Derive the one-dimensional heat conduction equation for a spher
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1. Derive the one-dimensional heat conduction equation for a sphere.
2. Derive the combined one-dimensional heat conduction equation.
3. Derive the general 3D heat conduction equation for a cylindrical coordinate.
4. Derive the general 3D-general heat conduction equation for a spherical coordinate.
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- Derive the general 3D-general heat conduction equation for a spherical coordinate.Convert heat conduction from cylindrical coordinate to Cartesian coordinate?Derive a 2 dimensional transient heat conduction equation for a hot coffee in a mug. Assume that the coffee has a uniform temperature of 56 degree Celsius. Sketch the schematic diagram and propose your assumption for the derivation of the heat transfer equation.
- After a thorough derivation by Doraemon to establish an equation for cylindrical fuel rod of a nuclear reactor. Here he was able to come up an equation of heat generated internally as shown below. 96 = 9. where qG is the local rate of heat generation per unit volume at radius r, ro is the outside radius, and qo is the rate of heat generation per unit volume at the centre line. Calculate the temperature drop from the centre line to the surface for a 2.5 cm outer diameter rod having k = 25 W/m K, if the rate of heat removal from the surface is 1650 kW/m2 A 619 °C 719 °C C) 819 °C 919 °C E 1019 °C F None of these... Derive the general 3D heat conduction equation for a cylindrical coordinate. Show step-by-step solution and schematic diagram.Question 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 1
- PROBLEM 1: The block of 304 stainless steel shown below is well insulated on the front and back surfaces, and the temperature in the block varies linearly in both the x- and y-directions. Find: (a) The heat fluxes and heat flows in the x- and y-directions. (b) The magnitude and direction of the heat flux vector. 15°C 5°C 5 cm y 5 cm- 10 cm The thermal conductivity of 304 stainless steel is 14.4 W/m K. 10°C 0°CAssume 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 1.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 -3x),and q = 6000 W, where A is in square meters, T in Kelvin’s, and x in meters. Consider x= 0 and 1.
- 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 1Consider the square channel shown in the sketch operating under steady state condition. The inner surface of the channel is at a uniform temperature of 600 K and the outer surface is at a uniform temperature of 300 K. From a symmetrical elemental of the channel, a two-dimensional grid has been constructed as in the right figure below. The points are spaced by equal distance. Tout = 300 K k = 1 W/m-K T = 600 K (a) The heat transfer from inside to outside is only by conduction across the channel wall. Beginning with properly defined control volumes, derive the finite difference equations for locations 123. You can also use (n, m) to represent row and column. For example, location Dis (3, 3), location is (3,1), and location 3 is (3,5). (hint: I have already put a control volume around this locations with dashed boarder.) (b) Please use excel to construct the tables of temperatures and finite difference. Solve for the temperatures of each locations. Print out the tables in the spread…5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?