Transient Response of a Coupled Conduction and Convection Heat Transfer Problem

Abstract

Systems of dynamic models involving the coupling of both conduction and convection offer significant theoretical challenges because of the interaction between parabolic and hyperbolic types of responses. Recent results of state space theory for coupled partial differential equation models are applied to conjugate heat transfer problems in an attempt to understand this interaction. Definition of a matrix of Green’s functions for such problems permits the transient responses to be resolved directly in terms of the operators’ spectral properties when they can be obtained. Application of the theory to a simple conjugate heat transfer problem is worked out in detail. The model consists of the transient energy storage or retrieval in a stationary, single dimensioned matrix through which an energy transport fluid flows. Even though the partial differential operator is nonself-adjoint, it is shown how its spectral properties can be obtained and used in the general solution. Computations are presented on the effect of parameters on the spectral properties and the nature of the solution. Comparison is made with several readily solvable limiting cases of the equations.