New delay differential equation models for heating systems with pipes

On delay partial differential and delay differential thermal models for variable pipe flow

“…as discussed in [8]. Though such models have been proven to be useful in applications within their derivation the transport phenomenon is considered twice: After approximating the transport equation by means of a first-order ODE and abandon the transport delay, the latter will be introduced again in a consecutive modeling step.…”

“…Commonly, one-dimensional partial-differential equations (PDEs) or delay-differential equations (DDEs) are used for these purposes. While the PDE-models are based directly on the mathematical description of the transport Indicies ∞ ambient del delayed in input m medium ma medium-ambient mw medium-wall out output s shell w wall wa wall-ambient phenomena in combination with the heat exchange between fluid and wall, the DDE-models are obtained heuristically by augmenting simple physically motivated ordinary-differential equation (ODE)-models with additional delays in order to account for the transport phenomenon [8]. A physically based modeling approach for constant flow rate is presented in [4,5] describing the thermal behavior of an oxidation catalyst.…”

Solving a Sequence of Recurrence Relations for First-Order Differential Equations

“…These problems include thermodynamic analysis models (Sheng & Tu, 2013;Bolatturk, 2006;Kalema et al, 2008;Stepanov et al, 2000;Valero, 2014;Torío et al, 2009;Romero & Linares, 2014), heat power system models (Goryachikh et al, 2010;Kicsiny, 2014;Bau et al, 2015;Kicsiny, 2017), combustion models (Messerle et al, 2013;Messerle et al, 2014;;Gao et al, 2010;Karpenko et al, 2016), local heat exchange system models (e.g., solar collectors (Kaminski & Krzyzynski, 2016;Hussain et al, 2016;Bég et al, 2016;Li & Chen, 2008;Smith et al, 2012;Thianpong et al, 2012), etc.…”

“…Sets of homogeneous and non-homogeneous differential equations are currently one of the basic tools for mathematical modeling of physical processes (Kicsiny, 2014). A set of homogeneous differential equations for adsorption chiller control is discussed by Bau et al (2015).…”

“…A solution is considered as a gradient process and no direct linear dependence is given. Richard Kicsiny discusses modern mathematical models of a piped heat system in his latest studies (Kicsiny, 2014;Kicsiny, 2017) based on differential equations of the Newton's law for pipe cooling. A rather common problem is building dynamic models of municipal heat networks to improve their efficiency.…”