Title: Radiative heat transfer in FLiBe molten salt participating medium in a vertical heated tube under forced and mixed convection laminar flows

Abstract

The contribution of radiative heat transfer (RHT) to convective heat transfer in a heated vertical pipe with laminar flow and constant wall temperature, for FLiBe molten salt, is investigated computationally. The combined effects of conduction in the fluid, forced convection, buoyancy, temperature-dependent physical properties, and thermal radiation are investigated. The P1 approximation is employed in the discretization of the Radiative Transfer Equation (RTE). The COMSOL Multiphysics software is used to generate the numerical solutions. The theoretical analysis developed here demonstrates that only for intermediate values of the optical thickness, i.e. ${\mathrm{\tau }}_{\text{D}}~\mathcal{O}\left(1\right),$ the participating media effects are expected to be important. This analysis is confirmed computationally and a value of ${\mathrm{\tau }}_{\text{D}}\approx 4$ is shown to lead to the highest increase in overall heat transfer behavior. Under forced convection, the Nusselt ratio $\text{N}{\text{u}}_{\text{total}}/\text{N}{\text{u}}_{\text{no}-\text{rad}}$ reaches a peak value of $1.76$ at ${\mathrm{\tau }}_{\text{D}}=4$ and $\mathrm{z/D}=200$, and is less than $1.1$ for ${\mathrm{\tau }}_{\text{D}}<0.1\text{and}{\mathrm{\tau }}_{\text{D}}>60$. Under aiding-flow mixed convection, $\text{N}{\text{u}}_{\text{total}}/\text{N}{\text{u}}_{\text{no}-\text{rad}}$ reaches a peak of $1.34$ at ${\mathrm{\tau }}_{\text{D}}=4.2$ and is less than $1.1$ for ${\mathrm{\tau }}_{\text{D}}<0.4\text{and}{\mathrm{\tau }}_{\text{D}}>36$. Under opposing-flow mixed convection, ${\text{Nu}}_{\text{total}}/{\text{Nu}}_{\text{no}-\text{rad}}$ reaches a peak of $1.81$ at ${\mathrm{\tau }}_{\text{D}}=4.2$ and is less than 1.1 for ${\mathrm{\tau }}_{\text{D}}<0.2\text{and}{\mathrm{\tau }}_{\text{D}}>50$. RHT effects on the overall heat transfer are most pronounced in opposing mixed convection, where $\text{N}{\text{u}}_{\text{total}}/\text{N}{\text{u}}_{\text{no}-\text{rad}}$ is $2.26$ observed at $\mathrm{z/D}=50.$ The sensitivity to wall emissivity is evaluated; in forced convection, the peak $\text{N}{\text{u}}_{\text{total}}/\text{N}{\text{u}}_{\text{no}-\text{rad}}$ is $1.66$ at ε = 0 (reflective wall) and $2.04$ at ε $=1$ (absorptive wall). Finally, the sensitivity to pipe diameter is also discussed. Overall, for a vertical heated tube, radiative heat transfer effects lead to enhancement of heat transfer by as high as a factor of two, and they depend on the optical thickness of the flow, mixed convection environment ( $\text{Gr}/\text{R}{\text{e}}^2$ and direction of flow relative to the gravitational force), surface emissivity, and entrance effects.

Authors:

Abou Dbai, Mohamed ^[1]; Scarlat, Raluca O. ^[2]; Trujillo, Mario F.  ^[1]

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+ Show Author Affiliations

1. Univ. of Wisconsin, Madison, WI (United States). Dept. of Mechanical Engineering
2. Univ. of California (United States). Dept. of Nuclear Engineering

Publication Date:

Thu Sep 17 00:00:00 EDT 2020

Research Org.:

Univ. of Wisconsin, Madison, WI (United States)

Sponsoring Org.:

USDOE Office of Nuclear Energy (NE), Nuclear Energy University Program (NEUP); USDOE

OSTI Identifier:

1850528

Alternate Identifier(s):

OSTI ID: 1810958

Grant/Contract Number:  

NE0008680

Resource Type:

Accepted Manuscript

Journal Name:

Nuclear Engineering and Design

Additional Journal Information:

Journal Volume: 368; Journal Issue: C; Journal ID: ISSN 0029-5493

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Nuclear Science & Technology; Radiative heat transfer; FLiBe; Molten salt; Mixed convection; Participating media; Optical thickness