Heat Transfer

A pipe with 3 m length, inner diameter is 15 cm and outer diameter is 18 cm, out surface temperature is 250°C, inner surface temperature is 260°C. The material of wall is carbon steel. Find the heat loss of this pipe.

The LMTD of a heat exchanger is supposed to be 23.2°C. The outside diameter of heat transfer tube is 2 cm. The thickness of tube is 3 mm. The heat transfer coefficient of inner side of tube is 9000 W/(m².°C) and 6000 W/(m².°C) for outside. The thermal conductivity of tube wall is 20 W/ (m°C). Find the linear power density of the tube. (Power of 1 meter tube).

1. Boil a hot dog in ten minutes in a pot you have at home 2. Determine the heat transferrable from a finned system in your home (e.g., air conditioning unit, back of the refrigerator).

2. (3 pt) Heat Transfer from Tubular Reactor (Problem 8 from Midterm #1) Hint: Read through ALL SUBPARTS of this problem, before starting. Consider a tubular reactor for which the wall is a cylindrical glass shell of inside radius r₁ = 1.0 cm and outside radius r₂ = 2.0 cm, and length L = 0.5 m. Inside the tube core (inside r₁) is a reaction mixture of uniform temperature T₁ = 60 °C, which generates q = 5 x 105 W/m³ heat due to exothermic reaction. A. The design goal calls for the temperature of the outer wall (7₂) to be less than 35 °C, for safety reasons. Is this goal met? Use k = 0.8 W/m-K for the glass wall and assume steady state and that the fluid inside the tube core is well-mixed, so that its resistance may be neglected. The two ends of the reactor are insulated. Hint: There is no generation in the glass tube walls; generation only occurs in the fluid mixture inside. B. The following equation can be found on your equation sheet for this class, under the section 3. Hollow spheres and cylinders with generation in core: T(r) = T(₁) + (q/4k)(r² - r²) Explain why this equation is not applicable for this particular scenario. C. Now, suppose the ambient air temperature in the room containing the reactor is To = 25 °C. A fan blows air over the reactor (perpendicular to the cylinder axis) at a velocity v = 0.25 m/s. Is the resulting forced convection enough to carry away the heat generated by the reactor? Use T₂ = 35 °C (rather than your result from Part A), along with Kair= 0.025 W/mK, Vair 1.6 x 10-5 m²/s, and Pr = 0.7 for air. D. Explain why the finding that Nup > 1 or even Nup >> 1 in Part C is insufficient to justify whether the resulting forced convection is enough to carry away the heat generated by the reactor.

3. (6 pt) Numerical analysis with MATLAB A hot pipe carrying steam runs horizontally through an empty room that has an air temperature of 25°C. The cylindrical pipe is made of oxidized cast iron, is 3 m long, and has an outer diameter of 0.47 m. The pipe is wrapped in 3 cm of insulation that lowers the thermal emissivity to 0.5. The heat flux due to free convection is 60 W/m² greater than the heat flux due to thermal radiation. You may assume the following properties of air: Ideal gas kf= 0.025 W/m.K 1 Pr = 0.7 v 1.5 x 10-5 m²/s A. Using Newton's Method with a tolerance of 10-5, find the temperature of the outside of the pipe. Write out all equations that you use and include your MATLAB script. For full credit, your MATLAB code must be turned in and include: . Your name commented in the file(s) • At least 3 commented lines in the Newton function explaining what the step on that line is doing in the calculation • Labels and include units (where applicable) on all variables in your script B. Compare the temperature that you found using Newton's method in part A and the temperature that you find using the fsolve function in MATLAB. (Hint: use your answer from part A to inform your initial point). C. What is the heat transfer coefficient for free convection? D. Is the thermal boundary layer greater than or less than the characteristic length of the pipe? E. How would removing the insulation on the pipe change the emissivity and rate of heat loss due to radiation?

Refrigerant R-134a enters a compressor at a pressure of 100.0 kPa at a rate of 2.500 kg/s. The refrigerant R-134a leaves the compressor at a pressure is 1200 kPa with a volumetric flow rate of 171,000 L/hr. The compressor is driven by an electrical motor that consumes 605.0 kW of electrical power and has an electrical to mechanical efficiency of 85.00%. Heat is lost from the compressor at a rate of 300.0 kW to the ambient air, which is at a temperature of 310.0 K.

5. (2 pts) Heat Sterilization of Canned Food (Adapted from Welty et al., Problem 18.22) In the canning process, sealed cans of food are sterilized with pressurized steam to kill any microorganisms initially present in the food and thereby prolong the shelf life of the food. A cylindrical can of food has a diameter of 4 cm and height of 4 cm. The food material can be treated as a solid with heat capacity of 4000 J/kgK, density of 1200 kg/m³, and thermal conductivity of 0.6 W/mK. In the process, steam at 120°C is used to sterilize the can. The convective heat-transfer coefficient is 60 W/m² K. The can and contents initially are at a uniform temperature of 20 °C. A. If the heat-transfer resistance offered by the thin can walls is neglected and the can ends are thermally insulated, how long will it take for the center of the can to reach a temperature of 80 °C, which is sufficient to kill all microorganisms? Hint: You will need to use one of the charts in Appendix F of Welty et al. B. What is the required time if the ends of the can are not insulated but are instead exposed to the steam? Hint: See Section 18.2 of Welty et al. for an approximate approach to this two- dimensional problem. It is tricky, though, as you know the left-hand-side of Eq. 18.24, but not the two terms on the right-hand-side. Thus, you will need iterate by making two educated guesses for the time required, then calculate the right-hand-side and then interpolate (or extrapolate) to get an improved estimate. Also, the variable a for this equation is the half-height of the can.

2. (2 pts) Cooling of a Spherical Object in Lumped Capacitance Model For Bi=h(V/A)/k ≤ 0.1, the transient temperature inside a solid object that is cooling under conditions of constant properties and no internal heat generation may be written as: T(t)-To=(To-Tz)e-t/t, where 7 is a characteristic time constant for the exponential decay of the temperature difference between the solid and the fluid. A. Using the solution from lecture or the text, find an expression for T in terms of the solid density p, the specific heat Cp, the volume-to-area ratio V/A, and the film heat-transfer coefficient h. B. For a spherical object made of mild steel (1% Carbon) falling through water, what is the value of t if the diameter is 0.1 cm? Evaluate all physical properties at 293 K. Hint: To determine the heat-transfer coefficient h, you must first find the terminal velocity of the sphere in water and then calculate the heat-transfer coefficient from an appropriate correlation (assume that forced convection dominates over free convection and radiation). For the terminal velocity, remember that drag and buoyancy are in balance, then start by assuming a drag coefficient Cp = 0.44 for spherical objects and perform an iteration using Figure 12.4 of Welty et al. if necessary. Use the Ranz and Marshall correlation (Eq. 20-38 in Welty et al.) for the heat loss. C. Repeat part (B) but for a silver object. Which material has the larger value of T, and why? D. For silver, calculate Nu, again, but this time using the Whitaker correlation (20-37 of Welty et al), with T = 293 K and T, = 313 K. By what % does this value differ from that from the Ranz and Marshall correlation?

A cylindrical pin fin of diameter 1.0 cm and length of 2 cm with negligible heat loss from the tip has an efficiency of 0.88. the effectiveness of this fin is:

3. Insulation of a steam pipe for safety of the students In a chemical engineering lab, the students are working with a steam engine that is fed by steam pipes. One of the students reaches over to make an adjustment and burns herself by bumping her arm on the exposed steam pipe. This prompts the lab coordinator to buy foam to cover the steam pipes, but first he needs to calculate how thick the foam needs to be. The lab coordinator measures the outside of the bare pipe, which has an outer diameter of 10 cm and is 2 m tall, to be 106°C. The lab coordinator also knows that the pipe is stainless steel, and the conductivity is 17.3 W/m-K. There needs to be at least enough insulation that the outside temperature is 50°C or less. The lab is uncomfortably warm at 27°C, so a fan is positioned next to the steam engine and blows air at 7 m/s. The steam inside the pipe is at 107°C and is flowing at 10 m/s. Use Appendix I in Welty et al. for all physical properties of liquids and gases. A. How thick does the insulation have to be if expanded polyethylene foam, which has a conductivity of 0.3 W/m-K, is used? Hint: Excel Solver is your friend! B. What is the inner diameter of the steam pipe?