Consider the thermosyphon of Problem 10.54. In many applications, a more realistic scenario is one where the condensation section is cooled by an external, flowing fluid. Determine the thermosyphon heat rate as well as the surface temperatures of the boiling and condensation sections if the vertical cylindrical surface of the condensation section is exposed to a fluid at \(20^{\circ} \mathrm{C}\) and a convection heat transfer coefficient of \(500 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). 

Data From Problem 10.54:-

A thermosyphon consists of a closed container that absorbs heat along its boiling section and rejects heat along its condensation section. Consider a thermosyphon made from a thin-walled mechanically polished stainless steel cylinder of diameter \(D\). Heat supplied to the thermosyphon boils saturated water at atmospheric pressure on the surfaces of the lower boiling section of length \(L_{b}\) and is then rejected by condensing vapor into a thin film, which falls by gravity along the wall of the condensation section of length \(L_{c}\) back into the boiling section. The two sections are separated by an insulated section of length \(L_{i}\). The top surface of the condensation section may be treated as being insulated. The thermosyphon dimensions are \(D=20 \mathrm{~mm}, L_{b}=20 \mathrm{~mm}\), \(L_{c}=40 \mathrm{~mm}\), and \(L_{i}=40 \mathrm{~mm}\). 

(a) Find the mean surface temperature, \(T_{s, b}\), of the boiling surface if the nucleate boiling heat flux is to be maintained at \(30 \%\) of the critical heat flux.
(b) Find the total condensation flow rate, \(\dot{m}\), and the mean surface temperature of the condensation section, \(T_{s, c}\).

Transcribed Image Text:

Ts.c Saturated steam Condensation film L Condensation section g L Insulation Saturated water Ly Boiling section Tyb Electric heater