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Advancing Microelectronics • Volume 28, No. 2 • March/April 2001
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Reducing Surface Temperature Gradients by Tailoring Convective Film Coefficients
John Patrick O’Connor, Texas Instruments, Incorporated, PO Box 869305 – MS 8479, Plano, Texas 75023, (972)-575-2109, jpo@ti.com
Abstract
There are two primary design requirements when considering thermal management of microelectronic packages. The first is to maintain the electrical components below a given threshold temperature, primarily for reliability considerations. The second is to maintain the electrical components within a given temperature band (gradient), primarily for performance and structural considerations. Specifically, for military phased-array radar microelectronics, it is essential that the transmit/receive function (TRF) devices operate at similar temperatures (~10(C) to assure similar amplitude and phase operation. The work described herein focuses on the temperature gradient requirement for liquid cooled (forced convection) systems, where the electrical waste heat is removed via the sensible heat of a cooling fluid flowing through a coldplate channel. A design methodology is outlined for a serial-flow coldplate that minimizes the surface temperature gradient by tailoring the convective impedance within the flow channel. The methodology is used to design a coldplate that employees a liquid coolant common to military electronic systems (PAO - Polyalphaolefin). The coldplate is analyzed using the finite-element method to demonstrate the validity of the design procedure, and an experimental investigation verifies both the design procedure and the finite-element results.
Key Words: electronic cooling, plate-fin heat exchangers, and phased-array thermal management.
Introduction & Summary of Previous Work
Electronic packaging trends and electrical performance criteria are requiring temperature and temperature gradient control of high power microelectronics. There are many applications for which it is desirable to have similar microelectronic components operate at similar temperatures to ensure consistent electrical performance. Specifically, for phased-array radar systems, it is essential that the transmit/receive function (TRF) device temperature differences are controlled to ensure that each TRF is providing nearly identical amplitude and phase operation.
The work described herein focuses on the development and validation of a design methodology to control surface temperature gradients of serial-flow liquid-cooled coldplates. A coldplate is a substrate to which electrical components are mounted, and by which their waste heat is removed via a coolant passing through a flow channel embedded within the coldplate. Although emphasis will be placed on phased-array radar systems, the methodology is valid for any application employing such a thermal management scheme.
 Tailoring the convective thermal impedance within a coldplate flow channel allows the surface temperature gradient to be controlled. The impedance is tailored by selecting and correctly placing the appropriate heat transfer geometries (“finstocks”) within the flow channel. Heat transfer geometries of this type are referred to as plate-fin surfaces because they are embedded between two plates.
A significant amount of information exists in the literature that discusses the use of plate-fin surfaces in flat-plate heat exchangers. Kays and London [1] provide a comprehensive discussion on this topic. Numerous plate-fin surfaces are identified and experimental heat transfer and momentum data are documented. Shah investigated the classification [2], selection method [3], design procedure [4], and design methodology [5] for plate-fin surfaces. London [6], Webb [7], and Shaw and London [8] provide additional design information and experimental correlations. Additionally, finstock vendors [9,10] can supply performance characteristics and design guidelines. The application of plate-fin surfaces to tailor the convective thermal impedance and minimize the surface temperature gradient across a coldplate surface has not been documented.
Problem Definition & Solution Approach
Figure 1 illustrates the basic layout of a TRF which is a grouping of electrical devices (four are shown but there can be more). Many TRFs are required to comprise a phased-array radar system, and in practice, they are placed in series across several mounting substrates (coldplates). The device structure of each TRF is identical, device-1 (D1) of TRF-1 performs the same function as device-1 of TRF-2, and so on. The thermal design requirement is to maintain a given device type (D1 or D2, etc.) within a specified temperature band (~10°C) across all TRFs.
A literature search was conducted to identify available plate-fin heat exchanger surfaces and heat transfer and momentum data were documented. A design methodology was outlined that allows the proper selection and placement of the heat transfer surfaces within a cold plate flow channel, with the objective being to minimize surface temperature gradients.
The design methodology was employed to design a coldplate cooled with a liquid available on existing military aircraft (PAO - Polyalphaolefin). Typical allocated military flowrates are 0.0302 kg/s-kW (4 lbm/min-kW) and 0.015 kg/s-kW (2 lbm/min-kW), corresponding to a PAO temperature rise of 15°C/kW and 30°C/kW, respectively. The design accounted for existing TRF power dissipation levels (25 W/in2), and volumetric requirements associated with phased-array radar systems. To verify the design methodology, the designed coldplate was modeled and analyzed using the finite-element method, then built and tested under operational conditions.
Overview of Plate-Fin Surfaces
Plate-fin surfaces (“finstocks”) are typically corrugated and can be manufactured to provide continuous or disrupted flow passages. The finstocks may be bonded or vacuum-brazed into a flow channel. Vacuum brazing decreases the conductive impedance between the surface and coolant but increases cost. The cross-sectional shapes of the passageways can be controlled (rectangular, triangular, etc.), and the passageways can be straight or curved. Additionally, the passageways may be “cut” into rows along the flow direction and offset from one row to the next. The fin surfaces may be perforated or louvered to enhance coolant mixing. Any fin feature that disrupts boundary layer growth will enhance thermal performance at the expense of increased pressure drop.
Design Methodology
To initiate the design procedure, the following information must be known:
• coolant type (PAO)
• coolant mass flowrate (m)
• coolant inlet temperature (Tf_in)
• total power dissipation (Qtotal)
• acceptable flow path pressure drop (DPf)
• max allowable device temperature (Td_max)
• estimate of flow station number (N)
The number of flow stations (N) is the number of different finstocks to be placed into the channel (Figure 4 shows N = 4). From the above information, the coolant temperature (Tf_j) at any flow station midpoint can be calculated using an energy balance:
Initial flow station midpoint:
Mid and last flow station midpoints:
Knowing the fluid temperature at the last flow station midpoint (Tf_N), the maximum allowable device temperature (Td_max), and the power dissipation from the last flow station (Qtotal/N), the desired thermal impedance of that flow station (Rth_N) can be determined:
The designer would then use available heat transfer performance data to select a finstock that met the above criteria. A plate-fin surface with the correct film coefficient (hf), surface area (Aht), and fin efficiency (hfin) would be selected.
Finstocks for any upstream flow station are determined in the same fashion. For example, assume the desired flow channel had four flow stations. The heat transfer surface for station 3 is found by setting the device temperature at station 3 equal to the maximum device temperature (Td_3 = Td_max). Then Eq. (4) is used at station 3 as follows:
The difference between Eqs (4) and (6) lies in the numerator temperature difference, where Tf_3 is less than Tf_4 leading to the required thermal impedance at station 3 being larger than at station 4. This procedure can be repeated for any number of upstream stations. The designer must check to verify that the total pressure drop through the flow channel has not exceeded the allowable pressure drop. If so, the process must be repeated using different finstocks.
The above methodology assumed uniform waste heat dissipations for each flow station (Qtotal/N). Although this simplifies the design process, it is not a requirement and any power distribution may be addressed provided it is known beforehand. It should also be noted that to minimize the maximum device temperature (Td_max), the designer should select a finstock of the Nth section providing the minimum possible thermal impedance.
Coldplate Design & Finstock Selection
A coldplate was designed for verification of the outlined methodology. Design power dissipation values were based upon phased-array radar system requirements, approximately 25W/in2. The power dissipation surface area is 24in2 (top and bottom) leading to a total power dissipation of 600 watts. The plate was designed at the minimum coolant flowrate (0.0091 kg/s - 1.2 lbm/min) resulting in the largest coolant temperature rise.
The design methodology was employed to select four finstock surface sections (each 7.62 cm / 3 inches in length). When selecting a finstock, the design engineer must select the type (rectangular, triangular, wavy, lanced-offset, etc. - [1-10]), and identify specific geometric parameters. From these the hydraulic diameter and total heat transfer area are specified. To minimize the maximum device temperature (Td_max), a finstock providing the lowest thermal impedance was selected for the last section. For liquid coolants this is an off-set strip fin.
The offset strip fin geometry is a rectangular finstock that is divided into sections of specified lengths, with each successive downstream section offset from its neighboring upstream section. The amount of off-set can vary but the fins of each downstream section divide the flow path created by its neighboring upstream section. This type of design promotes developing boundary layers on each successive fin row and enhances heat transfer. The fin pitch (number of fins per unit width) is double the inverse of the fin spacing. Because of the channel heights (0.1016 cm / 0.040 inches – driven by TRF spacing and device height) associated with these types of plates, manufacturing limitations [9] restrict the fin pitch to 35 fins-per-inch (fpi).
Completing the design process resulted in the finstock selections identified in Table 1. The rectangular finstock correlations are from Shaw and London [8] and the lanced-offset data were provided by Marston Palmer [10]. All finstocks have a fin height of 0.1016 cm (0.040 inches) and a fin thickness of 0.0102 cm (0.004 inches).
Computational and Experimental Results
To verify the design methodology and gain insight into the heat transport fundamentals, a computational (finite-element) analysis of the plate was conducted. Due to symmetry, only half of the coldplate was modeled resulting in 550 nodes and 300 brick elements. The computational coldplate was divided into 24 equal length (1.27cm /0.5 inch) “cells” along the flow channel axis. This axial resolution allowed the film coefficient variation to be adequately captured. Because the fins were not modeled (only flat plates), the computational film coefficients were corrected to account for actual fin surface area and fin effectiveness.
The film coefficient (dashed line – left hand axis) and thermal impedance (solid line – right hand axis) variation through the flow channel is illustrated in Figure 2. The horizontal axis represents distance from the channel entrance (inches). Each of the finstocks are approximately 7.62 cm (3.0 inches) in length. The plot is divided into 24 columns, each representing a cell (1.27 cm/0.5 inches). The impedance numerical value is the inverse of the modified film coefficient. The data indicate four distinct impedance regions, and in general, the impedance decreases as the coolant moves downstream in the channel. These film coefficients were applied to the 24 cells of the flow channel elements in the model.
The computational and experimental surface temperature results are illustrated in Figure 3. Again the plot is divided into 24 columns (each represents a cell 1.27cm/0.5 inch). The coolant temperature rise is approximately 30°C. Two surface temperature data sets are illustrated, the computational prediction being represented by the dashed line, and the experimental data by the solid line/triangles. For the initial 65% of the first finstock section (5.08 cm – 2 inches), the experimental data and computational results differ by up to 10°C, with the variation decreasing in the downstream direction. This variation is due to entrance region effects and will be discussed.
Downstream of this point the agreement between experiment and computational data are good. The experimental surface temperatures vary by approximately 5°C (51°C < Tsur < 56°C), a result which can be attributed to impedance tailoring. The data in this region (~84% of the plate surface) verify the design methodology and imply that this is a viable technique for controlling surface temperature gradients.
When the plates were originally designed the correlation (Shah and London [8]) used for the first finstock section did not account for the entrance region effects when x_star < 0.02 (Eq. 7).
A correlation for laminar developing flow between parallel plates was taken from Kays and London [1] (Fig. 6-17 page 134). This revised correlation provided film coefficients for the region of interest (0.0015 < x_star < 0.02). The coefficients were generated and inserted back into the computational model. The revised film coefficients and convective thermal impedance values are illustrated in Figure 2 (box symbols). The entrance region effects are significant. The revised surface temperatures are in excellent agreement with test data (Figure 3 – box symbols).
Because of entrance effects, the overall surface temperature gradient exceeds the allowable gradient (~10°C), however, 84% of the surface is within a 5°C band. Future development efforts must address the entrance region issue. Possible solutions would be to increase the conductive impedance between source and sink over this region, or a modified finstock, perhaps open channel for the initial 3.81 cm (1.5 inches), and the rectangular 15 fpi finstock over the remaining 3.81 cm.
Temperature Gradient Reduction Benefit
Figure 4 illustrates the temperature gradient benefit by comparing surface temperatures from the tailored four finstock plate and a plate with a single finstock (lanced-offset 15 fpi). Computational results are represented by dashed lines and experimental data are represented by the solid lines/symbols (four finstock plate – triangles, single finstock plate - boxes). The agreement between computation and experiment is good. Comparing data from each plate downstream of the 5.08 cm (2 inch) axial location, the four finstock plate experiences a gradient of 5°C whereas the single finstock plate experiences a gradient of approximately 22°C (40°C to 62°C). This 17°C improvement in gradient reduction is significant and illustrates the benefit of the tailored design.
Conclusions
The use of liquid cooled coldplates to absorb the waste heat from electrical components is a viable thermal management scheme. Tailoring the thermal impedance within the coldplate flow channel is a possible means of controlling surface temperature gradients. Microelectronic systems that are required to operate within a specified temperature band are candidates for this type of thermal management solution. The following conclusions can be drawn from the current study.
1) There is an abundance of plate-fin surfaces along with performance characteristics defined in the literature. These surfaces are candidates for tailoring the convective impedance within flat-plate heat exchangers.
2) There are penalties associated with existing techniques whose function is to control surface temperature gradients (serial-flow and parallel-flow coldplates). The penalties are high flowrates, fabrication costs, and weight/volume requirements.
3) A design methodology has been outlined that was used to design a liquid-cooled coldplate. The coldplate was designed for military phased-array radar systems. The goal of the design methodology was to control surface temperature gradients to those required for phased-array radars (~10(C).
4) Finite-element predictions along with experimental data verify the design methodology. For the current PAO design, 84% of the coldplate surface was within a 5°C temperature band. The remaining 16% operated above this temperature band due to entrance region effects which must be accounted for in the design process.
Any reference or other information is available from the author.
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