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

t₁ = 378.668 K

Step-by-step 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 = \frac { t_1- t_2 }{R_(const) + (L)/(k) + (1)/(h) }`

`10^4 = (t_1 - 278)/(0.5 * 10^(-4) + (0.004)/(238) + (1)/(100) )`

`10^4 *( 0.5 * 10^(-4) + (0.004)/(238) + (1)/(100)) = t_1 - 278`

`100.668 = t_1 -278`

t₁ = 378.668 K