local Nusselt number are presented for both assisting and opposing flows. It is found that the dual solutions exist for the opposing flow, whereas the solution is unique for the assisting flow. Important features of the flow characteristics are displayed graphically. Comparison with the existing results for the steady case show an excellent agreement.