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 -