Numerical solution of the problem of a thermal explosion taking account of free convection

1971 ◽  
Vol 7 (2) ◽  
pp. 137-146 ◽  
Author(s):  
É. A. Shtessel' ◽  
K. V. Pribytkova ◽  
A. G. Merzhanov
Keyword(s):  
Free Convection ◽  
Numerical Solution ◽  
Thermal Explosion

scholarly journals Numerical Solution of Non-Newtonian Fluids Flow Past an Accelerated Vertical Infinite Plate in the Presence of Free Convection Currents

2013 ◽  
Vol 18 (3) ◽  
pp. 761-777
Author(s):  
M. Patel ◽  
M.G. Timol
Keyword(s):  
Fluid Flow ◽  
Free Convection ◽  
Prandtl Number ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Infinite Plate ◽  
Similarity Analysis ◽  
Convection Current ◽  
Linear Ordinary Differential Equations ◽  
Flow Past

Abstract A similarity analysis of non-Newtonian fluid flow past an accelerated vertical infinite plate in the presence of free convection current is carried out. A group theoretic generalized dimensional analysis is employed to achieve the governing non-linear ordinary differential equations in the most general form. Numerical solutions of these equations are given with the plot of their velocity profiles with the effects of Pr-Prandtl number and Gr-Grashof number

scholarly journals Free and forced convection around line sources of heat and heated cylinders in porous media

2001 ◽  
Vol 427 ◽  
pp. 389-409 ◽  
Author(s):  
VADIM N. KURDYUMOV ◽  
AMABLE LIÑÁN
Keyword(s):  
Porous Media ◽  
Free Convection ◽  
Numerical Solution ◽  
Forced Convection ◽  
Line Source ◽  
Free Stream ◽  
Outer Region ◽  
Circular Cylinders ◽  
Stream Velocity ◽  
Wide Range

An analysis is presented for the steady, two-dimensional, free convection around line sources of heat and heated cylinders in unbounded saturated porous media. It is extended to account also for the effects of forced convection. The study is based on the Boussinesq equations, with the velocities calculated using Darcy's law.The analysis begins with the non-dimensional formulation and numerical solution of the problem of pure free convection around a line source of heat. When this analysis is extended to include the effects of forced convection, two parameters appear in the non-dimensional formulation: the non-dimensional value, V∞, of the free-stream velocity and its angle γ of inclination with respect to the vertical. We first describe the asymptotic form of the solution for large and small values of the distance to the source. The far-field description, which is also applicable to the flow around heated cylinders, is needed to facilitate the numerical solution of the problem. It includes a thermal wake, aligned with the free stream, and an outer irrotational flow with a sink and a vortex at the line source. The temperature distribution near the source involves a constant A0(V∞, γ), to be calculated with the numerical solution of the complete problem, which is used in the evaluation of the heat transfer from heated cylinders when the Rayleigh and Péclet numbers are small compared with unity. In this case we find an inner region where heat conduction is dominant, and an outer region where the cylinder appears as a line source of heat. The asymptotic analysis is complemented with the numerical solution of the general problem for circular cylinders with a wide range of Rayleigh numbers and some representative values of V∞ and γ. We give correlations for the Nusselt number in the limiting cases of pure free convection and pure forced convection.

Sign in / Sign up

Export Citation Format

Share Document