**Transport
Effects in Homogeneous-Heterogeneous Combustion **

Imran
Alam^{1}, David H. West^{2 }and Vemuri
Balakotaiah^{1}

^{}

^{1}Chemical and Biomolecular Engineering Department,

University of Houston, 4800 Calhoun Road, Houston, TX 77004

^{2}SABIC Technology
Center, Sugarland, TX 77478

*Author emails*: Imran Alam : ialam@uh.edu, David
West:dwest@americas.sabic.com ,Vemuri Balakoataiah* *:
bala@uh.edu

ABSTRACT

Introduction

Catalytic partial oxidation is an attractive technology for meeting future energy demands and production of intermediate chemicals. The models describing this process typically involve both catalytic and homogeneous reactions. Homogeneous ignition in catalytic combustion has been investigated in various settings such as stagnation point flows, external boundary layer flows and two-dimensional channel flows. However, most of these studies have been numerical, mostly relying on CFD packages. In this work, we seek to understand the effects of various transport parameters representing the heat and mass transfer phenomena on coupled homogeneous-heterogeneous combustion. Our approach uses tools of Linear Operator theory to provide analytical expressions for concentration and temperature in two-dimensional domains. We also obtain expressions for relevant transport parameters such as the Nusselt and Sherwood numbers. These results provide insights on the qualitative features of the thermally coupled homogeneous-heterogeneous combustion process.

Mathematical Models & Analysis

We present mathematical models for the combustion in monolith and parallel plate reactors. We focus on the limiting case where the catalytic reaction is very fast and the system is in the mass transfer controlled regime. We consider a homogeneous reaction and solve the resulting partial differential equations in two space dimensions. This yields contour plots for temperature and concentration. We study this system for Dirichlet and Danckwerts inlet conditions, for varying Lewis and radial Peclet numbers. We observe that hot spot formation may be possible both near the wall and near the center, and that the temperature variation in the direction transverse to flow need not be monotonic. In either case, temperature at the center never exceeds the adiabatic value as claimed by Zheng and Mantzaras, [1].

**Results and
Discussion**

We show below typical contour plots for concentration and temperature. Different values of Lewis number, Peclet number and Thiele modulus yield different qualitative behavior. Figure 1 shows a typical concentration contour plot for a 2-D model for parallel plate reactor with a homogeneous reaction and Danckwerts inlet conditions. The Thiele modulus is 1.0 and the radial Peclet number is taken to be 5.0. Next we have shown in figure 2, two temperature contour plots- (i) a system with a radial Peclet number 5, Lewis number of 0.5 and Thiele modulus of 3, and (ii) a system with a radial Peclet number of 5, Lewis number of 2.5 and Thiele modulus of 30. Figure 2 (i) shows the situation where the wall is always hotter than the center while figure 2 (ii) shows that the center can be hotter than the wall as well. In figure 3, we show a plot for the Nusselt number as a function of axial distance for a radial Peclet number 10, Lewis number of 5 and Thiele modulus of 1. This plot shows a minimum near the inlet and to our knowledge, is a novel result.

The physical insight derived from this analysis can be useful in a bifurcation study of a combustion system. In our earlier work ([2]), we found that the thermally coupled hysteresis locus is virtually unchanged from the hysteresis locus for a system with infinitely fast wall reaction. Hence an analysis for homogeneous combustion with a very fast catalytic reaction is useful to understand and compute bifurcation features of thermally coupled combustion systems. A comprehensive analysis of the system will be presented.

**Figure 1: **Concentration contour plot for a 2-D model for
parallel plate reactor with a homogeneous reaction. The Thiele modulus is 1.0
and the radial Peclet number is taken to be 5.0.

(i)

(ii)

**Figure 2: **Temperature contour plots for a 2-D model for
parallel plate reactor with a homogeneous reaction. The parameters are (i) radial Peclet number 5, Lewis
number 0.5 and Thiele modulus 3, and (ii) radial Peclet
number 5, Lewis number 2.5 and Thiele modulus 30.

**Figure 3: **Nusselt number as a
function of axial distance for a radial Peclet number
10, Lewis number of 5 and Thiele modulus of 1.

**References**

[1]. X. Zheng, J. Mantzaras, Combustion and Flame **161**
(2014) 1911-1922.

[2]. I. Alam, D. H. West, V. Balakotaiah, Chem. Eng. Journal (under review).

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