GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

Question : 54 of 65

Marks: +1, -0

0.2 {m}

thick infinite black plate having a thermal conductivity of

3.96 {W} {/} {m}- {K}

is exposed to two infinite black surfaces at

300 {K}

and

400 {K}

as shown in the figure. At steady state, the surface temperature of the plate facing the cold side is

350 {K}

. The value of Stefan-Boltzmann constant,

σ

, is

5.67 × 10^{-9} {W}{/} {m}^{2} {K}^{4} .

Assuming 1-D heat conduction, the magnitude of heat flux through the plate (in

{w} {/} {m}^{2})

is_______(correct to two decimal places).

Your Answer:

Validate

Solution:

Since there is steady state, the heat transfer between plate and surface is equal to heat transfer between the two surfaces, which is equal to heat transferred through the plate.
Heat flux between plate and surface,

q{''}=\;{σ ×(350^{4}-300^{4})}/{{1}/{E_{1}}+\;{1}/{E_{2}}-1}

∊_{1}=∊_{2}=1

, Surfaces are black

q''=391.612 {W} {/} {m}^{2}

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