Question

An electrical device is insulated on all sides except one face. That face is bonded to a 4mm thick aluminum plate which is cooled by air. The electrical device dissipates 10^4 W m2 The resistance of the joint between the device and aluminum plate is 0.5E-4 m2K W The conductivity of the aluminum is 238 W mK The temperature of the air is 278 K and the convection coefficient from the aluminum plate to the air is 100 W m2K What is the operating temperature of the device

Answer 1

Answer:

t₁ = 378.668 K

Explanation:

From the given information:

The heat dissipated (q) from the electrical device = $10^4 W/m^2$

The contact resistance between device and aluminium;

(R_{const} ) = 0.5× 10⁻⁴ m² K/W

Conductivity of aluminum (k)  = 238 \ W/mK

The thickness of aluminum plate (L) = 0.004 m

Convection coefficient (h) = 100 \ W/m^2 K

Surrounding temperature (t_2) = 278 \ k

According to Fourier's law of heat conduction.

$q = \dfrac { t_1- t_2 }{R_{const} + \dfrac{L}{k} + \dfrac{1}{h} }$

$10^4 = \dfrac{t_1 - 278}{0.5 \times 10^{-4} + \dfrac{0.004}{238} + \dfrac{1}{100} }$

$10^4 *( 0.5 \times 10^{-4} + \dfrac{0.004}{238} + \dfrac{1}{100}) = t_1 - 278$

$100.668 = t_1 -278$

t₁ = 378.668 K