Concept explainers
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
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Fundamentals of Heat and Mass Transfer
- A plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.arrow_forwardAs 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_forwardA plane wall of thickness 2L has internal heat sources whose strength varies according to qG=qocos(ax) Where qo is the heat generated per unit volume at the center of the wall (x=0) and a is a constant. If both sides of the wall are maintained at a constant temperature of Tw, derive an expression for the total heat loss from the wall per unit surface area.arrow_forward
- Shape 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_forwardThe inner and outer radii of a hollow cylinder are 15 mm (r, ) and 25 mm (r, ), respectively. The temperatures of the inner and outer walls are 400°C (T,) and 350°C (T,), respectively. The thermal conductivity of the cylinder material obeys the relationship K = (400-0.05T) W/mK where T is in degrees Celsius. Find the heat transferred from the hollow cylinder per unit length. The thermal conductivity,arrow_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
- What 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_forwardDetermine k, thermal conductivity of a wall if q = 1000 kcal/m2 -hr at thickness, k = 33 mm and ∆t = 30°C.arrow_forwardConsider a copper plate that has dimensions of 3 cm x 3 cm x 7 cm (length, width, and thickness, respectively). As shown in the following figure, the copper plate is exposed to a thermal energy source that puts out 126 J every second. The density of copper is 8,900 kg/m³. Assume there is no heat loss to the surrounding block. 126 J Copper Insulation Ⓡ What is the specific heat of copper (in J/(kg K))? J/(kg. K) What is the mass of the copper plate (in kg)? kg How much energy (in J) will be consumed during 11 seconds? J Determine the temperature rise (in K) in the plate after 11 seconds.arrow_forward
- under steady-state conditions. If you are given T1 = 200 °C and T2 = 164 °C, determine: a) the conduction heat flux, q,.cond, in m2 W from x = 0 to x = L b) if the dimensions of the triangle ares 15 mm and h 13 mm, calculate the heat transfer due to convection, q,y, in W at x = L Finsulation T2 T T = 20°C h = 500 W/m2.K Triangular Prism x L x 0 L= 50 mm k = 100 W/m-Karrow_forwardDetermine the heat conduction of a boiler if you are given the following data: The thickness of the boiler is 15 cm, the T1 is the temperature of the water is 25°C and the T2 of the steam is 110°C, the thermal conductivity The boiler material is iron (use presentation table), the boiler area is 4.5 m^2arrow_forwardA 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_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning