Summary. Laminar free convection from a vertical permeable circular cone maintained at nonuniform surface temperature is considered. Non-similar solutions for boundary-layer equations are found to exist when the surface temperature follows the power law variations with the distance measured from the leading edge. The numerical solutions of the transformed non-similar boundary-layer equations are obtained by using three methods, namely, (i) a finite difference method, (ii) a series solution method, and (iii) an asymptotic solution method. Solutions are obtained in terms of skin friction, heat transfer, velocity profile and temperature profile for smaller values of Prandtl number and temperature gradient are displayed in both tabular and graphical forms. Finite difference solutions are compared with the solutions obtained by perturbation and asymptotic techniques and found to be in excellent agreement.
We investigate the radiative heat transfer in a co-flowing turbulent nonpremixed propane-air flame inside a three-dimensional cylindrical combustion chamber. The radiation from the luminous flame, which is due to the appearance of soot particles in the flame, is studied here, through the balance equation of radiative transfer which is solved by the Discrete Ordinates Method (DOM) coupling with a Large Eddy Simulation (LES) of the flow, temperature, combustion species and soot formation. The effect of scattering is ignored as it is found that the absorption dominates the radiating medium. Assessments of the various orders of DOM are also made and we find that the results of the incident radiation predicted by the higher order approximations of the DOM are in good agreement.
The problem of laminar natural convection from a vertical circular cone maintained at either a uniform surface temperature or a uniform surface heat flux, and placed in a thermally stratified medium is considered. The governing non‐similarity boundary layer equation for uniform surface temperature are analyzed by using two distinct solution methodologies; namely, (i) a finite difference method and (ii) a local non‐similarity method. For uniform surface heat flux case, the solutions of the governing non‐similarity boundary layer equations are obtained by using three distinct solution methodologies, namely, (i) a finite difference method, (ii) a series solution method and (iii) an asymptotic solution method. The solutions are presented in terms of local skin‐friction and local Nusselt number for different values of Prandtl number and are displayed graphically. Effects of variations in the Prandtl number and stratification parameter on the velocity and temperature profiles are also shown graphically. Solutions obtained by finite difference method are compared with the other methods and found to be in excellent agreement.
Large Eddy Simulation (LES) technique is applied to investigate the Soot formation in a model cylindrical combustor. Gaseous propane (C3H8) is injected through a circular nozzle attached at the centre of the combustor inlet and preheated air with temperature of 773K is supplied through the annulus surrounding of the nozzle. The non-premixed combustion process is based on the conserved scalar approach with laminar flamelet model, while the Soot formation is included through the balance equations for soot mass fraction and soot particle density. In LES the governing equations are filtered using a spatial filtering approach to separate the flow field into large scale eddies and small scale eddies. The large scale eddies which contain most of the turbulent energy are resolved explicitly while the unresolved small scale eddies are modelled via sub-grid scale (SGS) modelling approach.
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