An experiment is devised to measure liquid flow andconvective heat transfer rates in microscale channels.The mass flow rate through a channel is determined bymeasuring the amount of liquid that has flowedthrough the channel and dividing by the duration ofthe experiment. The mean temperature of the outletfluid is also measured. To minimize the time needed toperform the experiment (that is. to collect a significant amount of liquid so that its mass and temperature canbe accurately measured),arrays of microchannels aretypically used. Consider an array of microchannels ofcircular cross section, each with a nominal diameter of
(a) Consider the case in which three microchannels are machined in the copper block. The channel diameters exhibit some deviation due to manufacturing constraints and at of actual diameter
(b) If the water exiting each of the three channels is collected and mixed in a single container, calculate the average how rate through each of the three channels and the average mixed temperature of the water that is collected from all three channels.
(c) The enthusiastic experimentalist uses the averageflow rate and the average mixed outlet temperature to analyze the performance of the average
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- 7.43 Liquid sodium is to be heated from 500 K to 600 K by passing it at a flow rate of 5.0 kg/s through a 5-cmID tube whose surface is maintained at 620 K. What length of tube is required?arrow_forwardAnswer this ASAP The diameter of the tube is 25 mm. The specific heat of water is 4.18 kJ/kg.°C. The overall heat transfer coefficient is 0.7 kW/m².°C. 1. Schematic of temperature distribution 2.ΔTLMTD 3.Actual heat transfer rate 4.Cmin 5.Maximum heat transfer ratearrow_forwardWrite legibly, provide manual step by step solution, and diagram for below given problem. Saturated steam at 500oK flows in a 0.20 m inside diameter, 0.21 m outside diameter pipe. The pipe is covered with 0.08 m of insulation with a thermal conductivity of 0.10 W/m-K. The pipe’s conductivity is 52 W/m-K. The ambient temperature is 300oK. The unit convective coefficients are h1 = 18,000 W/m2-K and ho = 12 W/m2-K. Determine the heat loss from 4 m of pipe. a. 778.21 watts b. 825.80 watts c. 830. 80 watts d. 835.80 wattsarrow_forward
- A Figure illustrates the tube-flow system. The heat transfer under developed flow conditions when the flow remains laminar. The wall temperature is Tw, the center of the tube temperature is Te the radius of the tube is re, and the velocity at the center of the tube is uo. The velocity distribution equation is: 1 uo Prove that: 1 aT uor. T - T= a ax 4 ro Start the solution of the equation : P{żar drjuc,T 1 a ()- aT 1 әт ur дr ar « дхarrow_forwardWater going into a pipe with a tempeture of T1 and going out T2 . ambient tempeture is T0. flow rate q. Develop an expression for T2 ( based on heat transfer) Length of the pipe Lh0 - convective heat transfer coefficient of the airhW -convective heat transfer coefficient of the waterk- pipe thermal conductivity (W/m·K)d – pipe diameter Use any other varilable that you need and can be found online easily .arrow_forwardThe TPD method measures temperature elevations in a tissue region during a heating pulse and its later temperature decay after the pulse. It is then using the Pennes bioheat equation to perform a curve fitting to determine the local blood perfusion rate. If the TPD probe is placed in the vicinity of very large blood vessel, will the TPD technique provide an accurate measurement of the local blood perfusion in the vicinity of this large blood vessel? Explain briefly. (Hint: Is the Pennes bioheat equation accurate surrounding a large blood vessel?)arrow_forward
- 6 In a boiler test, the following observations wcre made: 358 A Text Book of Thermal Engineering Feed water temperaturç e= 12" C; Pressure of steam = 11 bar; Dryness fraction of steam 095 Mass of coal burnt 300 kg/h, Calorific value of coal 32 000 kJkg of coal; Mass of water supplied to boiler in 7 hrs 14 min= 14 625 kg. The mass of w ster in the boiler at the end of the test was less than that at the commencement by 900kg. Calculate I. Actual evaporation per kg of coal: 2 Equivalent evaporation from and at 100 C per kg [Ans. 7 15 kg, 8 33 kg: 58.75 % of coal ; and 3. Thermal efficiency of the boilerarrow_forwardExample(1-14): mixture gas and liquid flow through 0.02 m inside diameter pipe at total flow rate of 0.2 kg/s. if the gas weight fraction is 0.149 what is the pressure drop per unit length of pipe. Where the pipe roughness 0.00015 mm, liquid and gas viscosities are 2x103 pa.s and 1x10-5 pa.s respectively. finaly the liquid and gas densities are 1000 kg/m³ and 60 kg/m³ pa.s respectively.arrow_forwardDetermine the mean heat-transfer coefficient and the quantity of heat transferred in water flowing in a horizontal tube 3 mm in diameter (d) and 2 m long (l), if ω = 0.3 m/sec; tf = 60 deg C and tω = 20 deg C. Constants: @ tf = 60oC, λf = 0.567 kcal/m-hr-oC; νf = 0.478 x 10-6 m2/sec β = 5.11 x 10-4 1/oC and Prf = 2.98. @ tω = 20oC, Pr? = 7.02arrow_forward
- Demonstrate that the heat flowing from a simple pipe of length L, radii ro and ri, surface temp To and Ti and having a thermal conductivity k may be found by using the expression. Here Am is the logarithmic mean areaarrow_forwardConsider pressurized water, engine oil (unused), and Nak (22%/78%) flowing in a 20-mm-diameter tube. (a) Determine the mean velocity, in m/s, the hydrodynamic entry length, in m, and the thermal entry length, in m, for each of the fluids when the fluid temperature is 366 K and the flow rate is 0.01 kg/s. (b) Determine the mass flow rate, in kg/s, the hydrodynamic entry length, in m, and the thermal entry length, in m, for water and engine oil at 300 and 400 K and a mean velocity of 0.022 m/s. Part A Determine the mean velocity, in m/s, the hydrodynamic entry length, in m, and the thermal entry length, in m, for each of the fluids when the fluid temperature is 366K and the flow rate is 0.01 kg/s. Liquid Um (m/s) Xfdh (m) Xfd,t (m) water i engine oil i i i Nak iarrow_forwardObtain by dimensional analysis a functional relationship for the wall heat transfer coefficient h (W/m2-K) for a fluid flowing through a straight pipe of circular cross section. Assume that the effects of natural convection may be neglected in comparison with those of forced convection. Taking the heat transfer coefficient, h, as a function of the fluid velocity, density, viscosity specific heat and thermal conductivity, v, p, H, Cp and k, respectively, and of the inside diameter of the pipe, d. For recurring set, the variables d, u, k, and p. It found by experiment that, when the flow is turbulent, increasing the flowrate by a factor of 2 always results in a 60 percent increase in the coefficient. How would a 50 percent increase in density of the fluid be expected to affect coefficient, all other variables remaining constant?arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning