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Sample_Calculation2(use_this)

# Sample_Calculation2(use_this) - 1 FREE CONVECTION SAMPLE...

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1. FREE CONVECTION SAMPLE CALCULATION (5V) Before we start the calculations, below are lists of constants that will be useful in the calculation of the results; Constants Acceleration due to gravity (g) = 9.81 ms -2 Heating Element Diameter (D) = 0.01 m Heated Area (A s ) = 0.0022 m 2 Stefan Boltzmann Constant (σ) = 5.67 x 10 -8 Wm -2 K 4 Voltage (V) Current (I) Q total (W) Q rad (W) Q conv (W) Q unaccounted (W) T 9 (K) T 10 (K) T mean (K) . - k 10 3 (W/m.K) Morgan Morgan 5 0.82 4.10 1.226 8 1.755 1.119 293.05 362.15 327.60 28.34 8 1.30 10.40 3.466 4.054 2.880 293.45 433.15 363.30 31.01 10 1.62 16.20 6.040 5.947 4.213 293.65 486.15 389.90 33.03 12 1.93 23.16 9.533 7.899 5.728 293.75 538.15 415.95 34.92 15 2.41 36.15 18.48 3 11.421 6.246 294.45 628.15 461.30 49.35 Emissivity (ε) ≈ 1 . - β 10 3 (K -1 ) . - α 10 6 (m 2 /s) . - υ 10 6 (m 2 /s) Nu h (Wm 2 / K) Ra Morgan Morgan 3.053 26.58 18.67 4.074 11.546 4168.9 2.753 32.13 22.38 4.254 13.190 5246.1 2.565 36.60 25.30 4.251 14.042 5230.3 2.404 41.14 28.32 4.207 14.691 4947.4 2.168 49.35 33.92 4.087 15.557 4239.6

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The values of Kinematic Viscosity ( υ ), Thermal Diffusivity (α) and Thermal Conductivity (k) of air has to be interpolated from Table A.4 of Fundamentals Heat and Mass Transfer Textbook (6 th Ed) by Incropera. Kinematic Viscosity of air at 5 volts ( . - - ) 327 60 300 350 300 = ( . . . ) ν5v 15 89 20 92 15 89 = . × - / ν5v 18 67 10 6 m2 s Thermal Diffusivity of air at 5 volts ( . - - ) 327 60 300 350 300 = ( α5v . . 22 50 29 90 . ) 22 50 = α5v . × - 26 58 10 6 / m2 s Thermal Conductivity of air at 5 volts ( . - - ) 327 60 300 350 300 = ( k5v . . 26 30 30 00 . ) 26 30 = k5v . × - 28 34 10 3 / . W m K = × Qtotal Voltage Current = × . 5 0 82 = . 4 10W = Qrad εσAs - T104 T94 = . × - ( . ) 15 67 10 8 0 0022 . - . 362 154 293 054
= . 1 226W = + Tmean T10 T92 = . + . 362 15 293 052 = . 327 60K = β 1Tmean = . 1327 60 = . × - - 3 053 10 3K 1 Q loss Calculations (using Morgan’s Correlation) ( )= - Rayleigh Number RaD gβT10 T9D3να = . ( . × - 9 81 3 053 10 ) . - . ( . ) 3 362 15 293 05 0 01 3 . × - 18 67 10 6 ( . × - ) 26 58 10 6 . 4168 9 According to Table 9.1, since our Ra D number is between 10 2 and 10 8 , we apply the Morgan Correlation with C=0.850 and n=0.188. ( )= = . ( . . ) Nusselt Number NuD CRaDn 0 85 4168 90 188 = . 4 0 74 Nusselt Number can also be expressed in the form of; ( )= × Nusselt Number NuD h Dk = . ×( . × - ) . = . / h 4 074 28 34 10 3 0 01 11 546 Wm2 K = Qconv hAs - = . × . × . - . T10 T9 11 546 0 0022 362 15 327 60 = . 1 755W

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= Qtotal + + Qrad Qconv Qunaccounted = . - . - . = . Qunaccounted 4 10 1 755 1 226 1 119W
V o l t a g e ( V ) C u r r e n t ( I ) Q ( Q ( Q conv (W) Q unaccounted (W) T 9 (K) T 10 (K) Hil C h u r c h i l l Z a k a u k a s Hil C h u r c h i l l Z a k a u k a s 5 0 .

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Sample_Calculation2(use_this) - 1 FREE CONVECTION SAMPLE...

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