TY - JOUR

T1 - Heat transfer enhancement of a periodic array of isothermal pipes

AU - Leontiou, Theodoros

AU - Ikram, Magzhan

AU - Beketayev, Kenes

AU - Fyrillas, Marios M.

N1 - Funding Information:
The work was funded by Porfyrios Glass Ltd . The authors would like to thank Klaus Schittkowski for providing his NLPQL numerical optimization code [32] . A

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We address the problem of two-dimensional heat conduction in a solid slab whose upper and lower surfaces are subjected to uniform convection. In the midsection of the slab there is a periodic array of isothermal pipes of general cross section. The main objective of this work is to find the optimum shapes of the pipes that maximize the Shape Factor (heat transport rate). The Shape Factor is obtained by transforming the periodic array of pipes into a periodic array of strips, using the generalized Schwarz-Christoffel transformation, and applying the collocation boundary element method on the transformed domain. Subsequently we pose the inverse problem, i.e. finding the shape that maximizes the Shape factor given the perimeter of the pipes. For large Biot number the optimum shapes are in agreement with the isothermal case, i.e. circular for sufficiently small perimeters/heat transfer, and elongated towards the surfaces of the slab for larger perimeters/heat transfer. Furthermore, for the isothermal case, we were able to discover a new family of optimum shapes for large thickness of the slab and large perimeters, which do not have their maximum width on the horizontal axis of symmetry. For small Biot number the optimum pipes are flatter than the isothermal ones for a given perimeter. The flatness becomes more apparent for larger perimeters. Most important, for large perimeters there exists a critical thickness which is characterized by maximum heat transfer rate. This is further investigated using the finite element method to obtain the critical thickness of a slab and the critical depth of the periodic array of circular pipes.

AB - We address the problem of two-dimensional heat conduction in a solid slab whose upper and lower surfaces are subjected to uniform convection. In the midsection of the slab there is a periodic array of isothermal pipes of general cross section. The main objective of this work is to find the optimum shapes of the pipes that maximize the Shape Factor (heat transport rate). The Shape Factor is obtained by transforming the periodic array of pipes into a periodic array of strips, using the generalized Schwarz-Christoffel transformation, and applying the collocation boundary element method on the transformed domain. Subsequently we pose the inverse problem, i.e. finding the shape that maximizes the Shape factor given the perimeter of the pipes. For large Biot number the optimum shapes are in agreement with the isothermal case, i.e. circular for sufficiently small perimeters/heat transfer, and elongated towards the surfaces of the slab for larger perimeters/heat transfer. Furthermore, for the isothermal case, we were able to discover a new family of optimum shapes for large thickness of the slab and large perimeters, which do not have their maximum width on the horizontal axis of symmetry. For small Biot number the optimum pipes are flatter than the isothermal ones for a given perimeter. The flatness becomes more apparent for larger perimeters. Most important, for large perimeters there exists a critical thickness which is characterized by maximum heat transfer rate. This is further investigated using the finite element method to obtain the critical thickness of a slab and the critical depth of the periodic array of circular pipes.

KW - Convective heat transfer

KW - Critical depth of the pipes

KW - Critical thickness of slab

KW - Generalized Schwarz-Christoffel transformation

KW - Laplace equation

KW - Optimum shapes of pipes

KW - Shape optimization

KW - Solid slab with periodic array of pipes

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U2 - 10.1016/j.ijthermalsci.2016.02.001

DO - 10.1016/j.ijthermalsci.2016.02.001

M3 - Article

AN - SCOPUS:84960917872

VL - 104

SP - 480

EP - 488

JO - Revue Generale de Thermique

JF - Revue Generale de Thermique

SN - 1290-0729

ER -