skip to main content


Title: Inverse Determination of Spatially Varying Heat Capacity and Thermal Conductivity in Arbitrary 2D Objects
A methodology for non-destructive simultaneous estimation of spatially varying thermal conductivity and heat capacity in 2D solid objects was developed that requires only boundary measurements of temperatures. The spatial distributions were determined by minimizing the normalized sum of the least-squares differences between measured and calculated values of the boundary temperatures. Computing time was significantly reduced for the entire inverse parameter identification process by utilizing a metamodel created by an analytical response surface supported by an affordable number of numerical solutions of the temperature fields obtained by the high fidelity finite element analyses. The minimization was performed using a combination of particle swarm optimization and the BFGS algorithm. The methodology has shown to accurately predict linear and nonlinear spatial distributions of thermal conductivity and heat capacity in arbitrarily shaped multiply-connected 2D objects even in situations with noisy measurement data thus proving that it is robust and accurate. The current drawback of this method is that it requires an a priori knowledge of the general spatial analytic variation of the physical properties. This can be remedied by representing such variations using products of infinite series such as Fourier or Chebyshev and determining correct values of their coefficients.  more » « less
Award ID(s):
1642253
NSF-PAR ID:
10072435
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
International Symposium on Advances in Computational Heat Transfer, paper CHT-17-106, Naples, Italy, May 28-June 1, 2017
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The development of cryogenic semiconductor electronics and superconducting quantum computing requires composite materials that can provide both thermal conduction and thermal insulation. We demonstrated that at cryogenic temperatures, the thermal conductivity of graphene composites can be both higher and lower than that of the reference pristine epoxy, depending on the graphene filler loading and temperature. There exists a well-defined cross-over temperature—above it, the thermal conductivity of composites increases with the addition of graphene; below it, the thermal conductivity decreases with the addition of graphene. The counter-intuitive trend was explained by the specificity of heat conduction at low temperatures: graphene fillers can serve as, both, the scattering centers for phonons in the matrix material and as the conduits of heat. We offer a physical model that explains the experimental trends by the increasing effect of the thermal boundary resistance at cryogenic temperatures and the anomalous thermal percolation threshold, which becomes temperature dependent. The obtained results suggest the possibility of using graphene composites for, both, removing the heat and thermally insulating components at cryogenic temperatures—a capability important for quantum computing and cryogenically cooled conventional electronics.

     
    more » « less
  2. Abstract

    Ice content (θi) is a critical parameter affecting soil thermal, mechanical, and hydraulic properties in cold regions. Few techniques are available for accurately determining θiin laboratory samples and in situ. A combined heat‐pulse and time domain reflectometry (thermo‐TDR) sensor, which measures soil thermal properties and electrical properties simultaneously, can be used to estimate θi. The thermo‐TDR method determines θiby using a heat‐capacity‐based (C‐based) approach or a thermal‐conductivity‐based (λ‐based) approach. Here, we describe the principles and procedures of such approaches. TheC‐based thermo‐TDR approach is simple to use and provides reasonable θivalues at temperatures below −5°C, but it fails at higher temperatures. The λ‐based approach, which solves for θifrom thermo‐TDR measurements with an iterative method, gives more accurate θiestimates than does theC‐based approach and extends the thermo‐TDR measurement range to temperatures near the freezing point of water. Therefore, the λ‐based thermo‐TDR method is preferred for determining θiin partially frozen soils.

     
    more » « less
  3. In electronics cooling, water is increasingly replacing air for applications requiring high heat flux. Water is the ideal substitute due to its high specific heat capacity and density. Indeed, high values of heat capacity (high density and specific heat capacity) enable water to receive, store and carry higher amounts of energy compared to air. Water's incompressibility and very low specific volume also requires smaller amounts of mechanical work for fluid circulation. Using warm water instead of chilled water makes the cooling process more economical, but requires more efficiently designed cold-plates. Our current work focuses on modeling and optimization of a V-groove mini-channel cold-plate using warm water as the coolant. Our results show that the performance of an impinging channel heat sink is significantly different compared to parallel channel designs. Dividing the flow into two branches cuts the fluid velocity and flow path in half for the impinging design. This reduction in the fluid velocity and flow length affects the developing thermal boundary layer and is an important consideration for a shorter length heat exchanger (where the channel length is comparable to the thermal entrance length). Distributing the coolant uniformly to every channel is a challenge for impinging cold-plates where there are strict limitations on size. 
    more » « less
  4.  
    more » « less
  5. The study of thermal convection in porous media is of both fundamental and practical interest. Typically, numerical studies have relied on the volume-averaged Darcy–Oberbeck–Boussinesq (DOB) equations, where convection dynamics are assumed to be controlled solely by the Rayleigh number ( Ra ). Nusselt numbers ( Nu ) from these models predict Nu – Ra scaling exponents of 0.9–0.95. However, experiments and direct numerical simulations (DNS) have suggested scaling exponents as low as 0.319. Recent findings for solutal convection between DNS and DOB models have demonstrated that the ‘pore-scale parameters’ not captured by the DOB equations greatly influence convection. Thermal convection also has the additional complication of different thermal transport properties (e.g. solid-to-fluid thermal conductivity ratio k s / k f and heat capacity ratio σ ) in different phases. Thus, in this work we compare results for thermal convection from the DNS and DOB equations. On the effects of pore size, DNS results show that Nu increases as pore size decreases. Mega-plumes are also found to be more frequent and smaller for reduced pore sizes. On the effects of conjugate heat transfer, two groups of cases (Group 1 with varying k s / k f at σ  = 1 and Group 2 with varying σ at k s / k f  = 1) are examined to compare the Nu – Ra relations at different porosity ( ϕ ) and k s / k f and σ values. Furthermore, we report that the boundary layer thickness is determined by the pore size in DNS results, while by both the Rayleigh number and the effective heat capacity ratio, $\bar{\phi } = \phi + (1 - \phi )\sigma$ , in the DOB model. 
    more » « less