Tufts University  |  School of Engineering  |  Find People  |  Give  | 


Marc Hodes
Associate Professor, Department of Mechanical Engineering


My area of research is Transport Phenomena. My BS, MS and PhD degrees are all in Mechanical Engineering and are from the University of Pittsburgh (magna cum laude), the University of Minnesota and MIT, where I minored in Chemical Engineering, respectively. I spent 10 years at Bell Labs Research and I have spent extended periods at the National Institute of Standards and Technologies (NIST), the University of Limerick and Imperial College London. I joined the Department of Mechanical Engineering at Tufts University in 2008. My course rotation consists of Fluid Mechanics and Heat Transfer at the undergraduate level and Thermal Management of Electronics, Heat Transfer and Advanced Transport Phenomena at the graduate level.

I've conducted both fundamental and applied research, but, currently, I am largely focused on the former in an applied mathematics context. During my career, I've focused on 4 sub-topics within the broad area of Transport Phenomena, i.e., in chronological order, 1) the thermal management of electronics, 2) mass transfer in supercritical fluids, 3) analysis and design of thermoelectric modules and 4) transport phenomena in the presence of apparent slip. Representative problems previously considered in each area are summarized below and followed by information on current research.

Representative Completed Projects:

Fig. 1. Solution for thermally coupling heat sinks on
components in an EMI-shielded circuit pack to external
air flow.

Thermal Management of Electronics: Figure 1 shows a solution for cooling multiple (packaged) components inside a circuit pack shielded from electromagnetic interference (EMI). The challenge concerned the variability of the gaps between the tops of the components and the bottom of the original cooling plate (not shown) because of the tolerances specified for component stack-up heights and component-cooling plate parallelism. Moreover, the geometry of the gaps varied over time because of thermal and mechanical stresses during operation. Thermally coupling the tops of the packages to the bottom of the cooling plate via thick layers of thermal grease proved unreliable in the original design. In our solution, each component is efficiently cooled by an individual heat sink that protrudes into an external airflow through openings in the lid of the EMI shield. Importantly, the base of each heat sink is thermally coupled to the top of the corresponding package by an optimally thin layer of thermal grease. The pressure exerted at the grease-filled thermal interfaces is sufficiently high to achieve low thermal contact resistance, but sufficiently low to avoid significant mechanical stress on the components. This is accomplished by utilizing compliant electrically conductive gaskets to form perimeter seals between lips along the bases of the heat sinks and the bottom of the Al lid of the enclosure. Further details on this technology may be found in References [1] and [2].

Fig. 2. Photographs of a hot finger before (a) and
after (b-d) it was exposed to an aqueous solution
of sodium sulfate at supercritical conditions.

Mass Transfer in Supercritical Fluids: Figure 2 shows a photograph of a hot finger before (a) and after (b-d) it was inserted in an aqueous solution of sodium sulfate at supercritical conditions at a temperature and pressure of 375oC and 250 bar, respectively. The surface of the hot finger was maintained above the saturation temperature of the salt in solution and salt deposition was by double-diffusive natural convection mass transfer. The research was performed in the context of understanding fouling during the supercritical water oxidation (SCWO) process whereby hazardous waste, e.g., methylene chloride, is oxidized in supercritical water. This remediation process exploits the low dielectric constant of supercritical water, which causes it to behave like an ordinary non-polar solvent and has some advantages over incineration, e.g., it's a lower temperature process. Additional details on this effort may be found in References [3] and [4].

Analysis and Design of Thermoelectric Modules: Figure 3 shows a schematic of a thermoelectric module (TEM), a solid-state device used to, e.g., refrigerate a photonics component below ambient temperature or generate electric power from waste heat. Research on TEMs focused on optimizing the geometry (height and cross-sectional area) of the semiconductor pellets therein to minimize power consumption for refrigeration [5] and precision temperature control [6] applications and maximize conversion efficiency in generation applications [7]. TEM-variable conductance heat pipe assemblies to further reduce the power required for precision temperature control have also been considered [8]. The majority of the work that I have done on thermoelectric modules has been as a sole investigator.

Fig. 3. Schematic of a thermoelectric module.

Transport Phenomena in the Presence of Apparent Slip: Figure 4 shows a schematic of a superhydrophobic surface (a) and a mm-scale water droplet with ZnCl2 dissolved in it to increase its electrical conductivity in various states (b-d). The surface was microfabricated by 1) depositing an oxide film on Si, 2) depositing a conductive poly-Si film on the oxide, 3) etching nanopillars into the poly-Si, 4) growing an oxide on the poly-Si and 5) coating the latter oxide with a hydrophobic polymer [9]. The nanopillars are 500 nm diameter x 4.8 µm tall and their pitch is 2 µm. When the droplet is deposited on the structured surface it is in the Cassie (unwetted) state as per Fig. 4b. Upon applying a voltage difference between the droplet and poly-Si film to reduce the solid-liquid surface tension, the droplet transitions to the Wenzel (wetted) state as per Fig. 4c. Finally, by releasing the voltage and running a pulse of current through the Poly-Si, bubbles which nucleate during transition boiling lift the droplet back to the Cassie state as per Fig. 4d.

Fig. 4. Structured surface (a). mm-scale water-ZnCl2 droplet gently deposited on surface in Cassie state (b), transitioned to Wenzel state upon electrowetting (c) and returned to Cassie state by transition boiling (d).

Representative Current Projects:

Fig. 5. (a) Longitudinal fin heat sink with fin height (H),
fin spacing (s) and fin thickness (t). (b) Numerical
domain for conjugate problem under thin fin assumption.

Thermal Management of Electronics: A long-standing challenge in this field has been to optimize the geometry of heat sinks, e.g., the fin thickness, fin spacing, etc. in the case of longitudinal-fin heat sinks as per Fig. 5. We are numerically solving a suite of canonical heat sink problems for the conjugate Nusselt number such that this may be done rapidly and accurately. When, e.g., the flow is hydrodynamically and thermally fully-developed, the conjugate Nusselt number is dependent upon dimensionless fin spacing and thickness. Utilizing dense tabulations such Nusselt numbers, we have developed the means to compute the optimal values of fin thickness, fin spacing and fin length, to minimize the thermal resistance of a longitudinal-fin heat sink of prescribed fin height with a prescribed pressure drop imposed across it [10].

Mass Transfer in Supercritical Fluids: Aerogels are low density nanoporous materials that can be utilized to, e.g., superinsulate buildings, but are prohibitively expensive for many applications. During aerogel manufacturing, supercritical carbon dioxide (SCCO)-based extraction is commonly utilized to remove liquid from a gel while preserving the solid nanostructure of the gel because it eliminates capillary forces. This process accounts for much of aerogel manufacturing cost, requires copious amounts of carbon dioxide and energy and stifles throughput. We measure and model extraction rates as a function of operating conditions, i.e., carbon dioxide mass flow rate, temperature, pressure and reactor and gel geometries. A photograph of the custom rig developed in our laboratory for this purpose, an aerogel monolith dried using it and representative experimental data are shown in Fig. 6 [11]. Our ultimate goal is to commoditize aerogels. Our current industrial partner is Aerogel Technologies.

Figure 6.  Photograph of a) Tufts SCCO2 drying rig and b) an aerogel monolith with dimensions of 46 mm ID × 56 mm OD × 220 mm on Al spindle.  c) Mass flow rate of ethanol extracted from aerogel in b).

Figure 7.  Liquid flow in the Cassie state over a
structured surface in the vicinity of the structures.
(Not drawn to scale.)

Transport Phenomena in the Presence of Apparent Slip: Figure 7 shows a liquid flowing (into the page) over a ridge-type structured surface in the Cassie (unwetted) state in the presence of heat transfer. Along the surface the velocity field is subjected to, e.g., a no-slip boundary condition along the solid-liquid interfaces and a no shear boundary one along menisci. Additionally, the temperature field is subjected to, e.g., a constant heat flux boundary condition along the solid-liquid interfaces and an adiabatic one along menisci. Additional complications are due to, e.g., meniscus curvature, molecular slip in the vapor phase, interfacial shear, phase change along menisci and thermocapillary stress along menisci. Clearly, such transport problems are packed with interesting physics and present a suite of challenging mathematical problems. We use a combination of analytical (conformal maps, perturbation methods, etc.), semi-analytical (eigenfunction expansions, etc.) and numerical (finite difference methods, collocation methods, etc.) techniques to solve such problems for the key engineering parameters for internal flows, i.e.,  Poiseuille and Nusselt numbers as a function of the relevant dimensionless independent variables as per, e.g., references [12] and [13]. Applications include, e.g., lubrication in microchannel flows and enhanced direct liquid cooling of microelectronics [14].


[1]    Bolle, C., Hodes, M. and Kolodner, P., 2007, "Thermal Management for Shielded Circuit Packs," U.S. Patent 7,254,034.

[2]    Hodes, M., Bolle, C. and Kolodner, P., 2007, "Efficient Cooling of Multiple Components in a Shielded Circuit Pack," ASME J. Electronic Packaging, 129, pp. 216-218.

[3]    Hodes, M., Smith, K., Griffith, P., Hurst, W., Bower, Jr., W., Sako, K., 2004, "Salt Solubility and Deposition in High Temperature and Pressure Aqueous Solutions," AIChE J., 50(9), pp. 2038-2049.

[4]    Hodes, M., Marrone, P., Hong, G., Smith, K.A., and Tester, J., 2004, "Salt Precipitation and Scale Control in Applications of Supercritical Water Oxidation - Part A: Fundamentals and Research," J. Supercritical Fluids, 29, pp. 265-288.

[5]    Hodes, M., 2012, "Optimal Design of Thermoelectric Refrigerators Embedded in a Thermal Resistance Network," IEEE Trans. on Components, Packaging and Manufacturing Technology, 2(3).

[6]    Zhang, R., Hodes, M., Brooks, D., Manno, V., 2012, "Optimized Thermoelectric Module-Heat Sink Assemblies for Precision Temperature Control," ASME J. Electronic Packaging, 134.

[7]    Brownell, E., Hodes, M., 2014, "Optimal Design of Thermoelectric Generators Embedded in Thermal Resistance Networks," IEEE Trans. on Components, Packaging and Manufacturing Technology, 4(4).

[8]    Melnick, C., Hodes, M., Ziskind, G., Cleary, M., and Manno, V., 2012, "Thermoelectric Module-Variable Conductance Heat Pipe Assemblies for Reduced Power Temperature Control," IEEE Trans. on Components, Packaging Manufacturing Technology, 2(3).

[9]    Krupenkin, T., Taylor, J., Wang, E., Kolodner, P., Hodes, M., Salamon, T., 2007, "Reversible Wetting-Dewetting Transitions on Electrically Tunable Superhydrophobic Nanostructured Surfaces," Langmuir, 23(18).

[10]  Karamanis, G., Hodes, M., "Longitudinal-Fin Heat Sink Optimization Accounting for Non-Uniform Heat Transfer Coefficient under Fully-Developed Conditions." Submitted to ASME Journal of Science and Engineering Applications.

[11] Griffin, J., Mills, D., Cleary, M., Nelson, R., Manno, V., and Hodes, M, 2014, "Continuous Extraction Rate Measurements During Supercritical CO2 Drying of Silica Alcogel," J. Supercritical Fluids, 92, pp. 38-47.

[12]  Enright, R., Hodes, M., Muzychka, Y., Salamon, T., 2014, "Isoflux Nusselt Number and Slip Length Formulae for Superhydrophobic Microchannels," ASME J. Heat Transfer, 136(1).

[13]  Hodes, M., Lam, L., MacLachlan, S., and Enright, R., 2015, "Effect of Evaporation and Condensation at Menisci on Apparent Thermal Slip," ASME J. Heat Transfer, 136.

[14]  Lam, L., Hodes, M., and Enright, R., 2015, "Galinstan-Based Microgap Cooling Enhancement Using Structured Surfaces," ASME J. Heat Transfer, 137.