Medhat M. Helal

Steady Flow of an Electrically Conducting Incompressible Viscoelastic Fluid over a Heated Plate

The transformation group theoretic approach is applied to the problem of the flow of an electrically conducting incompressible viscoelastic fluid near the forward stagnation point of a heated plate. The application of one-parameter transformation group reduces the number of independent variables, by one, and consequently the basic equations governing flow and heat transfer are reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions by employing the shooting numerical technique. The effect of the magnetic parameter M, the Prandtl number Pr and the non-dimensional elastic parameter representing the non- Newtonian character of the fluid k on velocity field, shear stress, temperature distribution and heat flux are carefully examined.

Semi Analytical Solutions of a Heat-Mass Transfer Problem Via Group Theoretic Approach

Problem of heat-mass transfer in non-Newtonian power law, two-dimensional, laminar, boundary layer flow of a viscous incompressible fluid over an inclined plate has been studied by applying the method of group theoretic approach. The governing system of nonlinear partial differential equation describing the flow and heat transfer problem are transformed into a system of nonlinear ordinary differential equation which has been solved semi analytically. Exact solutions for the dimensionless temperature and concentration profiles, are presented graphically for different physical parameters and for the different power law exponents \(n\in (0,0.5)\) and for \(n>0.5.\) Also the effect of n, the Prandtl number, and the heat generation parameter on both the temperature and the concentration of the fluid inside the boundary layer have been studied.

Mathematical modelling for solving nonlinear heat diffusion problems of pavement spherical roads in Makkah

Pavement temperature is one of the most important factors affecting the design and performance of roads. Actual pavement temperature is required to be considered in design standards for pavements roads which have spherical shapes. The heat distribution is highly influential in pavement structural design and have a large effect on indirect tensile stiffness modulus. This importance calls for special attention and interest in research to develop procedures for design and analysis that account for temperature considerations. However, temperatures at different depths in the pavement are difficult to measure. Therefore, a mathematical model for pavement temperature estimation from climatic data such as air temperature and solar radiation is presented. Maximum and minimum pavement temperatures are usually needed for design, evaluation and analysis of pavements. In this study, these temperatures are both calculated from the air temperatures.

Application of a fractional step method for the numerical solution of the shallow water waves in a rotating rectangular basin

A numerical method is applied to the problem of an incompressible fluid in a slowly rotating rectangular basin for the simulation of wave propagation in shallow water. The present work is a complete study of the wave motion through evaluation of the wave height and the velocity components. The results are found by the application of a fractional step method and illustrated graphically. The technique is applied by splitting the shallow water equations and successive integration in every direction along the characteristics using the Riemann invariants associated with cubic spline interpolation. It has the advantage of reducing the multidimensional matrix inversion problem into an equivalent one-dimensional problem. Numerical results are represented in three dimensions for the velocity components at different times. The distribution of temperature and concentration are also calculated and plotted.