Question

Fluid X is flowing in a circular pipe with a constant velocity ν (m/s). The fluid is cooled by a jacket kept at constant temperature, Tj. Fluid velocity is plug shaped , in other words uniform at radial positions. Assume that temperature is uniform in radial positions because of turbulent flow conditions; ρ and Cp of the fluid are constants. The inlet temperature (at z=0) is constant and uniform at To (To>Tj). Assume that thermal conduction of heat along the z axis is small relative to convection. Heat transfer film coeffiecient h is given as 40 (J/m2.°C.s).

Δz

Cooling jacket, Tj

v, To, ρ, Cp
R

    

z z=0

a. Perform an unsteady state energy balance using shell balance technique and obtain a PDE model. Do not solve.

b. Perform a steady state energy balance using shell balance technique to obtain an ODE model . Solve the model to find the steady state temperature distribution as a function of axial position z. Take Tref=0.

c. Given that; at t=0, To=90°C; ν=0.5 m/s; h=40 J/(m2.°C.s); R=0.1m; ρ=100 kg/m3; Tj=10 °C and Cp=10J/(kg°C); find the temperature value at z=1 m? (Ans.= 26 °C)

Answer 1

using energy balane we can find the unsteady state PDE and using steady assumption we can find tmeprature distribution in pipe

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