Constructal conjugate cooling channels with internal heat generation

• Published in: International journal of heat and mass transfer Vol. 55; no. 15-16; pp. 4385 - 4396
• Main Authors: Olakoyejo, O.T., Bello-Ochende, T., Meyer, J.P.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.07.2012; Elsevier
• Subjects: Applied sciences; Channels; Computational fluid dynamics; Constructal theory; Cooling; Dynamic-Q; Energy; Energy. Thermal use of fuels; Exact sciences and technology; Fluid flow; Forced convection; Heat transfer; Hydraulics; Laminar flow; Mathematical analysis; Mathematical models; Optimal geometry; Optimisation; Optimization; Peak temperature; Theoretical studies. Data and constants. Metering; Thermal resistance; Forced convection; Dynamic-Q; Laminar flow; Thermal resistance; Optimisation; Peak temperature; Constructal theory; Optimal geometry; Rectangular pipe; Internal source; Constructive theory; Pipe flow; Circular pipe; Geometrical configuration; Algorithm; Modeling; Optimization; Cooling system; Numerical simulation; Heat transfer
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2012.04.007

This paper presents a geometric optimisation of conjugate cooling channels in forced convection with internal heat generation. Two configurations were studied; circular channels and square channels. The configurations were optimised in such a way that the peak temperatures were minimised subject to the constraint of fixed total global volume. The fluid was forced through the cooling channels by the pressure difference across the channels. The structure has one degree of freedom as design variable: channel hydraulic diameter and once the optimal channel hydraulic diameter is found, optimal elemental volume and channel-to-channel spacing result. A gradient-based optimisation algorithm is applied in order to search for the best and optimal geometric configurations that improve thermal performance by minimising thermal resistance for a wide range of dimensionless pressure difference. This optimiser adequately handles the numerical objective function obtained from CFD simulations. The results obtained show the behaviour of the applied pressure difference on the optimised geometry. There are unique optimal design variables for a given pressure difference. The numerical results obtained are in agreement with the theoretical formulation using scale analysis and method of intersection of asymptotes.