A solid, truncated cone serves as a support for a system that maintains the top (truncated) face of the cone at a temperature
The thermal conductivity of the solid depends on temperature according to the relation
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Introduction to Heat Transfer
- As a designer working for a major electric appliance manufacturer, you are required to estimate the amount of fiberglass insulation packing (k = 0.035 W/m K) that is needed for a kitchen oven shown in the figure below. The fiberglass layer is to be sandwiched between a 2-mm-thick aluminum cladding plate on the outside and a 5-mm-thick stainless steel plate on the inside that forms the core of the oven. The insulation thickness is such that the outside cladding temperature does not exceed 40C when the temperature at the inside surface of the oven is 300C. Also, the air temperature in the kitchen varies from 15Cto33C, and the average heat transfer coefficient between the outer surface of the oven and air is estimated to be 12.0W/m2K. Determine the thickness of the fiberglass insulation that is required for these conditions. What would be the outer surface temperature when the inside surface of the oven is at 475C?arrow_forward4x F2 # 3 E 4, F3 54 $ R F4 Ac = 1m² ▬ H DII x= 1 m (4) Consider a wall (as shown above) of thickness L-1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h= 1 W/m²K and an ambient temperature T. 1 K. There is no heat generation inside the wall. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). % To,1 = 1 K h₁ = 1 W/m²K 5 Q Search F5 T T₁ A 6 x=0 F6 à = 0 W/m³ k= 1W/mK L=1m Y 994 F7 & 7 T₂ U Ton2 = 1 K h₂ = 1 W/m²K1 PrtScn F8 Page of 7 ) 0 PgUp F11 Parrow_forwardWhat will be the rise in temperature in 30 minutes of a block of copper of 500-gram mass if it is joined to a cylindrical copper rod 20 cm long and 3.0 mm in diameter when a temperature difference of 80 degree Celsius is maintained between ends of the rod? The thermal conductivity of copper is 1.02 cal/cm2-sec-°C/cm (neglect heat losses). Please include FBDarrow_forward
- A square steel bar of side length w = 0.21 m has a thermal conductivity of k = 15.6 J/(s⋅m⋅°C) and is L = 2.7 m long. One end is placed near a blowtorch so that the temperature is T1 = 95° C while the other end rests on a block of ice so that the temperature is a constant T2. a. input an expression for the heat transferred to the cold end of the bar as a function of time using A=w^2 as the cross-sectional area of the bar. b. how much energy in joules was conducted in 1 hour, assuming t2=0*C c. input an expression for the mass of the water melted in one hour using Q1 from above and Lf in the latent heat of fusion. mw=arrow_forwardShape Factor Conduction Problem A cylindrical pipeline that is used for the transport of crude oil is buried in the soil horizontally such that its centerline is 1.5 m (z) below the surface. The pipe has the outer diameter of 0.5 m (D) and is coated with a 100 mm thick layer of glass insulation on the outside. Assume that heated oil at 120 °C flows through the pipe and the soil surface temperature is at 0 °C (T2). The soil thermal conductivity is known as 0.5 W/m-K, and the glass insulation thermal conductivity is known as 0.07 W/m-K. What is the rate of heat loss per unit length of the pipe (W/m)? Soil Glass insulation Oil, Tarrow_forwardQ1/A long cylindrical shell of inner radius R, = 1 cm, outer radius R₂ = 2 cm, and length L = 10 m is shown in the Figure. The inner wall of cylindrical shell is maintained at constant temperature T₁ = 10 C and outer wall is maintained at constant temperature T2 Calculate the temperature at r = 1.5 cm (Consider radial conduction only). 20 C. Assumptions: System is in steady state. Thermal conductivity, k= 22.5 W/m C, is constant. System follows Fourier's law of heat conduction. Heat loss in axial direction is negligible, T₁ - R₂ T₂arrow_forward
- 2-1. Temperature Response in Cooling a Wire. A small copper wire with a diameter of 0.792 mm and initially at 366.5 K is suddenly immersed in a liquid held constant at 311 K. The convection coefficient h 85.2 W/m K. The physical properties can be assumed constant and are k =374 W/m K, c, = 0.389 kJ/kg K, and p = 8890 kg/m2. (a) Determine the time in seconds for the average temperature of the wire to drop to 338.8 K (one-half the initial temperature difference). (b) Do the same but for h 11.36 W/m2 K (c) For part (b), calculate the total amount of heat removed for a wire 1.0 m р u (A long. (a) t 5.66 s Ans. the Smou hire is lons asbume Nhere rraolius , here radlius yinder hitu x Chapter 14 Principles of Unsteady-State Heat Transferarrow_forwardDetermine k, thermal conductivity of a wall if q = 1000 kcal/m2 -hr at thickness, k = 33 mm and ∆t = 30°C.arrow_forwardThe figure shows the cross section of a wall made of three layers. The thicknesses of the layers are L1. L2 =0.500 L1. and L3 = 0.350 L1. The thermal conductivities are k1, k2 = 0.800 k1, and k3 = 0.680 k1. The temperatures at the left and right sides of the wall are TH = 20 °C and Tc = -10 °C, respectively. Thermal conduction is steady. (a) What is the temperature difference AT2 across layer 2 (between the left and right sides of the layer)? If k2 were, instead, equal to 1.100 k1, (b) would the rate at which energy is conducted through the wall be greater than, less than, or the same as previously, and (c) what would be the value of AT2? k1 ko k3 TH Tc L1 L9 L3 (a) AT2 = i (b) (c) AT2= iarrow_forward
- 6. a. The heat flux applied to the walls of the biomass combustion furnace is 20 W/m2. The furnace walls have a thickness of 10 mm and a thermal conductivity of 12 W/m.K. If the wall surface temperature is measured to be 50oC on the left and 30oC on the right, prove that conduction heat transfer occurs at a steady state!b. Heating the iron cylinder on the bottom side is done by placing the iron on the hotplate. This iron has a length of 20 cm. The surface temperature of the hotplate is set at 300oC while the top side of the iron is in contact with the still outside air. To reach the desired hotplate temperature, it takes 5 minutes. Then it takes 15 minutes to measure the temperature of the upper side of the iron cylinder at 300oC. Show 3 proofs that heat transfer occurs transientlyarrow_forwardPlaster Insulation Brick Inside Outside Air Air R/2 R3/2 G R/2 A particular house wall consists of three layers and has a surface area A. The inside layer is made of plaster board, the middle layer is made of fiberglass insulation, and the outside layer is made of brick. The thermal conductivity of all three layers is known, and the thickness of the plaster board and siding are also known. The convection coefficient for the inside and outside wall surfaces are known: System_Parameters - (h; = 40.0 h, = 60.0 k = 0.2 k = 0.04 k3 = 0.3 A= 30.0) System_Parameters = (L = 10.0 L2= unknown L3 = 100.0 cp1 = 950.0 c p2 = 10.0 cp3= 800.0 P1 = 700.0 Pz = 0.5 P3= 2000.0) W - mm; A ~ m²; k ~. m °C ;p~ 8: T ~ °C kg °C L m² °C m- a) If the thermal capacitances of the walls is ignored, How thick must the insulation layer be so that the heat loss is no greater than 400W if the outside temperature is -15-C? b) Now consider the situation where the thermal capacitance is also considered. Develop the state…arrow_forwardWhich of the following statements are correct in the context of thermal conductivity? (Check all that apply.) Check All That Apply The thermal conductivity of gases is proportional to the square root of absolute temperature. The thermal conductivity of liquids is proportional to the square root of absolute temperature. The thermal conductivity of most liquids decreases with increasing temperature. The thermal conductivity of most liquids increases with increasing temperature.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning