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Research Papers: Forced Convection

# Numerical and Experimental Investigation of Laminar Channel Flow With a Transparent Wall

[+] Author and Article Information
Jing He1

Department of Mechanical Science and Engineering, University of Illinois, 1206 West Green Street, Urbana, IL 61801jinghe2@illinois.edu

Liping Liu

Department of Mechanical Engineering, Lawrence Technological University, 21000 West Ten Mile Road, Southfield, MI 48075

Anthony M. Jacobi

Department of Mechanical Science and Engineering, University of Illinois, 1206 West Green Street, Urbana, IL 61801

Inclusion of the extended section in the computational domain caused marginal differences in the immediate vicinity of the end of the heated section yet increased the computational expense drastically; thus it was not considered in the simulation and not shown in Fig. 5.

1

Corresponding author.

J. Heat Transfer 133(6), 061701 (Mar 09, 2011) (9 pages) doi:10.1115/1.4003547 History: Received June 05, 2010; Revised January 10, 2011; Published March 09, 2011; Online March 09, 2011

## Abstract

A numerical and experimental investigation is undertaken for developing laminar flow in a duct with one opaque, uniformly heated wall and one transparent wall. In the numerical model, mixed convection, radiative exchange, as well as two-dimensional conduction in the substrate are considered. Experiments are conducted in a high-aspect-ratio rectangular channel using infrared thermography to validate the numerical model and visualize the temperature field on a heated surface. An extended parametric study using the validated model is also carried out to assess the impact of channel height, and thermal conductivity and thickness of the substrate. For a channel height of $H=6 mm$ and a heating power of $qs=257 W/m2$, as Re increases from 150 to 940 the fraction of heat transfer by convection from the heated surface rises from 65% to 79%. At $Re=150$, as $H$ increases from 6 mm to 25 mm, radiation from the heated surface increases from 35% to 70% of the total heating power. The influence of substrate conductivity and thickness on local flux distributions is limited to regions near the channel inlet and outlet. Over the entire parametric space considered, radiation loss from the interior duct surfaces to the inlet and outlet apertures is less than 2% of the total heat input and thus unimportant.

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## Figures

Figure 1

Schematic of parallel-plate channel

Figure 2

Radiative exchange in an enclosure with a transparent wall

Figure 3

Comparison between the present model and prior work in treatment of conjugate heat transfer: (a) interface temperature distribution at various thermal conductivity ratios for a conjugate convection and conduction problem (see Fig. 3 in Ref. 9); (b) normalized convective flux distribution on both channel walls for a conjugate convection and radiation problem (see Fig. 6 in Ref. 8)

Figure 4

Schematic of the wind tunnel: (1) inlet, (2) flow conditioning, (3) contraction, (4) test section, (5) diffuser, (6) blower, (7) exit plenum, and (8) discharge to outside of laboratory (adopted from Ref. 16, with modification)

Figure 5

Diagram of the test section; all dimensions in millimeters

Figure 6

(a) 2D thermal images for the steady-state temperature distribution at Re=150 (top) and Re=940 (bottom); (b) 3D temperature graph at Re=150

Figure 7

Comparison of the span-averaged temperature distribution on the heated surface between the experimental and numerical results

Figure 8

Streamline plot at Re=150

Figure 9

Normalized temperature field, θ/θ0, at (a) Re=150, (b) Re=340, (c) Re=570, and (d) Re=940. The black line in the graph represents the fluid-solid interface.

Figure 10

Components in energy dissipation: E1—ratio of heat advected away by the airflow, E2—ratio of heat radiated from the exterior surface of the transparent sheet, E3—ratio of heat transferred via natural convection, and E4—ratio of radiation loss from the interior surfaces of the channel

Figure 11

Distributions of normalized convective, conductive, and radiative fluxes along the heated surface at varying channel height

Figure 12

Interface temperature distribution at varying thermal conductivity ratios

Figure 13

Distributions of normalized convective, conductive, and radiative fluxes along the heated surface at varying thermal conductivity ratios

## Errata

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