Question

there is a plate with 2ft width, 4ft length and 130°F of the surface temperature. awater with 50°F of temperature flows on this plate with 9ft/s velocity. Calculate the average heat transfer coefficient and the convective heat loss in this plate. For the calculation please use the following constant properties.
heat conductivity(k)=0.36 Btu/(hr ft °F)
viscosity=5.14×10^(-4) lbm/(ft s)
density=62.11 lbm/(ft^(3))
Pr=5.12
Nu=0.036×Pr^(1/3)×Re^(2/3):laminar flow
Nu=0.036×Pr^(1/3)×(Re^(0.8)-23200):turbulent flow

Answer 1

Given

Width of plate d = 2ft

Length of plate L = 4ft

Surface temperature T1 =130°F

Water flows temperature T2 = 50°F

dT = T1 - T2 = 130 - 50 = 80°F

velocity of flow v = 9ft/s

heat conductivity(k) = 0.36 Btu/(hr ft °F)

convective heat loss in this plate dQ = hcAdT = ?

Renolds number Re = vL/ = 62.11x9x4/5.14×10^(-4) = 435x10^(4) > 4000, the flow is turbulent

Nu=0.036×5.12^(1/3)×(4350000^(0.8) - 23200) = - 10508 for turbulent flow

i) Average (convective) heat transfer coefficient - h_c = Nuk/L = 10508x0.36/4 = 945.75 Btu/(ft² h ^oF)

ii) the convective heat loss in this plate Q = h_c AdT = 945.75 x 4x2x80 = 605282 Btu/(ft² - ^oF)