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The approximation of the solution of the heat equation by using the spectral decompositions of the distributions on circular region where initially heat source concentrated at a point is studied. A solution of the problem represented as the Fourier Bessel series that will be understood in terms of distributions. Regularized solutions for different values of the order of Riesz means at a singular point are analysed. The numerical approximation of the solution of heat equations on the circular plate with the singular initial heat source is carried out with the help of MATLAB software. The optimization of the regularization of the series solutions at a non-singular point of the plates at initial time and critical index is established, which guaranteed to achieve the good convergence of the Riesz means at the index exceeding a critical point. [ABSTRACT FROM AUTHOR]

Thermal-diffusion and chemical reaction effects on mixed convection heat and mass transfer flow past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a system of linear partial differential equations using appropriate non-dimensional variables. Using Laplace transform method the resulting equations are solved analytically and the expression for velocity, temperature and concentration are obtained. They satisfy all imposed initial and boundary conditions. Numerical results for temperature and concentration are shown in various graphs for embedded flow parameters and discussed in details. [ABSTRACT FROM AUTHOR]

Numerical solution for the steady free convection boundary layer flow near the lower stagnation point of a horizontal circular cylinder subjected to a convective boundary condition, where the heat is supplied to the fluid through a bounding surface with a finite heat capacity are presented in this paper. The governing boundary layer equations are transformed using non-similar variables into non-similar equations and were solved numerically using an implicit finite difference scheme known as the Keller-box method. The solutions are obtained for the skin friction coefficient, the local wall temperature, as well as the velocity and temperature profiles with two the variations of two parameters, namely the conjugate parameter β and the Prandtl number Pr . [ABSTRACT FROM AUTHOR]

In this paper, the mathematical model for free convection boundary layer flow in a micropolar fluid near the lower stagnation point of a solid sphere with convective boundary conditions, in which the heat is supplied through a bounding surface of finite thickness and finite heat capacity, is considered. The transformed and reduced boundary layer equations in the form of ordinary differential equations are solved numerically using an implicit finite difference scheme known as the Keller-box method. Numerical solutions are obtained for the local wall temperature and the local skin friction coefficient, as well as the velocity, angular velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the material or micropolar parameter K, the Prandtl number Prand the conjugate parameter γare analyzed and discussed. [ABSTRACT FROM AUTHOR]

In this study, the steady magnetohydrodynamic (MHD) boundary layer flow over a stretching sheet with radiation effect under convective boundary conditions, where the heat is supplied to the convecting fluid through a bounding surface with a finite heat capacity, is considered. The governing system of partial differential equations is transformed into ordinary differential equations, which are then solved numerically via the Keller-box method. The effects of the governing parameters on the flow and heat transfer characteristics are analyzed and discussed. It is found that as the Prandtl number Pr and the radiation parameter increase, the temperature profile decreases, while as the magnetic and convective parameters decrease, the temperature profile also decreases. [ABSTRACT FROM AUTHOR]

In this paper, the mathematical model of free convection boundary layer flow over a permeable vertical flat plate embedded in a porous medium under the mixed thermal boundary conditions and radiation effects is considered. The transformed governing equations are solved numerically using the shooting method. Numerical solutions are obtained for the local wall temperature, the heat transfer coefficient, as well as the temperature profiles. The features of the flow and heat transfer characteristics for different values of the radiation parameter, the mixed thermal boundary condition parameter and the suction or injection parameter are analyzed and discussed. [ABSTRACT FROM AUTHOR]

The steady stagnation point flow and heat transfer towards an exponentially stretching/shrinking sheet with constant heat flux is investigated in this paper. The transformed governing nonlinear boundary layer equations are solved numerically by using Runge-Kutta-Fehlberg method. Numerical solutions are obtained for the local wall temperature, local skin-friction coefficient as well as velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the stretching/shrinking parameter and the Prandtl number are analyzed and discussed. [ABSTRACT FROM AUTHOR]

In this study, heat and mass transfer flow of a viscoelastic (Walter’s liquid-B model) nanofluid over a stretching sheet with slip velocity condition is considered. The governing equations for the model which is non-linear partial differential equations are first transformed by using similarity transformation. Runge-Kutta-Fehlberg (RKF) method is employed to solve the transformed ordinary differential equations. Numerical solutions are obtained for the reduced Nusselt number, the Sherwood number and the skin friction coefficient. It is found that the Walter’s viscoelastic nanofluid provided the higher heat and mass transfer rate compared to the ordinary nanofluid and the presence of the velocity slip reduces the effects of the stretching parameter on the skin friction coefficient. [ABSTRACT FROM AUTHOR]

Present study solved numerically the velocity slip effect on stagnation point flow past a stretching surface with the presence of heat generation/absorption and Newtonian heating. The governing equations which in the form of partial differential equations are transformed to ordinary differential equations before being solved numerically using the Runge-Kutta-Fehlberg method in MAPLE. The numerical solution is obtained for the surface temperature, heat transfer coefficient, reduced skin friction coefficient as well as the temperature and velocity profiles. The flow features and the heat transfer characteristic for the pertinent parameter such as Prandtl number, stretching parameter, heat generation/absorption parameter, velocity slip parameter and conjugate parameter are analyzed and discussed. [ABSTRACT FROM AUTHOR]

This paper discusses a mathematical model of the large, short-lived pressure by waves breaking against inclined coastal structures. The theory of pressure impulse, P proposed by Cooker which simplify the highly timedependent and very nonlinear problem by considering the time integral of the pressure over the duration of the impact pressure-impulse is used in this study. P satisfies Laplace's equation and perturbation theory is applied to this model and is solved analytically using MATLAB. The correlation between the pressure impulse and the inclination angle of a wall is investigated theoretically. It is found that as angle of inclination seawall increases, the pressure impulse also increases. [ABSTRACT FROM AUTHOR]

In this paper, the boundary layer magnetohydrodynamics (MHD) flow of Williamson nanofluids over a stretching sheet with Newtonian heating in the presence of thermal radiation effect is analyzed. Using a similarity transformation, the governing equations are reduced to a set of nonlinear ordinary differential equations (ODEs). These equations are solved numerically using a shooting method. The effects of Williamson parameter, magnetic parameter, radiation parameter, Prandtl number, Lewis number, Schmidt number, heat capacities ratio, thermophoretic diffusivity and conjugate parameter on velocity, temperature and concentration fields are shown graphically and discussed. It is found that the rate of heat transfer is higher for Williamson nanofluids compared to the classical viscous fluid. Also, the comparisons with existing results are provided in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the effect of Magnetohydrodynamic (MHD) towards the flow and heat transfer for the upper - convected Maxwell (UCM) fluid over a stretching/shrinking sheet with prescribed heat flux (PHF) is considered. The governing equations are transformed into a set of ordinary differential equations (ODEs) by using the similarity transformation. Shooting technique is applied to solve the transform ODEs. Numerical solutions of the local temperature, reduced skin friction coefficient, velocity and temperature profiles are obtained. The features of the flow and heat transfer characteristics for various values of the Prandtl number Pr, the magnetic parameter M, the suction parameter S,thestretching/shrinking parameter S and the Maxwell parameter β are analyzed and discussed. [ABSTRACT FROM AUTHOR]

In this paper, the effect of Magnetohydrodynamic (MHD) towards the flow and heat transfer for the upper - convected Maxwell (UCM) fluid over a stretching/shrinking sheet with prescribed heat flux (PHF) is considered. The governing equations are transformed into a set of ordinary differential equations (ODEs) by using the similarity transformation. Shooting technique is applied to solve the transform ODEs. Numerical solutions of the local temperature, reduced skin friction coefficient, velocity and temperature profiles are obtained. The features of the flow and heat transfer characteristics for various values of the Prandtl number Pr, the magnetic parameter M, the suction parameter S,thestretching/shrinking parameter ε andthe Maxwell parameter β are analyzed and discussed. [ABSTRACT FROM AUTHOR]

The stagnation point flow of a vicous fluid towards a stretching sheet with slip conditions and viscous dissipation is studied. With the help of similarity transformation, the govering equations are converted to nonlinear ordinary differential equations and then solved numerically by Runge-Kutta-Fehlberg (RKF) technique. Numerical results for the local Nusselt number and skin friction coefficient as well as the temperature and velocity field are elucidated through tables and graphs. The influence of Prandtl number, stretching parameter, Eckert number, thermal and velocity slip parameter on the flow and heat transfer characteristics are analyzed and discussed. [ABSTRACT FROM AUTHOR]

An analysis of the exact solutions of second grade fluid problem for unsteady magnetohydrodynamic (MHD) flows past an infinite inclined plate in a porous medium is presented. It is assumed that the bounding infinite inclined plate has a constant temperature with radiation effects. Based on Boussinesq approximation the expressions for dimensionless velocity, temperature and concentration are obtained by using Laplace transform method. The derived solutions satisfying the involved differential equations, and all the boundary and initial conditions. The influence of various parameters on the velocity has been illustrated graphically and analyzed. [ABSTRACT FROM AUTHOR]

An analysis to establish the exact solution of second grade fluid problem for unsteady magneto hydrodynamic (MHD) flows and rotating effects past an infinite inclined plate in a porous medium is presented in this paper. It is assumed that the bounding infinite inclined plate has an isothermal plate. Based on Boussinesq approximation the expressions for dimensionless velocity, temperature and concentration are obtained by using Laplace transform method. The derived solutions satisfying the involved differential equations with imposed boundary and initial conditions. The graphical result on the influence of various parameters on the velocity has been analyzed and discussed in this paper. [ABSTRACT FROM AUTHOR]

The effects of rotation on coupled heat and mass transfer by unsteady magnetohydrodynamic (MHD) free convection flow in a porous medium past an infinite inclined plate has been investigated. Exact solution using Laplace transforms technique has been obtained for the velocity, temperature and concentration fields. The analytical expressions for nondimensional skin-friction, Nusselt number and Sherwood number have been computed. The solutions of rotation parameters and inclination angle influences the flow fields have been discussed in detail. It is found that inclination angle tend to retard fluid flow in the primary and secondary flow directions, whereas rotation has a retarding influences on the primary flow direction but to accelerate in the secondary flow direction. [ABSTRACT FROM AUTHOR]