Answer:
NL = 207
Explanation:
Solution
Now,
The mean temperature is measured as:
Tm = (T₁ - T₀)/2
= (15 + 65)/2
= 40°C
So,
we find all the thermo-physical properties of water from the table, that is properties of saturated water at T =40°C
Thermo conductivity, k = 0.631 W/m . K
Specific heat Cp = 4179 J/kg . K
Density р = 992. 1 kg/m³
The dynamic viscosity, μ = 0.653 * 10 ^⁻3 kg/m *s
Prandtl number, Pr = 4.32
At T = 15°C
рi = 992.1 kg/m³
At T = 90°C
Prandtl number, Prs = 1.96
Thus,
The maximum flow of velocity is known from the equation stated as:
Vmax = ST/ST - D *V
Here,
ST is refereed to as the transverse pitch for inline arrangements of the rods
so,
Vmax = 3/3-1 * 0.8
= 1.2 m/s
Now
The Reynolds number is determined from the equation given below
ReD =ρVmax D/μ
= 922.1 * 1.2 *(1 *10^⁻²)/ 0.653 * 10^⁻³
= 18231.55
From the table, The Nusselt number correlations fro cross flow over the tube banks for inline arrangement over the range of ReD is shown as
1000 - 2 * 10⁵
Now, the Nusselt number is determined by
NuD = 0.27ReD ^0.63 Pr^ 0.36 (Pr/Prs)^0.25
= 0.27 * (18231.55)^0.63 (4.32)^0.36 * (4.32/1.96)^0.25
=269.32
Then,
The convective transfer of heat water coefficient is determined from the equation shown by Diametral Nusselt Number
NuD =hD/k
So,
we re-write and solve for h
h = NuD * k/D
=269.32 * 0.631/(1 * 10 ^⁻2)
=16993.9 W/m² .K
Now,
The heat transfer surface area for a tube in a row is NT = 1
As = NT NLπDL
= 1*NL* π * (1 * 10^⁻2) * 4
= 0.1257NL
The logarithmic mean temperature of water is represented as
ΔTlm = Te - Ti/ln (Ts - Ti/Ts- Te)
= 65- 15/ln (90 -15/ 90 -65) = 45.51°C
Thus,
The rate of the heat transfer is determined from the equation shown below,
Q =hAsΔTlm
=16993.9 *0.1257 * NL* 45.51.......equation (1)
The mas flow rate of water is determined by the equation below
m =ρiAcV
= ρi * (STL) * V
= 999.1 8 ( 3* 10^⁻2 * 4) * 0.8
= 95.91 kg/s
The rate of heat transfer of water is determined by the equation below
Q = mcp (Te- Ti)
= 95.91 * 4179 * (65-15)
=20041146.72 W..........(Equation 2)
Now,
The number of tube rows in the direction flow is determined by measuring both equations 1 and 2 as
97219.61 NL = 20041146.72
NL =206.14
NL = 207
Therefore, the number of tube rows NL in the flow direction needed to achieve the indicated temperature rise is NL = 207
=
