Answer:
a = 40
b = 29
Explanation:
Give a place holder for the numbers that we don't know.
Lets call the two numbers a and b.
From the given info, we can write an expression and solve it:
"one number is 11 more than another number"
a = 11 + b
from this, we know that a > b.
''three times the larger number exceeds four times the smaller number by 4"
3a = 4b + 4
Now we have 2 equations, we can use them to solve using whatever method you want.
a = 11 + b
3a = 4b + 4
I will be using matrices RREF to solve for this.
a - b = 11
3a - 4b = 4
[tex]\begin{bmatrix}1 & -1 & 11\\3 & -4 & 4 \end{bmatrix}[/tex]
[tex]\begin{bmatrix}1 & 0 & 40\\0 & 1 & 29 \end{bmatrix}[/tex]
a = 40
b = 29
A horizontal poly crystalline solar panel module has to be investigated by natural cooling. For crystal silicon, the thermal coefficient approximately 0.0045/K is used. Investigate the effect of air velocity on the cooling performance of PV panels at 0-5 m/s air velocities, 25-40 ºC ambient temperatures, and 400-1000 W/ m2 solar radiation
Solution :
It is given that :
Thermal coefficient = 0.0045/K
Ambient temperature, [tex]$T_a = 25 - 40^\circ$[/tex]
air velocity, v = 0-5 m/s
Solar radiation, [tex]$G= 400-100 \ W/m^2$[/tex]
[tex]$P=50 \ W$[/tex]
Model calculations :
Cell temperature ([tex]$T_c$[/tex])
[tex]$T_c = T_a + \left(\frac{0.25}{5.7+3.8 \ v_w}\right) G$[/tex]
where [tex]$ v_w - v_a = $[/tex] wind speed / air speed
∴ [tex]$T_c = 2 \pi + \left(\frac{0.25}{5.7+3.8 \times 1}\right) \times 400$[/tex]
[tex]$T_c = 35.526 ^\circ$[/tex]
[tex]$\Delta T = T_c -25$[/tex]
= 35.526 - 25
= 10.526 K
Thermal coefficient = 0.0045 x 10.526
= 0.04737
Pv power = [tex]$(1 -C_T) \times P \times \frac{G}{1000}$[/tex]
[tex]$=(1 -0.04737) \times 50 \times \frac{400}{1000}$[/tex]
= 17.0526 W