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# Answer to Question #163371 in Electrical Engineering for Mital sosa

Question #163371

1.      Consider a square plate of 0.5 m x 0.5 m in a room at 30 C. One side of the plate is kept at a uniform temperature of 74 C while the other side is insulated. Determine the rate of heat transfer from the plate by free convection under the following three situations: (i) The plate is kept vertical (ii) The plate is kept horizontal with hot surface facing up (iii) The plate is kept horizontal with hot surface facing down.

1
2021-02-16T07:29:26-0500

The properties of air at the film temperature of

"T_f = \\large\\frac{(T_s + T_{\\infin})}{2}" = "\\large\\frac{30+74}{2}" = "52^oC \\space" and 1 atm here

"k= 0.02808 W\/m ^o C"

"P_r= 0.7202"

"\\nu = 1.896*10^{-5} \\frac{m^2}{s}"

"\\beta = \\large\\frac{1}{T_f}" "=\\large\\frac{1}{333K}"

(a) Vertical. The characteristic length in this case is the height of the plate, which is L = 0.5m. The Rayleigh number is

"Ra_D = \\large\\frac{g\\beta (T_s - T_{\\infin})L^3}{V^2}""Pr = \\large\\frac{9.81*\\frac{1}{333}(74-30)*0.5^3}{(1.896*10^{-5})^2}""(0.722) = 3.254*10^{8}"

The natural convection Nusselt number

"Nu = \\lbrace 0.825 + \\large\\frac{0.387Ra_D^{\\frac{1}{6}}}{\\lbrack1+(\\frac{0.492}{Pr})^{\\frac9{16}}\\rbrack^{\\frac{8}{27}}} \\rbrace^2" "=\\lbrace 0.825 + \\large\\frac{0.387(3.254*10^{8})^{\\frac{1}{6}}}{\\lbrack1+(\\frac{0.492}{0.7202})^{\\frac9{16}}\\rbrack^{\\frac{8}{27}}} \\rbrace ^2" "=" 102.6

"h = \\frac{k}{D}Nu = \\frac{0.02808 W\/m ^oC}{0.5m}(102.6) = 5.76 \\frac{W}{m} C"

"A_s = L^2 = (0.5m)^2 = 0.25m^2"

and

"Q = hA_s(T_s - T_{\\infin}) = (5.76 \\frac{W}{m} C)(0.25m^2)(74-30)^oC = 63.36W"

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