Question

One side of a plane wall is held at 200°C while the other side is exposed to a convective environment having T10°C and h 100 W/m2 °C. The wall has a k - 2.6 W/m °C and is 30 cm thick. Calculate the heat flux through the wall. What is the temperature on the surface of the cold side of the wall? (Remember this problem!! wll come up frequently later in the course.)

Answer 1

Answer:

$\frac{\dot Q}{A} = 151.33 W/m^2$

$T_c = 25.153°C$

Explanation:

Given data:

one side wall temperature 200°C

other side wall temperature 10°C

h = 100 W/m^2 °C

k = 2.6W/m °C

wall thickness L = 30 cm

we know that heat flux is given as

$\frac{\dot Q}{A} = \frac{ T_A - T\infty}{\frac{L}{K} + \frac{1}{h}}$

$\frac{\dot Q}{A} = \frac{ 20- 10} {\frac{0.30}{2.6} + \frac{1}{100}}$

$\frac{\dot Q}{A} = 151.33 W/m^2$

$1515.33 W/m^2 = \frac{ T_A - T_c}{\frac{L}{K}}$

solving for temperature for cold surface is given as

$T_c = -1515.33 \times \frac{0.3}{2.6} + 200$

$T_c = 25.153°C$