Simultaneous Optimization of an Array of Heat Sinks
Abstract: 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.
Conjugate Nusselt Numbers for Simultaneously Developing Flow Through Rectangular Ducts
Abstract: 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.
Longitudinal-Fin Heat Sink Optimization Capturing Conjugate Effects Under Fully Developed Conditions
Abstract: 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.