Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: 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.

Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: (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).

Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: 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).

Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: (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).

Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: 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).

Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: (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

Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: 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.

Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: 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.

Date of download: 11/12/2017 Copyright © ASME. All rights reserved. From: Thermal Rectification Under Transient Conditions: The Role of Thermal Capacitance and Thermal Conductivity J. Heat Transfer. 2017;139(9):091301-091301-8. doi:10.1115/1.4036339 Figure Legend: (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).