Water at temperature T infinity = 20 [ degree C] flows along a wall held at temp

Question

Water at temperature T infinity = 20 [ degree C] flows along a wall held at temperature Tw = 47 [ degree C]. At a particular location along the wall the temperature distribution in the water is carefully measured as a function of y, where y is the distance along a line normal to the wall measured in [m] (y = 0 on the wall and y > 0 in the fluid). This temperature distribution is described by the following relation T-Ts / T infinity - Ts = 1 - e-m, a = 390.6 [1/m] Find the local heat transfer coefficient at this location; Find the rate of heat loss from the wall to the water For the wall made of brick (density rho = 3010 [kg/m3], conductivity k = 2.3 [W/m degree K], specific hat c = 838 [J/kg degree K]) temperature gradient in [ degree C/m) in the wall right at the surface.

Explanation / Answer

h/k = (d(T-Ts)/dy) /(Tambinet-Ts) at y=0: h/k = a*e^(0*a) = a = 390.6 h-> local heat transfer coefficient. k-> conductivity. h = k*a = 2.3*390.6 W/K = 898.38 W/m^2K(Ans) Q = h*A*(Tambinet-Ts) Q/A = 898.38 * (47-20) W/m2 = 24.256 kW/m2 (Ans)

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