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Research Papers

Optimization Under Uncertainty Applied to Heat Sink Design

[+] Author and Article Information
Suresh V. Garimella

e-mail: sureshg@purdue.edu
Cooling Technologies Research Center,
NSF IUCRC, School of Mechanical Engineering and Birck Nanotechnology Center,
Purdue University,
West Lafayette, IN 47907-2088

1Corresponding author.

Manuscript received April 1, 2012; final manuscript received June 20, 2012; published online December 6, 2012. Assoc. Editor: Akshai Runchal.

J. Heat Transfer 135(1), 011012 (Dec 06, 2012) (13 pages) Paper No: HT-12-1146; doi: 10.1115/1.4007669 History: Received April 01, 2012; Revised June 20, 2012

Optimization under uncertainty (OUU) is a powerful methodology used in design and optimization to produce robust, reliable designs. Such an optimization methodology, employed when the input quantities of interest are uncertain, yields output uncertainties that help the designer choose appropriate values for input parameters to produce safe designs. Apart from providing basic statistical information, such as mean and standard deviation in the output quantities, uncertainty-based optimization produces auxiliary information, such as local and global sensitivities. The designer may thus decide the input parameter(s) to which the output quantity of interest is most sensitive, and thereby design better experiments based on just the most sensitive input parameter(s). Another critical output of such a methodology is the solution to the inverse problem, i.e., finding the allowable uncertainty (range) in the input parameter(s), given an acceptable uncertainty (range) in the output quantities of interest. We apply optimization under uncertainty to the problem of heat transfer in fin heat sinks with uncertainties in geometry and operating conditions. The analysis methodology is implemented using DAKOTA, an open-source design and analysis kit. A response surface is first generated which captures the dependence of the quantity of interest on inputs. This response surface is then used to perform both deterministic and probabilistic optimization of the heat sink, and the results of the two approaches are compared.

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Figures

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Fig. 1

Nested approach to optimization under uncertainty employed in this work

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Fig. 2

(a) Isometric view with boundary conditions and (b) top view of pin-fin geometry considered

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Fig. 3

Schematic diagram of the heater block design problem

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Fig. 4

Two-dimensional channel flow with uncertain viscosity for the case of Re = 81.24: (a) current results and (b) results from Le Maitre et al. [14]

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Fig. 5

Nusselt number versus nondimensional fin spacing. The results from Ledezma et al. [10] are shown for comparison.

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Fig. 6

PDFs of (a) Nusselt number and (b) pressure drop for the uniformly distributed input parameters in Table 2

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Fig. 7

Response surface plots of Nusselt number as a function of various input parameters

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Fig. 8

Response surface plots of pressure drop as a function of various input parameters

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Fig. 9

Plots of Nusselt number shown for three most sensitive input parameters: (a) fin width, (b) fin height, and (c) length of the base, for OUU of pin-fin heat sinks

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Fig. 10

Nusselt number PDFs shown for the three most sensitive input parameters: (a) fin width, (b) fin height, and (c) length of the base, for OUU of pin-fin heat sinks

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Fig. 11

Convergence history for OUU with uncertain dimensions using (a) deterministic optimization for maximizing Nusselt number and (b) probabilistic optimization for maximizing mean value of Nusselt number

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Fig. 12

Convergence history for OUU with uncertain operating conditions using (a) deterministic optimization for maximizing Nusselt number and (b) probabilistic optimization for maximizing mean of Nusselt number

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