Question Solved1 Answer 4.18. Find the variation of the local heat transfer rate with axial distance for the thermally developing flow of oil through a pipe with an inside diameter of 1 cm and a beated length of 10 cm. The wall of the pipe is kept at a temperature of 50°C and the oil enters the heated section of the pipe at a temperature of 10°C. The mean velocity of the oil in the pipe is 1.3 m/s. Assume that the oil has a density of 890 kg/m”, a specific heat of 1.9 kJ/kg°C, a coefficient of viscosity of 0.1 kg/ms, and a thermal conductivity of 0.15 W/m K.

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Transcribed Image Text: 4.18. Find the variation of the local heat transfer rate with axial distance for the thermally developing flow of oil through a pipe with an inside diameter of 1 cm and a beated length of 10 cm. The wall of the pipe is kept at a temperature of 50°C and the oil enters the heated section of the pipe at a temperature of 10°C. The mean velocity of the oil in the pipe is 1.3 m/s. Assume that the oil has a density of 890 kg/m”, a specific heat of 1.9 kJ/kg°C, a coefficient of viscosity of 0.1 kg/ms, and a thermal conductivity of 0.15 W/m K.
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Transcribed Image Text: 4.18. Find the variation of the local heat transfer rate with axial distance for the thermally developing flow of oil through a pipe with an inside diameter of 1 cm and a beated length of 10 cm. The wall of the pipe is kept at a temperature of 50°C and the oil enters the heated section of the pipe at a temperature of 10°C. The mean velocity of the oil in the pipe is 1.3 m/s. Assume that the oil has a density of 890 kg/m”, a specific heat of 1.9 kJ/kg°C, a coefficient of viscosity of 0.1 kg/ms, and a thermal conductivity of 0.15 W/m K.
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Ans: Datagiven: quad D=1cm{:[L=10cm],[T_(omega)=50^(@)C],[T_(0i)=10^(@)C],[V=1.3m//s]:}Properties of oilReynolds number of flow:{:[R_(eD)=(rho_(0)VD)/(40)],[=(890 xx1.3 xx(1xx10^(-2)))/(0.1)],[=115.7quad" (which is less than 2300 thus "],[quad" flow inside pipe is Laminar.) "]:}Assumptions: rarr Effect of entry length is neglected and flow is throught to be fully developed throughout the length.for circuer tabe steady state conditions for circular tube, laminer flow empirical relationship for Nu number is given by: (constent wall temperature){:[Nu=3.66],[=>(hL_(c))/(k_(0))=3.66quad(L_(c)=D)],[=>h=(3.66 xx0.15)/((1xx10^(-2)))=>h=54.9w//m^(2)K]:}Let temperature of oil at a distance x from entry be T_(x). (as shown)for the dlement shown in above schematic, by writting energy balance at steady state: E^(˙)_("in ")=E^(˙)_("out "){:[=>quadQ^(˙)conv+m^(˙)c_(p_(0))T_(x)=m^(˙)c_(p_(0))(T_(x)+dT_(x))],[=>quad h(dA)xx(T_(omega)-T_(x))=m^(˙)c_(p_(0))(T_(x)+dT_(x))-m^(˙)c_(p_(0))T_(x)],[=>quad hx(pi Ddx)(T_(w)-T_(x))=m^(˙)c_(p_(0))dT_(x)],[=>quad(pi hD ... See the full answer