Answer:
the percentage difference is E = = 55.7% respect to the real value ( with resistance of the wall)
Explanation:
the resistance to heat flow R is
R= ( 1/h₁ + ln (re/ri)/(2π*k*L) + 1/h₂)
where
h₁= heat transfer coefficient for the hot fluid = 1600 W/m²K
h₂= heat transfer coefficient for the cold fluid = 1800 W/m²K
re/ri = ratio between external radius and internal radius of the pipe = 2.375 /2.067 for 2"" Sch 40 stainless steel
k= thermal conductivity = k = 14.9 W/m-K
L = length of the pipe = 1 ( unit length)
therefore replacing values
R₁= 1/h₁ + ln (re/ri)/(2π*k*L) + 1/h₂ = 1/1600 W/m²K + ln(2.375 /2.067)/(2π*14.9 W/m-K*1) + 1/1800 W/m²K = 2.664 *10⁻³m²K/W
when the resistance of the pipe wall is neglected then R would be
R₂= 1/h₁ + 1/h₂ = 1/1600 W/m²K 1+ 1/1800 W/m²K =1.180 *10⁻³ m²K/W
the percentage difference between the total resistance with and without the pipe wall resistance per unit length is
E = 1-(R₂/L) /( R₁/L) = 1- R₂/R₁=1- (1.180 *10⁻³/2.664 *10⁻³) = 0.557= 55.7%
E = = 55.7%
