Consider the fuel element of Example 5.11, which operates at a uniform volumetric generation rate of
(a) Calculate the temperature distribution 1.5 s after the change in operating power and compare your results with those tabulated in the example. Hint: First determine the steady-state temperature distribution for
(b) Use your FEHT model to plot temperature histories at the midplane and surface for
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Chapter 3 Solutions
Introduction to Heat Transfer
- Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are p=(1200*32)kg/mº, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux 9" =1000 W/m² is applied to the upper surface. The right and left surfaces are also kept at 0°C. Bottom surface is insulated. 9" (W/m) T=0°C T=0°C W=(10*32)cm B=(30*32)cmarrow_forwardA 1-D conduction heat transfer problem with internal energy generation is governed by the following equation: +-= dx2 =0 W where è = 5E5 and k = 32 If you are given the following node diagram with a spacing of Ax = .02m and know that m-K T = 611K and T, = 600K, write the general equation for these internal nodes in finite difference form and determine the temperature at nodes 3 and 4. Insulated Ar , T For the answer window, enter the temperature at node 4 in Kelvin (K). Your Answer: EN SORN Answer units Pri qu) 232 PM 4/27/2022 99+ 66°F Sunny a . 20 ENLARGED oW TEXTURE PRT SCR IOS DEL F8 F10 F12 BACKSPACE num - %3D LOCK HOME PGUP 170arrow_forward2. Consider the temperature distributions associated with a dx differential control volume within the one-dimensional plane walls shown below. T(x,00) T\x,00) * dx * dx (a) (Б) Tx,1) T(x,1) * dx dx (c) (d) (a) Steady-state conditions exist. Is thermal energy being generated within the differential control volume? If so, is the generation rate positive or negative? (b) Steady-state conditions exist as in part (a). Is the volumetric generation rate positive or negative within the differential control volume? (c) Steady-state conditions do not exist, and there is no volumetric thermal energy generation. Is the temperature of the material in the differential control volume increasing or decreasing with time? (d) Transient conditions exist as in part (c). Is the temperature increasing or decreasing with time?arrow_forward
- A long insulated tube is doped with an exothermic ma- terial which generates steady and uniform heat at rate of è [W/m³]. The tube has an inner radius r₁ and outer radius r₂. The temperature of the outer insulated sur- face is T₂. This tube is used to heat a liquid flowing through it. (a) Write the governing differential equation and boundary conditions to determine the tempera- ture distribution inside the tube. (b) What is the heat flux supplied to the liquid by the tube? e (√₂²-1₁²) / 21₁ 1 Fluid Figure 2: Schematic Insulation T₂ Narrow_forwardRadioactive wastes are packed in a thin-walled spherical container. The wastes generate thermal energy nonuniformly according to the relation ġ = ġ, 1–(r/r.)* | where ġ is the local rate of energy generation per unit volume, ġ, is a constant, and r, is the radius of the container. Steady- state conditions are maintained by submerging the container in a liquid that is at T, and provides a uniform convection coefficient h. Coolant T, h - ġ = 4, [1– (rlr,²] 11arrow_forward3.4 Estimate the rate of heat loss due to radiation from a covered pot of water at 95 ° C. How does this compare with the 60 W that is lost due only to convection and conduction losses? What amount of energy input would be needed to maintain the water at its boiling point for 30 minutes? The polished stainless steel pot is cylindrical, 20 cm in diameter and 14 cm high, with a tight-fitting flat cover. The air temperature in the kitchen is about 25 ° C. State any assumptions you make in deriving your estimatesarrow_forward
- Consider a wall of thickness 50 mm and thermal conductivity 14 W/m.K, the left side (x-0) is insulated. Heat generation (q,) is present within the wall and the one dimensional steady-state temperature distribution is given by T(x) = ax +bx+c [°CJ, where c 200 °C, a = -1144 °C/m is the heat fluxes at the right side, x L, (kW/m)? b= needs to he determined, and x is in meters. What 9, K 4L) Insulationarrow_forwardNUMBER 4 A food product wants to be produced in a small round shape (pellet) by freezing it in a water blast freezer freezer. Air freezer operates at -30 ° C. The initial product temperature is 25 ° C. The pellet has a diameter of 1.2 cm, and a density of 980 kg / m³. The initial freezing temperature is -2.5 ° C. The latent heat of freezing of the product is 280 kJ / kg. The thermal conductivity of the frozen product is 1.9 W / (m ° C). The convective heat transfer coefficient is 50 W / (m² K). Calculate the freeze time. t f = hourarrow_forwardThe composite wall of an oven consists of three materials, two of which are of knownthermal conductivity, kA = 20 W/m – K and kC = 50 W/m – K, and known thickness, LA =0.30 m and LC = 0.15 m. The third material, B, which is sandwiched between materialsA and C, is of known thickness, LB = 0.15 m, but unknown thermal conductivity kB.Under steady – state operating conditions, measurements reveal an outer surfacetemperature of 600 oC, and an oven air temperature of 800 oC. The inside convectioncoefficient h is known to be 25 W/m2 – K. total rate of heat transfer = 550 W/m2.What is the value of kB?arrow_forward
- Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are p= 62400 kg/m', k-400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux q%=1000 W/m² is applied to 2. the upper surface. The right and left surfaces are also kept at 0°C. Bottom surface is insulated. 9% (W/m³) y4 T = 0 °C T = 0°C W= 520 cm B=1560 cmarrow_forward(3) The thermal conductivity of helium at 400 K is 0.176 W m-! K-1. Knowing only this datum, estimate the thermal conductivity of helium at 800 K. Compare your estimate to the value obtained from the figure below. 06 as 02 01 co CO.N A HCI Cl, 200 400 00 Temperature, K 1200 1400 600 What do you conclude about the equation that you used for your estimate?arrow_forwardContinuous temperature distribution in a semi-permeable material with laser radiation on it, thickness L and with a heat conduction coefficient k, T(x)=-A/k.a^2.e^-ax+Bx+C It is given by equality. Here A, a, B and C are known constants. For this case, the radiation absorption in the material manifests itself in a uniform heat generation term in the form q (x). a) Obtain a relationship for the type that gives the conduction heat fluxes on the front and back surfaces. b) get a correlation for q(x) c) Obtain a relation that gives the radiation energy produced per unit surface area in the whole material.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning