Modified effectiveness and linear regression based models for heat exchangers under heat gain/loss to the environment

Abstract

Developing mathematical models for describing heat exchanger outlet temperatures is of great importance for the practice, since heat exchangers are unavoidable elements in any applications, where heat transfer is needed between hydraulically separated fluid parts. The conventional, well-tried physically-based E model (standing for the known effectiveness-NTU approach) is recalled. This model assumes energy balance between the two sides of a heat exchanger (without any interaction with the environment). Based on studies in the literature, mathematical models with similar simplicity and usability to that of the E model, but under heat gain/loss to the environment, are still lacking in the field. This work intends to contribute to filling this gap with two proposed models, called ME and LR models. Based on measured data, all three models are accurate enough for general engineering/modelling purposes, nevertheless, the partly physically-based, partly empirical ME model is more precise than the E model if the heat gain/loss to the environment is considerable, and the empirical (black-box type) LR model is more precise than both the E and ME models if the heat gain/loss is not negligible. Furthermore, the outlet temperatures can be explicitly expressed from the simple linear algebraic relations characterizing all models alike.

Multiple linear regression based model for the indoor temperature of mobile containers

“…Regarding Table 1 , it is worth mentioning that the uncertainty values of the MLR-based model (∼1 °C) are well in accordance with the corresponding values of other physically- and MLR-based models describing the outlet temperatures of different types of heat exchangers [ 32 ].…”

“…MLR-based or even simple (not multiple) linear regression based models have been already used successfully (with rather good accuracy) in predicting other kinds of variables, namely, air humidity and heat load for ventilated or air-conditioned rooms [ 30 ], temperature inside water storages [ 31 ], outlet temperatures of heat exchangers [ 32 ], pipes [ 33 ] etc. It encourages the authors to model the indoor temperature of mobile containers also with MLR in this paper.…”

New Physically-Based Mathematical Model and Experiments for a Recently Invented Solar Pot

“…When modelling tube-in-tube heat exchangers, energy balance is often assumed between the working media of the two sides, neglecting the environmental heat exchange [29,30]. In [31] various mathematical models for tube-in-tube heat exchangers similar to the solar pot examined in this paper were developed. The physically-based model takes into account the heat exchange with the environment, too.…”

“…The physically-based model takes into account the heat exchange with the environment, too. A black-box type mathematical model was also developed in [31] based on multiple linear regression, which also takes environmental heat exchange into account. The models were validated using measurements on a heat exchanger.…”

A Mathematical Modelling of the Internal and External Piping Configurations Effect on the Solar Thermal System

“…Hot water can also be produced using heat pumps and heat exchangers. Heat exchanger modelling to reduce losses is also reported in the literature (GÉCZI et al, 2019).…”