Heat exchangers are an essential constituent part of many combustion systems. The thermoacoustic instability in such systems is a common problem and it has been studied extensively. However, the heat exchanger has not gained much attention in the field of combustion thermoacoustics, leading to a lack of knowledge about the thermoacoustic interactions between the burner and the heat exchanger. In this paper, a modeling approach is introduced to study these interactions in an academic representation of a heating appliance, comprised of a perforated slit burner and a tube heat exchanger. Both elements are considered thermally and acoustically active. A CFD model is used in a two-dimensional domain to simulate the response of the system to small amplitude broadband velocity perturbations. The thermochemical and acoustic coupling between the burner and the heat exchanger is investigated and a method is introduced to decouple their effects and study them separately. The extents to which this method is valid are addressed by varying the distance between the elements. Results show that as long as the flames do not impinge on the heat exchanger surface, a linear network modeling approach can be applied to construct the acoustic response of the composed configuration from the responses of its constituting elements. This approach requires registering the average velocity on a properly chosen intermediate plane between the burner and heat exchanger. Choosing this plane may be to some point difficult, i.e. when the burner and heat exchanger are close and cannot be considered independent. Moreover, when flame impingement occurs, the interactions between the flame and heat exchanger affect their individual thermoacoustic behaviors and the burner plus heat exchanger assembly needs to be considered as one coupled acoustic element. Particularly, flame impingement changes the phase of the heat absorption response of the heat exchanger and it may significantly alter the acoustic properties of the coupled assembly. The physics lying behind the effects of such interactions on the thermoacoustics of the system is discussed. The obtained results signify that a correct stability prediction of an appliance with burner and heat exchangers requires considering active thermoacoustic behavior of both elements as well as their interactions. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.