An experiment is designed to study microscale forced convection. Water at Tm,i=300K is to be heated in a straight, circular glass tube with a 50−μm inner diameter and a wall thickness of 1 mm. Warm water at T∞=350K, V=2 ms is in cross flow over the exterior tube surface. The experiment is to be designed to cover the operating range 1≤ ReD≤2000, where ReD is the Reynolds number associated with the internal flow. a) Determine the tube length L that meets a design requirement that the tube be twice as long as the thermal entrance length associated with the highest Reynolds number of interest. Evaluate water properties at 305 K. b) Determine the water outlet temperature, Tm,o that is expected to be associated with ReD=2000. Evaluate the heating water (water in cross flow over the tube) properties at 330 K. c) Calculate the pressure drop from the entrance to the exit of the tube for eD=2000. d) Based on the calculated flow rate and pressure drop in the tube, estimate the height of a column of water (at 300 K) needed to supply the necessary pressure at the tube entrance and the time needed to collect 0.1 liter of water. Discuss how the outlet temperature of the water flowing from the tube, Tm,o, might be measured.

Question

An experiment is designed to study microscale forced convection. Water at Tm,i=300K is to be heated in a straight, circular glass tube with a 50−μm inner diameter and a wall thickness of 1 mm. Warm water at T∞=350K, V=2 ms is in cross flow over the exterior tube surface. The experiment is to be designed to cover the operating range 1≤ ReD≤2000, where ReD is the Reynolds number associated with the internal flow. a) Determine the tube length L that meets a design requirement that the tube be twice as long as the thermal entrance length associated with the highest Reynolds number of interest. Evaluate water properties at 305 K. b) Determine the water outlet temperature, Tm,o that is expected to be associated with ReD=2000. Evaluate the heating water (water in cross flow over the tube) properties at 330 K. c) Calculate the pressure drop from the entrance to the exit of the tube for eD=2000. d) Based on the calculated flow rate and pressure drop in the tube, estimate the height of a column of water (at 300 K) needed to supply the necessary pressure at the tube entrance and the time needed to collect 0.1 liter of water. Discuss how the outlet temperature of the water flowing from the tube, Tm,o, might be measured.

Benedict · Accepted Answer

a) Properties of water at T=305K are pulled from Table A.6: Density, ρ=995kgm3 Specific heat, cρ=4175JkgK Viscosity, μ=769⋅10−6Nsm2 Prandtl number, Pr=5.2 We&#039;ll calculate the thermal entry point with Equation 8.23: xfd,t≈0.05Re PrD ≈0.05⋅2000⋅5.20⋅50⋅10−6 ≈0.026m Therefore, the required length is twice the length of our thermal entry point: L=2⋅xfd,t=2⋅0.026 =52mm b) Properties of water in cross flow at T=330K are pulled from Table A.6: Density, ρ=984.3kgm3 Specific heat, cρ=4184JkgK Viscosity, μ=489⋅10−6Nsm2 Thermal conductivity, k=0.650WmK Prandtl number, Pr=3.15 To calculate the output temperature of air, we&#039;ll use Equation 8.45a: Ts−Tm,oTs−Tm,i=exp⁡(−U―Asm˙cp) →Tm,o=Ts−(Ts−Tm,i)exp⁡(−U―Asm˙cp) =Ts−(Ts−Tm,i)exp⁡∖(−U―Asm˙cp) We define U― on the inside area, so U― becomes U―i and As becomes Ss,i. Analogy to Equation 3.36, we&#039;ll write U―i as:

An experiment is designed to study microscale forced convection. Water at

Answered question

Answer & Explanation

New Questions in Other