Numerical modeling of the hydrodynamic stability in vertical annulus with heat source of different lengths

A numerical investigation of natural convection heat transfer stability in cylindrical annular with discrete isoflux heat source of different lengths is carried out. The adiabatic unheated portions and the discrete heat source are mounted at the inner wall. The top and bottom walls are adiabatic, while the outer wall is maintained at a lower temperature. The governing equations are numerically solved using a finite volume method. SIMPLER algorithm is used for the pressure–velocity coupling in the momentum equation. The numerical results for various governing parameters of the problem are discussed in terms of streamlines, isotherms and Nusselt number in the annulus. The results show that the increase of heat source length ratio decreases the critical Rayleigh number. We can control the flow stability and heat transfer rate in varying of the length of heat source

Convection Heat Transfer Analysis in a Channel with an Open Trapezoidal Cavity: Heat Source Locations effect

In this work, a numerical study of mixed convection inside a horizontal channel with an open trapezoidal enclosure subjected to a discrete heat source in different locations is carried out. The heat source with the length of ε = 0.75, is maintained at a constant temperature. The air flow with a fixed velocity and a cold temperature enters the channel horizontally. The other walls of the enclosure and the channel are adiabatic. The results are presented in the form of the contours of velocity, isotherms and Nusselt numbers profiles for various heat source locations, Prandtl number (Pr = 0.71) and Reynolds number (Re = 100) respectively. The distribution of the isotherms depends significantly on the position of the heat source. We noted that the best heat transfer is detected where the heat source is placed in the top of the left

Convection Heat Transfer Analysis in a Channel with an Open Trapezoidal Cavity: Heat Source Locations effect

In this work, a numerical study of mixed convection inside a horizontal channel with an open trapezoidal enclosure subjected to a discrete heat source in different locations is carried out. The heat source with the length of ε = 0.75, is maintained at a constant temperature. The air flow with a fixed velocity and a cold temperature enters the channel horizontally. The other walls of the enclosure and the channel are adiabatic. The results are presented in the form of the contours of velocity, isotherms and Nusselt numbers profiles for various heat source locations, Prandtl number (Pr = 0.71) and Reynolds number (Re = 100) respectively. The distribution of the isotherms depends significantly on the position of the heat source. We noted that the best heat transfer is detected where the heat source is placed in the top of the left

Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator

Solving nonlinear differential equation of a circular sector oscillator is of a scientific importance. Thus, to solve such equations, a single- step implicit block method involving one hybrid point with the introduction of a third derivative is proposed. To derive this method, the approximate basis solution is interpolated at {xn, xn + 3/5} while its second and third derivatives are collocated at all points {xn, xn + 3/5, xn + 1}on the integrated interval of approximation. Numerical results are presented in the form of table and graphs for the variation of different physical parameters. The study reveals that the proposed hybrid block method is zero stable, which proves that it is convergent beside a significant interval of absolute stability, thus making it suitable for solving stiff ODEs