A spherical, stainless steel (AISI 302) canister is used tostore reacting chemicals that provide for a uniform heat flux
(a) Assuming negligible temperature gradients in the canister wall and a constant heat flux
(b) What is the steady-state temperature of the wall?
(c) The convection coefficient depends on the velocity associated with fluid flow over the canister and whether the wall temperature is large enough to induce boiling in the liquid. Compute and plot the steady-state temperature as a function of h for the range
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Fundamentals of Heat and Mass Transfer
- A cylindrical liquid oxygen (LOX) tank has a diameter of 1.22 m, a length of 6.1 m, and hemispherical ends. The boiling point of LOX is -179.4C. An insulation is sought that will reduce the boil-off rate in the steady state to no more than 11.3 kg/h. The heat of vaporization of LOX is 214 kJ/kg. If the thickness of this insulation is to be no more than 7.5 cm, what would the value of its thermal conductivity have to be?arrow_forwardure f) A steel disc (k = 56.7 W/m.K, p = 7854 kg/m³, c = 487 J/kg. K) 30 cm in diameter and 10 cm thick, initially at uniform temperature of 265 °C is immersed in liquid at -15 °C. The convective coefficients on ends and on cylindrical side are 340 and 1420 W/m².K, respectively. What is the temperature at (a) center of disc, and (b) surface at centre of one end (c) Calculate heat transfer after 5 min have elapsed.arrow_forwardIndirect Cooling With Liquid Nitrogen. You are designing a system to cool an insulated silver plate of dimensions 2.00 cm × 2.00 cm x 0.40 cm. One end of a thermally insulated copper wire (diameter D = 2.70 mm and length L = 12.0 cm) is dipped into a vat of liquid nitrogen (T = 77.2 K), and the other end is attached to the bottom of the silver plate. (a) If the silver plate starts at room temperature (73.0°F), what is the initial rate of heat flow between the plate and the liquid nitrogen reservoir? (b) Assuming the rate of heat flow calculated in part (a), estimate the temperature of the silver plate after 30.0 seconds.arrow_forward
- (a) The heating power generated by the nuclear heating rod and the inner temperature of the metallic cylinder, T2. (b) The temperature liquid X, which is located between the nuclear heating rod and the meatllic cylinder, Tliquid. (c) The temperature at the surface of the heating rod, T1. (d) If the salt solution temperature is 300 degree Celcius, what is the value of convection heat transfer coefficient, h of the salt solution ? (e) If the heating rod is not covered by metallic cylinder and corresponds to the result of part (c) and (d), how much the rate of energy transfer to the salt solution ? (f) Compare and discuss the difference of heat transfer with and without the matallic cylinder.arrow_forwardA spherical, stainless steel (AISI 302) canister is used to store reacting chemicals that provide for a uniform heat flux qi'' to its inner surface. The canister is suddenly submerged in a liquid bath of temperature Tambient < Ti, where Ti is the initial temperature of the canister wall. (a) Assuming negligible temperature gradients in the canister wall and a constant heat flux qi'', develop an equation that governs the variation of the wall temperature with time during the transient process. What is the initial rate of change of the wall temperature if qi'' = 105 W/m^2? (b) What is the steady-state temperature of the wall? (c) Determine the wall temperature as a function of time.arrow_forwardAcertain superinsulation material having a thermal conductivity of 2*10^-4 W/m*^ C is used to insulate a tank of liquid nitrogen that is maintained at - 196 degrees * C : 199 kJ is required to vaporize each kilogram mass of nitrogen at this temperature. Assuming that the tank is a sphere having an inner diameter (ID) of 0.52 m, estimate the amount of nitrogen vaporized per day for an insulation thickness of 2.5 cm and an ambient temperature of 21 degrees * C . Assume that the outer temperature of the insulation is 21 degrees * C .arrow_forward
- An ordinary egg can be approximated as a 5.5-cm-diameter sphere whose thermal conductivity of roughly k = 0.6- W mk overall density of p = 1000; and heat capacity of C₂ = 3000- kg m² The egg is initially at a uniform temperature of T₂ = 10°C and is dropped into boiling water at T.. = 90°C W - determine how long it will take for the egg to m²K Taking the convective heat transfer coefficient to be h reach T = 70°C. In solving the problem, please follow the steps below. For the Lump Model In solving this problem, please use the lump model method (ignoring the requirement of small Biot number and discuss the outcomes, 1. 2. Compute the characteristic length Lc Compute the volume and surface area of the sphere (as the egg model) Vol As 3. Compute the diffusivity α = = 10- k p Cp = J kgk Compute non-dimensional excessive temperature 0 = h Lc k 4. Compute the Biot number using the characteristic length found above Bi = T-Too 5. Ti-Too 6. Calculate the Fourier number from the equation =…arrow_forwardA chromel–constantan thermocouple measuring the temperature of a fluid is connected by mistake with copper–constantan extension leads (such that the two constantan wires are connected together and the copper extension lead wire is connected to the chromel thermocouple wire). If the fluid temperature was actually 250 C and the junction between the thermocouple and extension leads was at 90 C, what e.m.f. would be measured at the open ends of the extension leads if the reference junction is maintained at 0 C? What fluid temperature would be deduced from this (assuming that the connection error was not known)?arrow_forwardHi, can you help me with the following problem? A thermally insulated tank of water 2 m x 2 m, depth 1 m is stirred with a paddle for threehours. If the paddle is driven by a motor whose shaft power is 8 kW determine the rate ofchange of temperature in degrees C per hr and the increase in temperature of the water.The specific heat of water is 4200 J/kgC. Identify a system and start your analysis from anappropriate form of the Fist Law of Thermodynamicsarrow_forward
- QUESTION 2 A stainless steel sphere AISI 316 (k = 18.3 W/m.°C, C, = 550 J/kg.°C and p = 8238 kg/m) is initially u %3D The sphere is suddenly placed in a controlled temperature water bath (k = 0.6 W/m.°C, C, = 4187 J/kg. with h = 146 W/m2.°C. If the characteristic length for the sphere Lc = 0.05, then Bi # is around !3! %3D !! %3D O 12.17 O None of the options. O 0.4 O 0.006 O 0.08arrow_forwardSuppose that a rod of length 150 cm is immersed in steam untill it's temperature is uo =2720c.At time t = 0,its lateral surface is insulated and its two ends are imbedded in ice at 0°C.Calculate the rod's temperature at at point on the rod at a distance x-95cm after 32 seconds ,for thermal diffisuvity K3D0.005.arrow_forwardThe physics of the conduction heat transfer of thermosses phenomenon and the mathematical model should be discussed.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning