Appropriate transient thermal analysis of an absorber plate in flat-plate solar collectors from beginning to end operational conditions

TL;DR

This paper develops a closed-form, two-dimensional transient heat transfer analysis for absorber plates in flat-plate solar collectors, comparing classical and thermal wave models to predict startup and shutdown behaviors accurately.

Contribution

It introduces an exact thermal response analysis using the thermal wave model during collector startup and shutdown, improving upon traditional 1-D models with detailed 2-D contours and plots.

Findings

Thermal wave model predicts higher temperature lag compared to classical model.

The geometry significantly influences the temperature distribution and heat transfer.

The study determines the precise time for the collector to reach the dead state during shutdown.

Abstract

This work establishes a closed-form analysis for two-dimensional transient heat transfer in an absorber plate based on the thermal wave model when the collector starts to work. The method of separation of variables is employed to determine the exact thermal response during the starting of a solar collector. The thermal field is represented by 2-D thermal contours and 3-D surface plots to provide an accurate prediction compared to the 1-D analysis using the time-lag theory. An influence of Fourier number on the heat flow in the absorber plate is studied for different thermal relaxation times. The present analysis highlights that the magnitude of plate temperature depends significantly on the physical geometry. Differences in two models of heat propagation, viz. classical and thermal wave, in the absorber plate have an alteration in predicted collector performances. The present study also develops another design situation for heat transfer in the absorber plate when the collector shutdowns to the ambient state from its steady condition. Laplace Transform Method (LTM) in combination with the product solution method uses to determine the temperature with the initial condition represented as a steady case. Due to the lagging nature of thermal behavior, a significant difference between the classical and thermal wave models for the propagation of heat was observed, and also this study determines the exact time to be taken to reach the dead state for the complete shutdown of the collector.