Does Bi<0.1 really suggest a negligible temperature gradient? A straight fin of uniform circular cross section is fabricated from a material with a constant thermal conductivity. The fin has a radius of 20 mm and a length of 100 mm. The convection heat transfer coefficient is 500 W/m²-K with an ambient fluid temperature of T=30 °C. The base of the fin is maintained at T,=100 °C, while the fin tip is heavily insulated. Temperature gradients in the circumferential direction of the fin are negligible. Using the finite-volume technique with volumes that are 2 mm on a side, estimate the temperature distribution within the fin for a fin with a thermal conductivity of (a) 50 W/m-K and (b) 0.5 W/m-K. 1. For both cases, plot the temperature along the fin axis on the centerline of the fin and on the outer surface of the fin. 2. For both cases, also calculate the fin heat transfer rate, qin- 3. Compare the fin heat transfer rate that you determined via FVM with the one- dimensional, analytical solution from Table 3.4. 4. Comment on the validity of the Biot number as a guide regarding the importance of temperature gradients.

Does Bi<0.1 really suggest a negligible temperature gradient? A straight fin of uniform circular cross section is fabricated from a material with a constant thermal conductivity. The fin has a radius of 20 mm and a length of 100 mm. The convection heat transfer coefficient is 500 W/m²-K with an ambient fluid temperature of T=30 °C. The base of the fin is maintained at T,=100 °C, while the fin tip is heavily insulated. Temperature gradients in the circumferential direction of the fin are negligible. Using the finite-volume technique with volumes that are 2 mm on a side, estimate the temperature distribution within the fin for a fin with a thermal conductivity of (a) 50 W/m-K and (b) 0.5 W/m-K. 1. For both cases, plot the temperature along the fin axis on the centerline of the fin and on the outer surface of the fin. 2. For both cases, also calculate the fin heat transfer rate, qin- 3. Compare the fin heat transfer rate that you determined via FVM with the one- dimensional, analytical solution from Table 3.4. 4. Comment on the validity of the Biot number as a guide regarding the importance of temperature gradients.

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.

Chapter8: Natural Convection

Section: Chapter Questions

Problem 8.53P

See similar textbooks

Similar questions

A steam pipe 50 mm diameter and 2.5 m long has been placed horizontally and exposed to still air at 25 degree Celsius. If the pipe wall temperature is 295 degree Celsius, determine the rate of heat loss. At the mean temperature difference of 160 degree Celsius, the thermo-physical properties of air are k =3.64 * 10 -2 W/m v =30.09 * 10 -6 m2/ P r =0.68 Β =1/160 + 273 = 2.31 * 10^-3/K
Find the minimum amount of diameter for the insulation of a spherical water tank? Radius of the tank is 10 m, thermal conductivity is 25 W/(m^2*K) and convective coefficient is 5 W/(m*K) 8 m not sufficient information 10 m 20 m 15 m
A 50-cm-diameter pipeline in the Arctic carries hot oil at 30◦C and is exposed to a surrounding temperature of −20◦C. A special powder insulation 5 cm thick surrounds the pipe and has a thermal conductivity of 7 mW/m · ◦C. The convection heat-transfer coefficient on the outside of the pipe is 9 W/m2 · ◦C. Estimate the energy loss from the pipe per meter of length. (Please give step-by-step solution)
Solution please, should correct determine the rate of heat loss of this cylindrical fin, where there is no heat loss from the ends of the cylinder. There is only convective heat loss from the curved surface of the cylinder. L = 0.5 m R = 0.02 m k = 400 W/mK h = 10 W/m^2K Ta = 298 K T0 = 773 K
Consider a composite wall made up of three separate walls and convective boundary conditions on each side, like so: a) Write the equation for total thermal resistance of the wall. b) If ? = 3m x 2m, L1, L2, and L3 = 1m, 0.5m, and 2m respectively, k1, k2, k3 = 400, 4, and 80 W/mk respectively, T∞1, T∞2 = 450 and 25 ̊C respectively, and h1, h2 = 40 and 200 W/mk respectively, what is the total thermal resistance? c) Given your answer to a and b, what is the junction temperature between the 1st and 2nd wall? d) What is the junction temperature between the 2nd and 3rd wall? e) What is the surface temperature of the end of the 3rd wall?
Q1) A polished metal pipe (8 cm) owtside diameter and 350 K temperature at the outer surface is exposed to ambient conditions at 285 K temperature. The emissivity of the surface is 0.3 and the convection coefficient of heat transfer is 13.5 Wim2-deg. What would be the overall coefficient of heat transfer by the combined mode of convection and radiation” Q2 find the pressure point (1) if the amospheric pressure is(70kpajihl =0 2,h2=0.4,h3=0. ‘)(p. =13600kg/m3. poil=850kg/m3)
A total of 10 rectangular aluminum fins (k =203 W/m·K) are placed on the outside flat surface of anelectronic device. Each fin is 100 mm wide, 20 mm highand 4 mm thick. The fins are located parallel to each otherat a center-to-center distance of 8 mm. The temperature atthe outside surface of the electronic device is 60°C. The airis at 20°C, and the heat transfer coefficient is 100 W/m2·K. Determine (a) the rate of heat loss from the electronic device to the surrounding air and (b) the fin effectiveness.
A modern cabin has a concrete floor that is 4.50 inches thick. Aroaring fire keeps the interior of the cabin at 21.0 0C while the airtemperature below the cabin is a chilly 2.00 0C. How much heat(J) is lost through the concrete floor in 4 hrs if the cabin measures4.50 m by 6.50m to 3 sig fig?
/ Hot square plate (1 m ×1 m) is to be cooled by attaching aluminum circular pin fins (D=0.25 cm, L= 3 cm) distributed with distance 0.6 cm as illustrated in Figs.(1-a) & (1-b). If the fin base temperature is 100°C, cooling air temperature is 30°C and h= 35 W/m. °C. Determine the total rate of heat transfer from the finned plate and the effectiveness of the fins? Assume k= 237 W/m.°C and nr=tanh mL/ mL.
The 4-mm-thick rear window of an automobile is defogged by passing warm air over its inner surface. Warm air temperature is at T,1 = 40C and corresponding convection coefficient is h1 =30 W/(m2·K). Outer ambient temperature T,2 = 5C and corresponding convection coefficient is h2 = 70 W/(m2·K). The size of the window is 0.5 m (height)  1.5 m (width). A. Draw two thermal circuits (one based on heat rate and one based on heat flux) considering the convection occurring over inner and outer surfaces and the conduction through the window. Show the equations for the thermal resistances in the circuits.B. Determine the total thermal resistance based on heat flux in m2K/W andoverall heat transfer coefficient U in W/m2K. Find the thermal conductivity of glass (sodalime at 300K)C. Determine the inner and outer temperatures of the glass (that are Ts,1 and Ts,2 shown above).
A 10-cm diameter pipe is covered by 2 layers of lagging. The insidelayer is 4 cm thick and has a coefficient of thermal conductivity of 0.08W/m-K. The outside layer is 3cm thick and has a coefficient of thermalconductivity of 0.15 W/m-K. The steam main conveys steam apressure of 1.7 MPa with 25 C superheat. The outside temperature ofthe lagging is 27 C. If the steam main is 30 m long, determine theinterface temperature of the lagging and overall coefficient of heattransfer based on outside area.
A domestic refrigerator with inner dimensions of 0.7 m by 0.7 m at the base and height 1 m was designed to maintain a set temperature of 6 ˚C. The bodies consist of two 10-mm-thick layers of Aluminium (k = 225 W/mK) separated by a 30 mm polyurethane insulation (k=0.028 W/mK). If the average convection heat transfer coefficient at the inner and outer surfaces are 11.6 W/m2K and 14.5 W/m2K respectively, calculate: Total inner surace area in m2 to 2 decimal places.