One-dimensional steady state heat transfer problem - Consider a 60-mm long aluminum fin W mK (k = 186 ) with thickness of 1 mm. The width (into the paper) is 5 mm. The aluminum is exposed to air with an ambient temperature of Tf = 15°C and convective heat transfer coefficient of h = 50- surface whose temperature is T₁ = 80° C. W m²K T base = 80 C T15 C h = 50 W/m2K The fin is utilized to remove heat from a Consider the problem as a one-dimensional steady state model and divide the fin into four (4) elements with equal size as shown in the figure above. Using the Finite Difference Method, obtain the discretization for each node (2,3,4, and 5). Please note that in addition to the conduction, each node (except 1) is exposed to lateral heat convection. So, you must include this factor when considering the heat balance on each node. For this problem A. Show the discretization for node 2 B. Show the discretization for node 5 C. Show the set of linear equations to be solved D. Show either the EES script or Matlab script E. Show the outcomes and make a plot of T vs x using Excel or Matlab F. Compute the total heat transfer by the fin based on the temperature outputs

One-dimensional steady state heat transfer problem - Consider a 60-mm long aluminum fin W mK (k = 186 ) with thickness of 1 mm. The width (into the paper) is 5 mm. The aluminum is exposed to air with an ambient temperature of Tf = 15°C and convective heat transfer coefficient of h = 50- surface whose temperature is T₁ = 80° C. W m²K T base = 80 C T15 C h = 50 W/m2K The fin is utilized to remove heat from a Consider the problem as a one-dimensional steady state model and divide the fin into four (4) elements with equal size as shown in the figure above. Using the Finite Difference Method, obtain the discretization for each node (2,3,4, and 5). Please note that in addition to the conduction, each node (except 1) is exposed to lateral heat convection. So, you must include this factor when considering the heat balance on each node. For this problem A. Show the discretization for node 2 B. Show the discretization for node 5 C. Show the set of linear equations to be solved D. Show either the EES script or Matlab script E. Show the outcomes and make a plot of T vs x using Excel or Matlab F. Compute the total heat transfer by the fin based on the temperature outputs

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.30P: 2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is...

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3.10 A spherical shell satellite (3-m-OD, 1.25-cm-thick stainless steel walls) re-enters the atmosphere from outer space. If its original temperature is 38°C, the effective average temperature of the atmosphere is 1093°C, and the effective heat transfer coefficient is , estimate the temperature of the shell after reentry, assuming the time of reentry is 10 min and the interior of the shell is evacuated.
Estimate the rate of heat loss per unit length from a 5-cm ID, 6-cm OD steel pipe covered with high-temperature insulation having a thermal conductivity of 0.11 W/(m K) and a thickness of 1.2 cm. Steam flows in the pipe. It has a quality of 99% and is at 150C. The unit thermal resistance at the inner wall is 0.0026(m2K)/W the heat transfer coefficient at the outer surface is 17W/(m2K) and the ambient temperature is 16C.
3.14 A thin-wall cylindrical vessel (1 m in diameter) is filled to a depth of 1.2 m with water at an initial temperature of 15°C. The water is well stirred by a mechanical agitator. Estimate the time required to heat the water to 50°C if the tank is suddenly immersed in oil at 105°C. The overall heat transfer coefficient between the oil and the water is , and the effective heat transfer surface is .
2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.
3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.
2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)
2.7 A very thin silicon chip is bonded to a 6-mm thick aluminum substrate by a 0.02-mm thick epoxy glue. Both surfaces of this chip-aluminum system are cooled by air at , where the convective heat transfer coefficient of air flow is . If the heat dissipation per unit area from the chip is under steady-state conditions, draw the thermal circuit for the system and determine the operating temperature of the chip.
2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.
Steam in a heating system flows through tubeswhose outer diameter is 5 cm and whose walls are maintainedat a temperature of 180°C. Circular aluminum alloy 2024-T6fins (k = 186 W/m·K) of outer diameter 6 cm and constantthickness 1 mm are attached to the tube. The space betweenthe fins is 3 mm, and thus there are 250 fins per meter lengthof the tube. Heat is transferred to the surrounding air at T` = 25°C, with a heat transfer coefficient of 40 W/m2·K. Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins.
Consider a copper tube with domestic hot water flowing inside (Tin =70◦C, um = 0.5m/s). The inner diameter of the tube is Din=13mm and outer diameter is Dout=15mm. The tube is located in a crawlspace and the surrounding temperature is T∞ =0 ◦C. The inner and outer heat transfer coefficients are hin = 250W/m2K and hout = 5W/m2K. The tube is insulated at the outer surface with insulating foam of thickness lf oam=17.5mm. The temperature drop of the water along the tube is 0.5◦C. 1. Draw a sketch that indicates the dimensions of the system, and the directions of heat transfer and fluid flow. 2. What is the length of the tube?
Steam flows in an insulated pipe at a temperature 130 C. The insideheat transfer coefficient is 79 W/m2-K and the outside coefficient is 15W/m2-K. The pipe is mild steel (k=57 W/m-K) and has an inside radiusof 50 mm and an outside radius of 57 mm. the pipe is covered with a25.4 mm layer( k=0.09 W/m-K). Determine the overall heat transfercoefficient if the surrounding air temperature is 21.1 C.
Steam in a heating system flows through tubes whose outer diameter is 5 cm and whose walls are maintained at a temperature of 198.06°C. Circular copper alloy fins (k =285 W/m · °C) of outer diameter 6 cm and constant thickness 1 mm are attached to the tube. The space between the fins is 3 mm, and thus there are 250 fins per meter length of the tube. Heat is transferred to the surrounding water at T= 43.06°C, with a heat transfer coefficient of 5300 W/m2 · °C. Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins and fin effectiveness