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Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius
where
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Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
- 2.34 Show that the temperature distribution in a sphere of radius . made of a homogeneous material in which energy is released at a uniform rate per unit volume , isarrow_forward1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.arrow_forwardA thermal system having a cylindrical form contains a sequence of cylindrical layers is used to cool hot gases. The thermal properties of the system materials are as follows : k = 231 W/m.K, c = 1033 J/kg.K and the density = 2702 kg/m^3. The gases to be cooled has a temperature equals to 500 C. Determine the temperature of the system that corresponds to 10 % of the maximum possible heat transfer between the gas and the system. Consider that the system has a characteristic length equals to 0.03 m. The heat convective coefficient is equal to 50 W/m^2.K. The initial temperature of the system is equal to 20 C. Select one: О а. 370 К O b. 489 K С. 341 К d. 410 Karrow_forward
- 1-D, steady-state conduction with uniform internal energy generation occurs in a plane wall with a thickness of 50 mm and a constant thermal conductivity of 5 W/m/K. The temperature distribution has the form T = a + bx + cx² °C. The surface at x=0 has a temperature of To = 120 °C and experiences convection with a fluid for which T.. surface at x= 50 mm is well insulated (no heat transfer). Find: (a) The volumetric energy generation rate q. (15) (b) Determine the coefficients a, b, and c. 20 °C and h 500 W/m² K. The To: = 120°C T = 20°C h = 500 W/m².K 111 Fluid T(x)- = q, k = 5 W/m.K L = 50 mmarrow_forwardA plane wall of thickness 2L = 2*33 mm and thermal conductivity k = 7 W/m-K experiences uniform volumetric heat generation at a rate q˙, while convection heat transfer occurs at both of its surfaces (x = −L, + L), each of which is exposed to a fluid of temperature T∞ = 31°C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a + bx + cx2 where a = 85°C, b = −-218°C/m, c = −-23,942°C/m2, and x is in meters. The origin of the x-coordinate is at the midplane of the wall. (a) Sketch the temperature distribution and identify significant physical features. (b) What is the volumetric rate of heat generation q˙ in the wall? (c) Obtain an expression for the heat flux distribution qx″(x). Is the heat flux zero at any location? Explain any significant features of the distribution. (d) Determine the surface heat fluxes, qx″(−L) and qx″(+L). How are these fluxes related to the heat generation rate? (e) What are the convection coefficients…arrow_forwardA plane wall of thickness 2L = 30 mm and thermal conductivity k = 7 W/m-K experiences uniform volumetric heat generation at a rate q, while convection heat transfer occurs at both of its surfaces (x = − L, + L), each of which is exposed to a fluid of temperature T = 20°C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a + bx + cx² where a = 82.0°C, b = -210°C/m, c = -2x 10°C/m², and x is in meters. The origin of the x-coordinate is at the midplane of the wall. (a) What is the volumetric rate à of heat generation in the wall? (b) Determine the surface heat fluxes, q" (L)and q ( + L). (c) What are the convection coefficients for the surfaces at x = - Land x = + L? The volumetric rate of heat generation in the wall, in W/m³: q = i W/m³ The surface heat flux, in W/m²: qx ( - L) = i The surface heat flux, in W/m²: q (+ L) = i W/m² W/m² The convection coefficients for the surface at x = - L, in W/m²-K: h(- L) = i W/m².K The convection…arrow_forward
- Thermodynamics In a solid sphere of 0.2 m diameter, heat is generated at the rate of 1.2 x 106 W/m3. The center temperature is 300°C. Conductivity is 50 W/m-K. What is the surface temperature?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_forwardWhich formula is used to calculate the heat conduction in the AXIAL direction in a vertically located pipe segment whose inner and outer surfaces are perfectly insulated. Here r, is inner radius, r, outer radius, Tri pipe inner surface temperature, Tro pipe outer surface temperature, L is the length of the pipe, T the temperature on the lower surface, Ty the temperature on upper surface. Tu r; Tro rarrow_forward
- Q1. Consider a plane wall (thermal conductivity, k = 0.8 W/mK, and thickness, fb1 = 100 mm) of a house as shown in Fig. Q1(a). The outer surface of the wall is exposed to solar radiation and has an absorptivity of a = 0.5 for solar energy, or=600 W/m². The temperature of the interior of the house is maintained at T1 = 25 °C, while the ambient air temperature outside remains at T2 = 5 °C. The sky, the ground and the surfaces of the surrounding structures at this location can be modelled as a surface at an effective temperature of Tsky = 255 K for radiation exchange on the outer surface. The radiation exchange inside the house is negligible. The convection heat transfer coefficients on the inner and the outer surfaces of the wall are h₁ = 5 W/m²-K and /1₂ = 20 W/m².K, respectively. The emissivity of the outer surface is = 0.9. T1 = 25 °C Ţ₁ Too1 = 25 °C T₁ k 100 mm Fig. Q1(a) Assuming the heat transfer through the wall to be steady and one-dimensional: (a) Solve the steady 1D heat…arrow_forwardWhat happens to heat transfer per unit time in conduction heat transfer as thermal conductivity decreases?arrow_forwardQ2. The inner and outer surfaces of a 6-m x 6-m brick wall of thickness 30 cm and thermal conductivity 0.69 W/m-°C are maintained at temperatures of 20°C and 5°C, respectively (Figure 2). Determine the rate of heat transfer through the wall, in W. Brick wall 20°C S°C 30 cm Figure 2arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning