Question

ice-water bath at o°C. There exist electrical resistance a heat power of 5 MW/m3 in the that Transfer @ Wais at 55C with a by 2cm square 100°C flow rate of 0.01 1g/s exters a duct in cross-section whose walls are maintained at a uniform temperature byeko dynamically developer flow. Determined the duct legfel required to heat the water to 70°C. ③ A two centimeter in diameter rood with a length of to an is grinded by grinder. During grinding, 20% of the power of the grinder dissipates into frictional heat at the time of grinding power is 1kw.instantly. Determine the temperature of the grinded surface and ur face at the end, if the free stream temperature is 20°C, combined-convective-radiation heat transfer coefficient s 10 v/m²K, and thermal conductivity (k) so X/m2K. CA square cross-sectional rod whose thermal conductivity is too tu / nk is from one and when the other side is subjected to the the metal rod is 20 5x5 cm am and generating rod. Determine the nodal tenpeatures at x=0, 5, 10115 by using a) numerical method b) analyfte method,

Answer 1

Please refer the following images for the solution.

0 Giveni Water inlet temperature Ti=500 Mass flow pate of water mw2 0.01 kg/s Size of duct Az 2cm x 2cm=0.0280-02= 0.0004 m2 Duct wall temperature Ts = 100°c Water outlet temperature, To = 706 Solution Properties of water at Titto so+70 .60°C 2 2 Kw =0,64) IN/mk Pr 3.045 2 = 4.79x10 m/s S = 983.13 kg/m3 Cp = 41835 1 kg k Volume flow rate of water, ý= miw 0.01 1.01716X163 m3/s 3 983.13 Velocity of water, v ♡ 1.017167165 0.02543 m/ А 0.0004 Reynolds number of the flow Re= von . D where, dn = 4A 4*10.0004) 0.02m Р 480102 0.02543 X 0.02 1061,7954 4.797167 003 ... Nu= 0.23 Repe Re= Von .: Nu= 0.23x (1061.7954) x (3.045) .. Nu = 84.652

.. Nu- hon K :h= Nuxk dh 84.65 2x0.641 0.02 ..h=2713.09 IN/m²K rebeat for constant wall temperature (hts) TS-To TS-Ti mcp e (-has mice e 100-70 100-50 (-has/incp) 0.6 = e In 0.6 = -h As mcp -0.5108 = -has mcp . As = 0.51087 0.01x 4183 27 13.09 As -0.0078754 m² where, As = surface area = 4XC0002XL) .: 480.02XL = 0.0078754 L=0.0984 m