A flat plate is subjected to a H2 flow parallel to it surface. The plate dimensi

Question

A flat plate is subjected to a H2 flow parallel to it surface. The plate dimension is 2 m times 2 m and suspended in a tunnel. The plate has a constant surface temperature 500 degree C. The free steam temperature and velocity H2 are 300 degree C and 50 m/s, respectively. Decide Total rate heat transfer from the plate to the H2 stream by forced convection. Convection heat transfer coefficient at middle point hx of the plate and corresponding velocity boundary layer thickness delta X, and thermal boundary layer thickness delta t respectively. Air is approaching a tube bank in the normal direction at 293 k @ 1 atm with a average velocity 312 m/min. The bank is 300 cm long and tube outside diameter is 16 mm. The tubes are staggered in arrangement with longitudinal and transverse pitches 40mm, respectively. Inside the tubes, steam is condensing at 373 k. There are 10 tubes in each row and total 20 rows. Find

Explanation / Answer

1)

a)

We evaluate properties at mean temperature Tf = (500 + 300)/2 = 400 deg C

Prandt No. Pr = 0.66,

Density rho = 0.03492 kg/m^3

Viscosity mu = 15.89*10^-6 kg/(m-s)

Sp. heat Cp = 14574 J/kg-K

Kinematic viscosity neu = 455.1*10^-6 m^2 /s

Thermal conductivity k = 6.903 W/m-K

Reynolds no. at trailing edge Re_l = UL/neu = 50*2 / 455.1*10^-6 = 219732

So the flow ought to be laminar til the traiing edge.

Nusselt no. is then Nu_l = 0.664*Re_l^0.5 *Pr^0.33 = 271.4

and mean h = Nu_l *k/L = 271.4*6.903 / 2 = 936.6 W/m^2 - K

Total heat flux is then q = h*A*delta T = 936.6*(2*2)*(500 - 300) = 749311 W = 749.311 kW

b)

At middle point, x = 0.5*2 = 1 m

Re_x = U*x / neu = 50*1 / 455.1*10^-6 = 109866

Nu_x = 0.332*Re_x^0.5 *Pr^0.33

Nu_x = 0.332*109866^0.5 *0.66^0.33 = 95.94

Nu_x = h_x *x/k

95.94 = h_x *1 / 6.903

Heat transfer coeff at mid-point h_x = 662.3 W/m^2 -K

Boundary layer thickness, delta = 4.92*x/ Re_x^0.5

delta = 4.92*1 / 109866^0.5 = 0.0148 m = 14.8 mm

Thermal boundary layer thickness, delta_t = delta*Pr^-0.33

delta_t = 14.8*0.66^-0.33 = 16.975 mm

PLEASE RATE 5-STARS....THANKS.

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