Consider a hydrodynamically and thermally fully developed flow through a tube of radius R. The…

Consider a hydrodynamically and thermally fully developed flow through a tube of radius R. The…
Consider a hydrodynamically and thermally fully developed flow through a tube of radius R. The velocity profile is parabolic. The governing equation for the radial variation is given by θ ′′ + (θ ′ /η) + λ 2 (1 − η 2 )θ = 0. A constant temperature boundary condition (T = Tw) is maintained at the wall. The non-dimensional temperature is given by θ = (T − Tw)/(Tc − Tw). Tc is the centreline temperature. Show that the radial variation of the temperature is given by
View complete question » Consider a hydrodynamically and thermally fully developed flow through a tube of radius R. The velocity profile is parabolic. The governing equation for the radial variation is given by θ ′′ + (θ ′ /η) + λ 2 (1 − η 2 )θ = 0. A constant temperature boundary condition (T = Tw) is maintained at the wall. The non-dimensional temperature is given by θ = (T − Tw)/(Tc − Tw). Tc is the centreline temperature. Show that the radial variation of the temperature is given by                        The parameter, −λ2 is the separation constant, used while applying the separation of variables technique. View less »Dec 08 2021 01:37 PM

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