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Assume steady-state, one-dimensional heat conduction through the symmetric shape shown.
Assuming that there is no internal heat generation, derive an expression for the thermal conductivity
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Introduction to Heat Transfer
- 2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .arrow_forward2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.arrow_forwardQuestion 5:Assume steady-state, one-dimensional heat conduction through the symmetric shape shown in Figure 1.Assuming that there is no internal heat generation, derive an expression for the thermal conductivity k(x) for these conditions: A(x) = (1 -x), T(x) = 300(1 - 2x -x3),and q = 6000 W, where A is in square meters, T in kelvins, and x in meters. Consider x= 0 and 1arrow_forward
- Classical Mechanics By writing the Fourier heat conduction equation, we can find the meaning of each term in the equation in units. Please explain.25mm in diameter, 30mm in length, the temperatures of both sides respectively T1 = 40.2oC, T2 = 38.9oC, a cylindrical size with a given thermal power amount of 22.4W Find the heat transfer coefficient of the material.arrow_forwardHow long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has properties similar to water with a density of = 1000 kg/m3 and thermal conductivity of k = 0.606 Watts/(mC) and specific heat of c = 4182 J/(kg C). Suppose that an egg is fully cooked when the temperature at the center reaches 70 C. Initially the egg is taken out of the fridge at 4 C and placed in the boiling water at 100 C. Since the egg shell is very thin assume that it quickly reaches a temperature of 100 C. The protein in the egg effectively immobilizes the water so the heat conduction is purely conduction (no convection). Plot the temperature of the egg over time and use the data tooltip in MATLAB to make your conclusion on the time it takes to cook the egg in minutes.arrow_forwardBy writing the Fourier heat conduction equation, we can find the meaning of each term in the equation in units. Please explain.25mm in diameter, 30mm in length, the temperatures of both sides respectively T1 = 40.2oC, T2 = 38.9oC, a cylindrical size with a given thermal power amount of 22.4W Find the heat transfer coefficient of the material.arrow_forward
- A vertical cylinder 6 ft tall and 1 ft in diameter might be used to approximate a man for heat-transfer purposes. Suppose the surface temperature of the cylinder is 78°F, h=2 Btu/h · ft2 . °F, the surface emissivity is 0.9, and the cylinder is placed in a large room where the air temperature is 68°F and the wall temperature is 45°F. Calculate the heat lost from the cylinder. Repeat for a wall temperature of 80°F. What do you conclude from these calculations? Known, Find, Schematic Diagram, Assumption, Properties, Analysis and Commentsarrow_forwardA vertical cylinder 6 ft tall and 1 ft in diameter might be used to approximate a man for heat-transfer purposes. Suppose the surface temperature of the cylinder is 78°F, h=2 Btu/h · ft2 . °F, the surface emissivity is 0.9, and the cylinder is placed in a large room where the air temperature is 68°F and the wall temperature is 45°F. Calculate the heat lost from the cylinder. Repeat for a wall temperature of 80°F. What do you conclude from these calculations?arrow_forwardThe composite wall of a furnace consists of three different materials, two of which have known thermal conductivity (ka = 20 W/m°C and kc = 50 W/m°C) and thicknesses La = 0.30 m and Lb = 0.15 m. The third material (B) is between A and C, with a thickness of 0.15 m, but its thermal conductivity (kb) is unknown. Under steady-state operating conditions, measurements reveal a temperature of 20 °C on the external surface, 600 °C on the internal surface, and a furnace ambient temperature of 800 °C. The internal convection coefficient is 25 W/m²°C. What is the value of kb?arrow_forward
- Question 5: Assume steady-state, one-dimensional heat conductionthrough the symmetric shape shown in Figure 1.Assuming that there is no internal heat generation, derivean expression for the thermal conductivity k(x) for theseconditions: A(x) = (1 -x), T(x) = 300(1 - 2x -x3),and q = 6000 W, where A is in square meters, T inkelvins, and x in meters. Consider x= 0 and 1arrow_forwardIn the given figure, the two-dimensional steady state heat conduction has a square network structure with dimensions 0≤x≤L and 0≤y≤L. Find the temperature values at m=1,2,3 and 4 nodes by subtracting the finite difference heat conduction equations for the given network structure with dimensions ∆x=∆y=L/3.arrow_forwardA uniform internal energy generation occurs in a plane wall with a thickness of 60 mm and a constant thermal conductivity of 3W / m. K. For these conditions, the temperature distribution has the form T (x) = a + bx + c x?. The surface at x = 0 has a temperature = T = 110 ° C and experiences convection with a fluid for which To = 25 ° C and h = 300 W / m². K. The surface at x = L is well insulated. For one - dimensional, steady - state conduction (a) calculate the volumetric energy generation rate. (b) determine the coefficients a, b, and c by applying the boundary conditions to the prescribed temperature distribution.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning