~) Pergamon Int. J. Heat Mass Transfer. Vol. 39, No. 9, pp. 1963-1978, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 001%9310/96 $15.00+0.00 0017-9310(95)00253--6 Laminar flow and forced convection heat transfer in plate-type monolith structures by a finite element solution RAOUL GIUDICI and ENRICO TRONCONI~" Dipartimento di Chimica Industriale e Ingegneria Chimica "G. Natta" del Politecnico, Piazza Leonardo da Vinci 32, 1-20133 Milano, Italy (Received 6 May 1994 and in final form 6 June 1995) Abstraet--A numerical solution is obtained by the finite element method for the Graetz problem of forced convection heat transfer in the channels of plate-type monolith catalysts. For this purpose a generalized model is constructed for the duct geometry, the fully developed laminar velocity profile is calculated, and the heat transfer problem is solved for both uniform wall heat flux or temperature. The results are summarized in interpolated functional forms providing the axial evolution of the Nusselt number. Such formulae represent a prerequisite to the development of design equations for mass-transfer coefficientsin plate-type monolith catalysts for the selectivecatalytic reduction of NOx with ammonia. INTRODUCTION Forced convection with laminar flow in straight ducts of a constant cross-section has important practical applications. Shah and London [1] have extensively surveyed the well known Graetz problem for different geometries: from ci~rcular ducts to parallel plates, from rectangular sections to triangle passages they attempted to systematize thermal boundary conditions, considering those most common in the literature and interesting in applications. They also reported solutions ['or sine ducts, elliptical forms, cir- cular sectors and other singly connected configur- ations, that is geometrical shapes delimited by a single closed line. Double and multiple connected ducts were considered, too. After Shah and London's publication, other authors have addressed the Graetz problem: different numerical methods have been tested on traditional shapes [2-11]; the less conventional geometries have been studied with regard to entrance effects [12-21]; axial conduction has been considered [22-24]; and finally the analysis of non-Newtonian fluids has begun to appear [25-28]. In this article we consider the forced convection heat transfer problem for ducts of complex geometry corresponding to the channels of plate-type monolith catalysts [29, 30]. We first examine the hydrodynamic problem to obtain information on the laminar velocity profiles inside the monolith channels; then we analyze the heat transfer problem, and eventually derive interpolated expressions for the axial evolution of the t Author to whom correspondence should be addressed. Nusselt number with regard to different boundary conditions. The novelty of this paper lies in the duct geometry considered, as well as in the algorithm adopted for numerical solution of the problem. The choice of the duct geometry is motivated according to two different arguments. First of all, the cross-sections of plate-type monoliths exhibit a peculiar configuration including two non interacting channels. In this paper we illus- trate an approach suitable to reduce such a situation to the analysis of a single duct. The same analysis is also expected to provide applied benefits, since cata- lytic monoliths in plate form are actually of com- mercial interest for the selective catalytic reduction (SCR) of NOx with ammonia, SCR processes being the most efficient technology available for the deni- trification of flue gases from power stations [30]. It has been shown in the literature [31] that gas-solid mass transfer coefficients in monolithic honeycomb SCR reactors with simple channel geometry (circular, square and triangular) are adequately predicted by relying on the similarity with the corresponding heat transfer problems for constant wall temperature or constant heat flux. It is of practical relevance for the modelling of industrial SCR monolith reactors to establish whether the same conclusions apply also to the class of plate-type monolith catalysts: as men- tioned above, however, solutions of the thermal prob- lem for this more complex geometry are not available. While the derivation of such solutions on a generalized basis is the scope of the present work, in a future article [32] they will be applied to the specific purpose of developing a design procedure for plate-type mono- lithic SCR reactors. 1963