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Q3: A fluid is flowing in a horizontal pipe and is heated from the outside. We are interested to find the heat transfer rate through

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Q3: A fluid is flowing in a horizontal pipe and is heated from the outside. We are interested to find the heat transfer rate through a unit of pipe wall area, q/A[Js1m2]. Using this, one could calculate the length of the pipe needed for a certain amount of total heat transfer (not required to do this for your assignment). The heat transfer rate per unit area depends on eight variables and constants: the difference between the temperature outside the pipe and the average temperature inside the pipe T[K ] (we assume the same average temperature inside the pipe over the whole length of the pipe), the pipe diameter d[m], the viscosity [kgm1s1], liquid density [kgm3], the velocity of the flow v[ms1], the length of the pipe l[m], the specific heat capacity of the fluid inside the pipe Cp[Jkg1K1], and the thermal conductivity k[Jm1K1s1]. Using the Buckingham-Pi theorem, formulate a model for the dimensionless heat transfer rate per area of pipe wall q/A, as a function of other dimensionless groups. Hint: use d,,,k, and T as the recurring variables

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