0
Research Papers: Conduction

Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity

[+] Author and Article Information
Francisco A. Herrera

Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: fherrer2@nd.edu

Tengfei Luo

Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556;
Center for Sustainable Energy at Notre Dame,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: tluo@nd.edu

David B. Go

Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556;
Department of Chemical and
Biomolecular Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: dgo@nd.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 22, 2016; final manuscript received February 24, 2017; published online May 2, 2017. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 139(9), 091301 (May 02, 2017) (8 pages) Paper No: HT-16-1530; doi: 10.1115/1.4036339 History: Received August 22, 2016; Revised February 24, 2017

A thermal rectifier transmits heat asymmetrically, transmitting heat in one direction and acting as an insulator in the opposite direction. For conduction at steady-state, thermal rectification can occur naturally in systems where the thermal conductivity of the material(s) varies in space and with temperature. However, in practical applications, rectification may often need to be controlled or understood under transient conditions. Using a bulk composite, specifically a two-slab composite, as a model system, we analyze transient rectifying behavior. We find that under some conditions transient rectification can be several times larger than steady-state rectification. Further, both the thermal diffusivity of the system and the temperature-dependent thermal conductivity or thermal capacitance play an important role in affecting the transient rectifying behavior of the system, with the nonlinearity of the system leading to unusual behavior where rectification is maximized.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Schematic of analytical domain studied in this problem. j+(x,t) and j−(x,t) denote the heat flux under forward and backward temperature biases, respectively. TH and TC indicate the temperatures of the hot and cold boundaries.

Grahic Jump Location
Fig. 2

(a) Typical time evolution of the heat fluxes (solid and dashed, left axis) at the cold boundaries and the subsequent rectification factor (solid, right axis). The temperature-dependent thermal conductivity parameter for material 1 is ε1=0.1, and the uniform thermal diffusivity is the same for both materials (α2¯/α1¯=1). (b) Identification of important parameters for rectification quantification on a plot of rectification factor as a function of time. The maximum rectification Rmax occurs at time t*=t1, and steady-state rectification RSS occurs for times t*>t2. The region highlighted is the area under the rectification curve defined as R̃ in Eq. (7).

Grahic Jump Location
Fig. 3

Transient response of the rectification factor for varying values of α¯1(1+ε1)/α¯2. (a) κ2¯/κ1¯=0.001, (b) κ2¯/κ1¯=1, and (c) κ2¯/κ1¯=1000. For all cases, the nonlinear thermal conductivity parameter in material 1 is fixed (ε1=0.1).

Grahic Jump Location
Fig. 4

(a) Maximum rectification factor as a function of the ratios of thermal diffusivities, α¯1(1+ε1)/α¯2. (b) Ratio of maximum rectification value relative to the steady-state value as a function of the ratios of thermal diffusivities, α¯1(1+ε1)/α¯2. For all cases, the nonlinear thermal conductivity parameter in material 1 is fixed (ε1=0.1).

Grahic Jump Location
Fig. 5

Time-integrated rectification factor R̃ as a function of the ratios of thermal diffusivities, α¯1(1+ε1)/α¯2. For all cases, the nonlinear thermal conductivity parameter in material 1 is fixed (ε1=0.1).

Grahic Jump Location
Fig. 6

(a) Maximum rectification factor Rmax as a function of the nonlinear factor ε1. (b) Ratio of maximum value relative to the steady-state value Rmax/RSS as a function of the nonlinear factor ε1

Grahic Jump Location
Fig. 7

Typical time evolution of the heat fluxes (solid and dashed, left axis) at the cold boundaries and the subsequent rectification factor (black, right axis). The uniform thermal diffusivity is the same for both materials (α¯2/α¯1=1). The temperature-dependent thermal conductivity parameter (εi) is nonzero in at least one of the materials: (a) ε1=−0.7, ε2=0, (b) ε1=0.35, ε2=−0.35, and (c) ε1=0.7, ε2=0.

Grahic Jump Location
Fig. 8

Typical time evolution of the heat fluxes (solid and dashed, left axis) at the cold boundaries and the subsequent rectification factor (black, right axis). The uniform thermal diffusivity is the same for both materials (α¯2/α¯1=1). The temperature-dependent specific heat parameter (λi) is nonzero in at least one of the materials: (a) λ1=−0.7, λ2=0, (b) λ1=0.35, λ2=−0.35, and (c) λ1=0.7, λ2=0.

Grahic Jump Location
Fig. 9

(a) Maximum rectification factor Rmax as a function of the absolute value of the difference of temperature-dependent thermal conductivity parameters |ε1−ε2|. (b) Maximum rectification factor Rmax as a function of the absolute value of the difference of temperature-dependent thermal conductivity parameters |λ1−λ2|. For all cases ((a) and (b)), the uniform thermal diffusivity is the same for both materials (α¯2/α¯1=1).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In