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A polished copper sphere of 10-mm diameter, initially at a prescribed elevated temperature
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Fundamentals of Heat and Mass Transfer
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- Subject mechanical. Caption: take time but solve handwriting accurate Solutions okarrow_forwardFor what situations will the lumped capacitance method be valid if a solid is in contact with a fluid? Circle all appropriate answers. (a) The resistance to conduction within the solid is small compared to the resistance to convection due to a fluid. (b) The temperature gradient within the solid is large. (c) The Biot number is small (less than 0.1). (d) All of the above. (e) None of the abovearrow_forwardA 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_forward
- 5.10 A steel sphere (AISI 1010), 100 mm in diameter, is coated with a dielectric material layer of thickness 2 mm and thermal conductivity 0.04 W/mK. The coated sphere is initially at a uniform temperature of 500°C and is suddenly quenched in a large oil bath for which T = 100°C and h = 3000 W/m² K. Estimate the time required for the coated sphere temperature to reach 150°C. Hint: Neglect the effect of energy storage in the dielectric material, since its thermal capacitance (pcV) is small compared to that of the steel sphere.arrow_forwardSix cylindrical core plugs of 2.54 cm diameter and 3.81 cm length were taken from an Alaskan North Slope reservoir. After cleaning, porosities of all the plugs were measured by a helium porosimeter. Subsequently, all samples were fully saturated with a 0.07 Ω m brine such that Sw = 1. Each sample was placed in a resistivity apparatus, and ΔV values were measured for a current flow of 0.01 A. Determine the formation factor F, for each core plug, and estimate parameters a and m for Archie’s formation factor equation. Core Plug ϕ (Fraction) ΔV (V) 1 0.175 1.72 2 0.19 1.45 3 0.165 1.99 4 0.23 1.1 5 0.16 2.15 6 0.15 2.45arrow_forwardFor metal-clad heating element of 6-mm diameter and emissivity ? = 1 is horizontallyimmersed in a water bath. The surface temperature of the metal is 255℃ under steady-stateboiling conditions. Estimate the power dissipation per unit length of the heater.arrow_forward
- 3.4 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_forward11. CD mmh A composite rod is made from stainless steel and iron and has a length of 0.50 m. The cross section of this composite rod is shown in the drawing and consists of a square within a circle. The square cross section of the steel is 1.0 cm on a side. The temperature at one end of the rod is 78 °C, while it is 18 °C at the other end. Assuming that no heat exits through the cylin- drical outer surface, find the total amount of heat Iron Stainless steel conducted through the rod in two minutes.arrow_forwardVolumetric expansion coefficients of simple materials are often well cataloged. However, the thermal expansion coefficient B of a human body is less well known. This could affect the human body's specific gravity and, therefore, measurements of its body-fat ratio. Suppose that a human body of weight wo on dry land is placed on a scale while completely immersed in formaldehyde of temperature T1- Once the temperature increases by AT, the scale reading drops by Aw. Derive an expression for ß in terms of AT, wo, and Aw by assuming that the ratio of the density of formaldehyde ef and the initial density of the body Po is R = Pf/pb. Assume also that pf does not change when heated. B = %3D If the body weighs 237.2 lb on dry land and his weight reading lowers by 0.237 lb when the formaldehyde is heated from 63.40 °F to 82.80 °F, calculate the coefficient of volume expansion of the body.* Assume R = 0.820. 1/°C B =arrow_forward
- P34.9 Two parallel metal plates separated by 1 cm are held at 300, and 298 K, respectively. The space between the plates is filled with N2 (or = 0.430 nm² and Cv, m = 5/2 R). Cv.m Determine the heat flux between the two plates in units of W cm².arrow_forwardA 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_forward8.2 From its definition and from the property values in Appendix 2, Table 13, calculate the coefficient of thermal expansion, , for saturated water at 403 K. Then compare your results with the value in the table.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning