Compute the heat flux thoroughly a 10 cm thick brick wall (k= 0.69 W/m-deg) Which has temperature of 105° C & 10° C maintained on its two faces. How this heat flux would vary when 3cm thick layers of magnesia insulation is added on the inside & outside faces of the wall?
Also determine the interface temperature for the composite wall.
Please help. its very urgentW
To compute the heat flux through a brick wall, we can use Fourier's Law of Heat Conduction. The equation for heat flux is:
q = (k * ΔT) / L
Where:
q is the heat flux (in W/m^2)
k is the thermal conductivity of the material (in W/m-deg)
ΔT is the temperature difference across the wall (in deg C)
L is the thickness of the wall (in meters)
Given:
k = 0.69 W/m-deg
ΔT = 105° C - 10° C = 95° C
L = 10 cm = 0.1 m
Plugging in the values into the formula, we have:
q = (0.69 * 95) / 0.1
q = 655.5 W/m^2
So, the heat flux through the 10 cm thick brick wall is 655.5 W/m^2.
Now, let's calculate the heat flux when 3 cm thick layers of magnesia insulation are added on the inside and outside faces of the wall.
Since the layers are added on both sides, the total thickness of the wall will now be:
L_total = L + 2 * layer thickness
L_total = 0.1 m + 2 * 0.03 m
L_total = 0.1 m + 0.06 m
L_total = 0.16 m
The temperature difference across the wall remains the same (95° C).
Plugging in the new values into the formula:
q_total = (0.69 * 95) / 0.16
q_total = 410.625 W/m^2
So, the heat flux through the composite wall with 3 cm thick magnesia insulation layers added on both sides is 410.625 W/m^2.
To determine the interface temperature for the composite wall, we can use the formula:
ΔT = q * L_total / k
Rearranging the formula to solve for ΔT:
ΔT = q_total * L_total / k
Plugging in the values:
ΔT = 410.625 * 0.16 / 0.69
ΔT = 95° C
Therefore, the interface temperature for the composite wall is 95° C.
To compute the heat flux through a brick wall, we can use the formula:
Q = (k * A * ΔT) / d
where:
Q is the heat flux (heat transfer rate per unit area),
k is the thermal conductivity of the material (0.69 W/m·°C for the brick),
A is the area of the wall perpendicular to the heat flow,
ΔT is the temperature difference across the wall, and
d is the thickness of the wall.
Before adding insulation layers, let's calculate the heat flux for the brick wall without insulation.
Given:
k = 0.69 W/m·°C,
ΔT = (105 - 10) = 95°C (temperature difference),
d = 10 cm = 0.1 m (wall thickness).
We need to convert the thickness to meters since thermal conductivity is given in W/m·°C. Substituting these values into the formula:
Q = (0.69 * A * 95) / 0.1
To determine the heat flux for the brick wall, we need to know the area of the wall. Assuming it is a rectangular wall, the area can be calculated by multiplying the length and height of the wall (A = length * height).
Now let's calculate the heat flux with the addition of 3cm thick layers of magnesia insulation on both faces of the wall.
Given:
Insulation thickness = 3 cm = 0.03 m.
We need to recalculate the thickness of the wall, taking into account the added insulation layers:
Total wall thickness = d + 2 * insulation thickness
= 0.1 + 2 * 0.03
= 0.16 m.
Substituting this new wall thickness into the formula, along with the other given values:
Q' = (0.69 * A * 95) / 0.16
The heat flux, Q', with insulation layers will be different from the heat flux, Q, without insulation layers.
To determine the interface temperature for the composite wall, we need to consider the heat conduction across the wall and the insulation layers. The interface temperature is the temperature at the boundary between the brick and insulation layers.
To calculate the interface temperature, we need to assume that there is no heat transfer through the insulation layers. This assumption is valid if the insulation has a low thermal conductivity compared to the brick.
We can use the formula:
ΔT_interface = Q * (d / (k_insulation * A))
where:
ΔT_interface is the temperature difference across the insulation layers,
Q is the heat flux through the brick wall (from the previous calculation),
d is the thickness of the brick wall (excluding the insulation layers),
k_insulation is the thermal conductivity of the insulation material, and
A is the area of the wall perpendicular to the heat flow.
By substituting the known values into the formula, we can calculate the interface temperature.