Analytic method for the minimum time for binder removal from three-dimensional porous green bodies
- PDF / 139,928 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 3 Downloads / 253 Views
Z.C. Feng Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211 (Received 16 June 2003; accepted 28 August 2003)
An analytical expression was derived to predict the heating profile that minimizes the cycle time for the thermal removal of binder from porous green ceramic bodies. The analytical equation was based upon the solution to a three-dimensional convective transport equation that describes flow in porous media arising from the thermal decomposition of binder. The solution to the transport problem was then combined with an algorithm derived from variational calculus. The analytical expression described the time for binder removal in terms of the body dimensions, isotropic permeability, volume fraction of binder, and threshold pressure within the green body.
I. INTRODUCTION
The specification of the heating cycle for removing binder from porous green ceramic bodies is a difficult problem because of the coupling between the reaction kinetics and the flow of gaseous decomposition products through the pore space of the body;1–10 the topic of binder removal has been reviewed elsewhere.1,2 In earlier work,11 we developed a one-dimensional analytical transport model for describing the pressure distribution in porous green bodies during binder removal; this model was then combined with a computational algorithm, based on variational calculus, for determining the minimum cycle time for binder removal. We extended the earlier transport model to describe the pressure distribution in three dimensional (3D) porous bodies during binder removal;12 the validity of the pseudo-steady state assumption, which was used to obtain the analytical solution, has been shown to be quite accurate as compared to numerical solution of the 3D time-dependent partial differential equation.13 More recently, we combined the solution to the 3D transport problem with the variational calculus algorithm for specifying the minimum time for binder removal.14 To obtain the minimum-time heating cycle, however, numerical methods were required, and it was thus not directly evident how the cycle time varies with the length scales of the body, the permeability, the volume fraction of binder, and the pressure within the green ceramic body.
a)
Address all correspondence to this author. e-mail: [email protected] J. Mater. Res., Vol. 18, No. 11, Nov 2003
http://journals.cambridge.org
Downloaded: 13 Mar 2015
In this work, we develop an approximate analytical minimum-time heating profile for the variational calculus problem. The solution is reasonably accurate and demonstrates clearly how the minimum cycle time for binder removal scales with the kinetic and transport quantities in the binder removal problem. II. MODEL
To find the minimum cycle time t* to remove binder from a porous green body, we first express the reaction of binder volume fraction ⑀b into degradation products as ⑀b → products
.
(1)
The rate of binder decomposition r(⑀b,T) is given as d⑀b = −r 共⑀b,T 兲 , dt
(2)
where the reaction rat
Data Loading...
