it is desired to understand the time - temperature behavior of a hot copper sphere. the sphere has a diameter D and Is buried a depth Z below the surface of the dry sand in a very large,very deep sand pit far from the edges of the pit. The initial temperature of the sphere is Ti, and the temperature at the surface of the sand is maintained at " T infinity". the difference between the temperature of the sphere and the surface, T-T infinity at any time is a function of the initial Temperature difference, Ti - Tinfinity ; the thermal conductivity of the sand, ks ; the thermal conductivity of the copper kc ; the sphere diameter D ; the depth at which it is buried Z; the elapsed time t, and the density times the specific heat Pcp of the copper. What is the best set of repeating variables for this problem? Find the appropiate functional relationship between these parameters in dimensionless form.

it is desired to understand the time - temperature behavior of a hot copper sphere. the sphere has a diameter D and Is buried a depth Z below the surface of the dry sand in a very large,very deep sand pit far from the edges of the pit. The initial temperature of the sphere is Ti, and the temperature at the surface of the sand is maintained at " T infinity". the difference between the temperature of the sphere and the surface, T-T infinity at any time is a function of the initial Temperature difference, Ti - Tinfinity ; the thermal conductivity of the sand, ks ; the thermal conductivity of the copper kc ; the sphere diameter D ; the depth at which it is buried Z; the elapsed time t, and the density times the specific heat Pcp of the copper. What is the best set of repeating variables for this problem? Find the appropiate functional relationship between these parameters in dimensionless form.

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.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.36P

See similar textbooks

Similar questions

A 0.6-cm diameter mild steel rod at 38C is suddenly immersed in a liquid at 93C with hc=110W/m2K. Determine the time required for the rod to warm to 88C.
Determine the rate of heat transfer per meter length from a 5-cm-OD pipe at 150C placed eccentrically within a larger cylinder of 85 magnesia wool as shown in the sketch. The outside diameter of the larger cylinder is 15 cm and the surface temperature is 50C.
A spherical communications satellite, 2 m in diameter, is placed in orbit around the earth. The satellite generates 1000 W of internal power from a small nuclear generator. If the surface of the satellite has an emittance of 0.3, and is shaded from solar radiation by the earth, estimate its surface temperature.
The wall of a furnace comprises three layers as shown in the figuie. The first layer is tery (whose maximum allowable temperature is 1400°C) while the second laver is Tracto:y Chose maximum allowable temperature is 1093°C). The third layer is a plate of 6 35 od thermal contact. Steet plare To 6.35x3 45A 1370 C Concerntiation veluciy 37.8 C mass Siynes Figure. Layers in a composite furnace wall. e temperature To on the inside of the refractory is 1370°C, while the temperature T; on the side of the steel plate is 37.8° The heat loss through the furnace HnIlisexpectet tobe
A brass plate has a circular hole whose diameter is slightly smaller than the diameter of an aluminum ball. Ifthe ball and the plate are always kept at the same temperature,(a) should the temperature of the system be increased or decreasedin order for the ball to fit through the hole? (b) Choose the bestexplanation from among the following:I. The aluminum ball changes its diameter more with temperature than the brass plate, and therefore the temperatureshould be decreased.II. Changing the temperature won’t change the fact that the ballis larger than the hole.III. Heating the brass plate makes its hole larger, and that willallow the ball to pass through.
Ok, sometimes the semi-infinite approach is about long times with semi-infinite geometries. The ground at northernclimates with sustained low temperatures will freeze to a certain depth, something to be aware of when burying waterpipes. Say an area exists where temperatures of -10°C can be sustained at the ground surface for up to 45 days. Howdeep should pipes be buried to keep from exposing them to freezing temperatures? Assume the ground starts at auniform 5°C. For the soil, use a thermal conductivity k of 0.35 W/m∙K and a thermal diffusivity  of 1.5 x 10-7 m2/s.
Q3: In iron whose base plaet is mad aluminum alloy is turn on : The time for the plate temperature to reach 140°C. Determine the plate temperature which is to be uniform at all times . Take for the aluminum p=2770 kg/m, C,-875 kJ/kg."C , a=7.3 m/s. The thermal conductivity of the plate k=177 W/m."C Air 22°C Ans : 51.8 °C IRON 1000 W ttt t t
Seh o I em Avertical cylinder with radlis 23 , ylinder height L eynat to i diameter, and surface temperature 70Cis standing iasalated Hout, and the sarrennding walls at 25 C. What is the antonnt of heat that lest by radiation "Watts" ben the vmiiity is .9 feiect one A 25 OD.113 E10101 NETE PREVIOUS PAGE CONTACTUS GET SOCIAL INPO
What is the minimum amount of ice at OPC that must be added to the contents of a can of diet cola (340m) to cool it down from 20.5C to 0C Assume that the specific heat and density of the diet colo are the same as for water and that no heat is gained or lost to the surroundings. The latent heat of fusion of ice à 3353/g Specific Heat of water 4.184 J/gK and Density of water is 1 g/mL
oii- A conductor transfers heat of 30 J t OECC oss it's length of Hiat it's 20 C17 in 6 seconds- Given cross- sectional airea A is 55om?. Determine the thermal condluctivity of the material if the temperature difference across the ends is 67°C - ii An object of emisivitiy 0'7 and co5oss- sectional of SSmm? at room tenmpeiature area of 30 losses energy What is the initial temperat ure of the object? I0=5.6703x 108 W/m/ +] at Tate of 38.65/8.
The first part of the question has been worked on, where the heat transfer was calculated to be 6.770 kilowatt, but the problem also asks to calculate the temperature of the outer most surface. What is the temperature of the outer most surface?
Find the temperature profile of the rectangular plate 4m x 4m, whose temperature at the side are given below: Take delx= del y= 1 m. 100 C 75 C OC 50 C