A 6 m long horizontal tube is heated by means of an electrical heating element wrapped...

 

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A 6 m long horizontal tube is heated by means of an electrical heating element wrapped uniformly around it. The inner diameter of the tube (d) is 0.040 m. The heating element provides heat at a rate of 4200 W total over the length of the tube for a heat flux into the fluid of 4200 W/(Inside Area of Pipe) or 4200 W/(m*d*L). A constant flow of 60 kg/hr of an oil enters the tube at an inlet temperature To = -8°C. The specific heat of the oil, Cp = 1.8 kJ kg-¹ K-¹. Assuming that there are temperature gradients only in the axial direction and that density is not a function of temperature, perform a shell balance on the pipe and: Determine an expression for the steady-state temperature of the fluid in the pipe as a function of position, z, where 0 ≤ z ≤ L. Determine the temperature of the oil at the outlet of the tube. Repeat (a) and (b) for the case where heat capacity of the oil is temperature dependent, Cp (kJ kg-¹ K-¹) = 1.8+ 0.003 (T- To). Analytical and/or numerical solutions are acceptable. (Hint: possibly useful MATLAB functions are roots and ode45.) A 6 m long horizontal tube is heated by means of an electrical heating element wrapped uniformly around it. The inner diameter of the tube (d) is 0.040 m. The heating element provides heat at a rate of 4200 W total over the length of the tube for a heat flux into the fluid of 4200 W/(Inside Area of Pipe) or 4200 W/(m*d*L). A constant flow of 60 kg/hr of an oil enters the tube at an inlet temperature To = -8°C. The specific heat of the oil, Cp = 1.8 kJ kg-¹ K-¹. Assuming that there are temperature gradients only in the axial direction and that density is not a function of temperature, perform a shell balance on the pipe and: Determine an expression for the steady-state temperature of the fluid in the pipe as a function of position, z, where 0 ≤ z ≤ L. Determine the temperature of the oil at the outlet of the tube. Repeat (a) and (b) for the case where heat capacity of the oil is temperature dependent, Cp (kJ kg-¹ K-¹) = 1.8+ 0.003 (T- To). Analytical and/or numerical solutions are acceptable. (Hint: possibly useful MATLAB functions are roots and ode45.)