Asian Journal of Current Engineering and Maths

In this short paper we introduce a new definition  - Integral Laplace Transform, , of a function belonging to the space of functions piecewise continuous in the interval and it is of exponential order .The importance of this new transform is a generalization of the Laplace transform both classical sense of the definition as in their properties and theorems. A table transform some features are present and in which the most important result is to calculate the  - Integral Laplace Transform of the singular kernel Riemman-Liouville. Also we study the action of this  - Integral Laplace Transform on the classical convolution product of functions.

Determination of the five elements of highway horizontal circular curve, which are tangent distance, T, external distance, E, middle ordinate, M, chord length C, and length of curve, L, is directly established in terms of the given radius R and deflection angle ∆.

Field features may cause the infeasibility of the  intersection point PI. Consequently, the deflection angle ∆ and the radius R cannot be measured which means the arising of  non-linear problem.

This paper presents a simple and direct solution for the problem by remodeling the non-linear problem  as a rational function in terms of the deflection angle.  The model’s  function has been designated due to the similarity of the graphs of  both  non-linear function and the rational function.

Such function has three coefficients and two  asymptotes,  x= π/2  as a vertical asymptote and y = a, the first coefficient, as a horizontal asymptote.

Coefficients of the model were determined addressing the least squares technique employing  different values of the deflection angle along the entire  0 < Δ < π/2 interval. 

Such model has been verified through adopting different random locations along the interval  of J, and the output has proven an almost 100% accuracy.

Also, the applicapility of the model for generating deflection angle and curve radius with fair accuracy was investigated numerically adopting designated values of L and T. The results exhibited fair accuracy in comparative to the previous methods in the favour of the iterative techniques of such methods which lack necessary initial guess.

In the present article, we study the effect of chemical reaction on unsteady heat and mass transfer in a vertical wavy channel with oscillatory flux and heat source. The governing partial differential equations are transformed into a system of ordinary differential equations by non-dimensional procedure and are then solved by using regular perturbation technique. The velocity, temperature and concentration profiles are analyzed graphically for different variations in the parameters. The physical interpretation to these expressions is examined through graphs and tables for the shear stress and rate of heat transfer coefficients at the vertical channel walls.