- WO2017120284A1 - Hybrid flow evaluation and optimization of thermal systems
- G. Karamanis and M. Hodes, “Simultaneous Optimization of an Array of Heat Sinks”. ASME Journal of Electronic Packaging, vol. 141, 2019.
We provide an algorithm to optimize the geometry of the fins in an array
of longitudinal-fin heat sinks (HSs) in, e.g., a blade server, which is
a prohibitively long task using computational fluid dynamics (CFD).
First, banks of CFD simulations are run to precompute dimensionless
thermal resistances (conjugate Nusselt numbers) as a function of
dimensionless HS geometry, thermophysical properties, and external
parameters. These precomputed CFD results are embedded in flow network
models (FNMs) in the form of look-up tables. This preserves much of the accuracy of CFD and the speed of FNM. The FNMs are, in turn, embedded in
a multivariable optimization algorithm (MVO). Our hybrid numerical
algorithm is provided, and we exercise it for an example problem. We consider conjugate forced-convection heat transfer in a rectangular
duct. Heat is exchanged through the isothermal base of the duct, i.e.,
the area comprised of the wetted portion of its base and the roots of
its two side walls, which are extended surfaces within which conduction
is three- dimensional. The opposite side of the duct is covered by an
adiabatic shroud, and the external faces of the side walls are
adiabatic. The flow is steady, laminar, and simultaneously developing, and the fluid and extended surfaces have constant thermophysical
properties. Prescribed are the width of the wetted portion of the base,
the length of the duct, and the thickness of the extended surfaces, all
three of them nondimensionalized by the hydraulic diameter of the duct,
and, additionally, the Reynolds number of the flow, the Prandtl number
of the fluid, and the fluid-to extended surface thermal conductivity
ratio. Our conjugate Nusselt number results provide the local one along
the extended surfaces, the local transversely averaged one over the
isothermal base of the duct, the average of the latter in the streamwise
direction as a function of distance from the inlet of the domain, and
the average one over the whole area of the isothermal base. The results
show that for prescribed thermal conductivity ratio and Reynolds and
Prandtl numbers, there exists an optimal combination of the
dimensionless width of the wetted portion of the base, duct length, and
extended surface thickness that maximize the heat transfer per unit area
from the isothermal base. We develop a method requiring minimal computations to optimize the fin
thickness and spacing in a fully shrouded longitudinal-fin heat sink
(LFHS) to minimize its thermal resistance under conditions of
hydrodynamically and thermally developed laminar flow. Prescribed
quantities are the density, viscosity, thermal conductivity and specific
heat capacity of the fluid, the thermal conductivity and height of the
fins, the width and length of the heat sink, and the pressure drop across it. Alternatively, the length of the heat sink may be optimized
as well. The shroud of the heat sink is assumed to be adiabatic and its
base isothermal. Our results are relevant to, e.g., microchannel cooling
applications where base isothermality can be achieved by using a heat spreader or a vapor chamber. The present study is distinct from the
previous work because it does not assume a uniform heat transfer
coefficient, but fully captures the velocity and temperature fields by
numerically solving the conjugate heat transfer problem in dimensionless form using an existing approach. We develop a dimensionless formulation
and compute a dense tabulation of the relevant parameters that allows
the thermal resistance to be calculated algebraically over a relevant
range of dimensionless parameters. Hence, the optimization method does
not require the time-consuming solution of the conjugate problem. Once
the optimal dimensionless fin thickness and spacing are obtained, their
dimensional counterparts are computed algebraically. The optimization
method is illustrated in the context of direct liquid cooling. |