Theoretical analysis of conjugated heat transfer with a single domain formulation and integral transforms

Abstract This paper presents the experimental and theoretical analysis of a micro heat exchanger designed for the waste heat recovery from a high concentration photovoltaic (HCPV) system. A test bench was built to analyze the thermal behavior of a heat exchanger targeted to work in a similar condition of an existing HCPV panel. A high power heater was encapsulated inside a copper cartridge, covered by thermal insulation, leading to dissipated heat fluxes around 0.6 MW/m2, representative of the heat flux over the solar cell within the HCPV module. The experimental campaign employed water as the coolant fluid and was performed for three different mass flow rates. An infrared camera was used to nonintrusively measure the temperature field over the micro heat exchanger external surface, while thermocouples were placed at the contact between the heat exchanger and the heater, and at the water inlet and outlet ports. In the theoretical analysis, a hybrid numerical–analytical treatment is implemented, combining the numerical simulation through the comsolmultiphysics finite elements code for the micro heat exchanger, and the analytical solution of a lumped-differential formulation for the electrical heater cartridge, offering a substantial computational cost reduction. Such computational simulations of the three-dimensional conjugated heat transfer problem were critically compared to the experimental results and also permitted to inspect the adequacy of a theoretical correlation based on a simplified prescribed heat flux model without conjugation effects. It has been concluded that the conjugated heat transfer problem modeling should be adopted in future design and optimization tasks. The analysis demonstrates the enhanced heat transfer achieved by the microthermal system and confirms the potential in reusing the recovered heat from HCPV systems in a secondary process.

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Conjugated Heat Transfer in Micro-Channels With a Single Domain Formulation and Integral Transforms

ASME 2012 Third International Conference on Micro/Nanoscale Heat and Mass Transfer ◽

10.1115/mnhmt2012-75287 ◽

2012 ◽

Cited By ~ 1

Author(s):

Diego C. Knupp ◽

Carolina P. Naveira Cotta ◽

Renato M. Cotta

Keyword(s):

Heat Transfer ◽

Analytical Solution ◽

Eigenvalue Problem ◽

Space Variable ◽

Variable Coefficients ◽

Single Domain ◽

Axial Conduction ◽

Micro Channels ◽

Conjugated Heat Transfer ◽

Transfer Problems

The present work is an extension of a novel methodology recently proposed by the authors for the analytical solution of conjugated heat transfer problems in channel flow, here taking into account the axial diffusion effects which are often of relevance in micro-channels. This methodology is based on a single domain formulation, which is proposed for modeling the heat transfer phenomena at both the fluid stream and the channel walls regions. By making use of coefficients represented as space variable functions, with abrupt transitions occurring at the fluid-wall interface, the mathematical model is fed with the information concerning the transition of the two domains, unifying the model into a single domain formulation with space variable coefficients. The Generalized Integral Transform Technique (GITT) is then employed in the hybrid numerical-analytical solution of the resulting convection-diffusion problem with variable coefficients. When the axial conduction term is included into the formulation, a non-classical eigenvalue problem must be employed in the solution procedure, which is itself handled with the GITT. In order to covalidate the results obtained by means of this solution path, we have also proposed an alternative solution, including a pseudo-transient term, with the aid of a classical Sturm-Liouville eigenvalue problem. The remarkable results demonstrate the feasibility of this single domain approach in handling conjugated heat transfer problems in micro-channels, as well as when fluid axial conduction cannot be neglected.

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