The temperature at the point (x, y, z) in a substance with conductivity K = 5.5 is u(x, y, z) = 4y2 + 4z2. Find the rate of heat flow inward across the cylindrical surface y2 + z2 = 7, 0 ≤ x ≤ 2.
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The temperature at the point (x, y, z) in a substance with conductivity K = 5.5 is u(x, y, z) = 4y2 + 4z2. Find the rate of heat flow inward across the cylindrical surface y2 + z2 = 7, 0 ≤ x ≤ 2.
I came up with 8466.59 and it's wrong.
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- 5. The temperature at the point (z,y) on a metal plate is modeled by T(x,y) = 400e-(+)/2 in °C, with 220, y 20. Find the directions of no change in heat on the plate from the point (3.5). Answer:A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by 15 – 9(x2 + y + z?) °C. Use the fact that heat flow is given by the vector field F w(x, y, z) -KVw and the rate of heat flow across a surface S within the solid is given by -K s Vw dS. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K 400 kW/(m · K)). (Use symbolic notation and fractions where needed.) -K Vw dS = kWThe subject is differential equations
- The shaft is supported by a smooth thrust bearing at A and a smooth journal bearing at B. (Figure 1) -0.8 m 600 N-m -0.8 m -0.8 m 900 N Draw the shear diagram for the shaft. Draw the moment diagram for the shaft.Using an appropriate method, find the general solution for the following differential equation, dy +2= cos 2x . dxAn electric heater producing 260 W of heat is used to warm up a room containing 7 m3 of air. If we assume the room is perfectly sealed and there is no heat loss through the room boundaries, such that all of the heater output goes into increasing the air temperature, how long will it take to heat up the air in the room from 5.0 °C to 24.1 °C? Give your answer to the nearest minute and assume that the specific volume (v = 0.85 m3/kg) and specific heat capacity at constant volume (cv = 1.005 kJ/(kg K)) remain constant throughout the heating process.
- 3. An ant is traveling along the edge of a helix-shaped surface and the path taken is gi by x= cost, y=sint, z= 2t , 0Problem 1 Show that if the following problem has a solution it is unique -k = f in (0,L)× (0,T), (1) u(0,t) = g,(t),"(L,t) = g,(t),0find a real general solution: * y + 4y' + 5y =x +2A net force F = 6t? along the x-direction acts on an object of mass m = seconds and F is in Newtons). The object is initially at rest and the force acts on the object during the 3kg (t is time in %3| time interval 04. Suppose an xy-coordinate system is located in space such that the temperature T at the point (x ; y) is given by T =00. Determine the gradient of T with x²+y2 respect to the distance at the point P(1; 3), use the gradient to find the directional derivative of T at P in the direction of a = i – j and then calculate the rate of change of T in this direction.3. Thermal conductivity of a substance is measured as k = k, TIT, . Find an average value for thermal conductivity in the temperature range of T1 and T2. [Ans. = (k, /272 xT} 2 – T}/2) (T2 – T;) 1|SEE MORE QUESTIONSRecommended textbooks for youElements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill EducationControl Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEYElements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill EducationControl Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY