Question

In cryogenic equipment, cold gas flows in parallel over the surface of a \(1-\mathrm{m}\)-long plate. The gas velocity is \(4 \mathrm{~m} / \mathrm{s}\) at a temperature of \(-70^{\circ} \mathrm{C}\). The gas has a thermal conductivity of \(0.01979 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), a kinematic viscosity of \(9.319 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\), and a Prandtl number of \(0.7440\). A stainless steel (ASTM A437 B4B) bolt is embedded in the plate at midlength. The minimum temperature suitable for the ASTM A437 B4B stainless steel bolt is \(-30^{\circ} \mathrm{C}\) (ASME Code for Process Piping, ASME B31.3-2014, Table A-2M). To keep the bolt from getting below its minimum suitable temperature, the plate is subjected to a uniform heat flux of $250 \mathrm{~W} / \mathrm{m}^{2}$. Determine whether the heat flux to the plate is sufficient to keep the bolt above the minimum suitable temperature of \(-30^{\circ} \mathrm{C}\).

Short answer

Re ≈ 4293.౩

Step-by-step solution

Calculate the Reynolds number

The Reynolds number is needed to determine the flow regime and heat transfer characteristics. It can be determined by the formula: Re = (U*L)/ν where Re is the Reynolds number, U is the gas velocity, L is the length of the plate, and ν is the kinematic viscosity. Re = (4 * 1)/(9.319 * 10^{-6}) Calculate Re: