Use separation of variables to solve the 2D transient heat equation on a rectangular domain with homogeneous temperature boundary conditions. ди Ot C 2u მ12მ2 (1) u(0, y, t) = u(a, y, t) = 0 (2) 13 ۵ u(x, 0,t) = u(x, b,t) = 0 u(x, y, 0) = f(x, y)
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- An unmanned submarine is equipped with temperature and depth measuring instruments and hasradio equipment that can transmit the output readings of these instruments back to the surface.The submarine is initially floating on the surface of the sea with the instrument output readingsin steady state. The depth measuring instrument is approximately zero order and the temperaturetransducer first order with a time constant of 50 seconds. The water temperature on the seasurface, T0, is 20C and the temperature Tx at a depth of x metres is given by the relation:Tx = T0- 0.01x(a) If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5metres/second, draw a table showing the temperature and depth measurements reported atintervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error ineach temperature reading(b) What temperature does the submarine report at a depth of 1000 metres?The Fourier heat conduction equation has been used to obtain the temperature-time response during the cooking of meat. However, recent experimental studies have found processsed bologna meat to exhibit an anomalous behavior. In one experiment, two identical samples at different temperatures were brought into contact with each other. One sample was refrigerated at 8.2 0C, the other was at a room temperature of 23.1 oC. Thermocouples were inserted at the interface and in the room temperature sample at a distance of 6.3 mm from the interface. The graph shows the measured temperature-time response. Compare this response with a predicted response based on the heat conduction euqation. Measured properties of bologna meat areHeat Transfer question In order to cool down a hot steel sphere (its diameter is 5 cm), CO2 gas is blown over it through a pipe with a diameter of 10 cm. The CO2 gas is kept at atmospheric pressure while moving through a smooth pipe at a speed of 6 m/sec. The gas temperature entering the pipe is 300K and exiting the pipe is 340 K. The pipe temperature at the entrance is 350K and at the exit is 550K. The sphere is located just about the pipe exit. Find the convective heat transfer coefficient of the gas moving in the pipe, the heat transfer rate at the pipe and the pipe length. What is the surface temperature of the sphere if the heat transfer rate between the sphere and the gas is 7W and its surface temperature is higher than the gas?
- The term dT/dx Where T is temperature and x is length, in Fourier law conduction, is called Temperature GradientRequired to answer. Single choice. OPTIONS: 1.May be 2.May not be 3.True 4.FalseQ5Two large containers A and B of the same size are filled with different fluids. The fluids in containers A and B are maintainedat 0° C and 100° C, respectively. A small metal bar, whose initial temperature is 100° C, is lowered into container A. After1 minute the temperature of the bar is 90° C. After 2 minutes the bar is removed and instantly transferred to the othercontainer. After 1 minute in container B, the temperature of the bar rises 10°. How long, measured from the start of theentire process, will it take the bar to reach 99.9° C?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.
- A cup of coffee with cooling constant k = 0.09 min- 1 is placed in aroom at temperature 20°C.(a) How fast is the coffee cooling (in degrees per minute) when its temperature is T = 80° C?(b) Use the Linear Approximation to estimate the change in temperatureover the next 6 s when T = 80°C.( c) If the coffee is served at 90°C, how long will it take to reach an optimaldrinking temperature of 65°C?Problem: Convection related Water enters a tube at 27°C with a flow rate of 450 kg/h. The rate of heat transfer from the tube wall to the fluid is given as qs′(W/m)=ax, where the coefficient a is 20 W/m^2 and x(m) is the axial distance from the tube entrance. (a) Beginning with a properly defined differential control volume in the tube, derive an expression for the temperature distribution Tm(x) of the water. (b) What is the outlet temperature of the water for a heated section 30 m long? (c) Sketch the mean fluid temperature, Tm(x), and the tube wall temperature, Ts(x), as a function of distance along the tube for fully developed and developing flow conditions.d) Find the time constant associated with this transient analysis. e) Find the time it takes for the temperature of the wire surface to reach a temperature that is within 2∘C of the steady-state temperature of the wire.
- A thermocouple junction of spherical form is to be used to measure the temperature of a gas stream. h = 400w/m^2 deg C; k(thermocouple junction) = 20 w/m deg C; cp = 400 J/kg deg C; and density = 8500 kg/m^3;Calculate the following:i. Junction diameter needed for the thermocouple to have the thermal time constant of one second.ii. Time required for the thermocouple junction to reach 198 deg C if junction is initially at 25 deg C and is placed in gas stream which is at 200 deg C.How 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.A J- type thermocouple is used to measure the temperature in a heating process. Sheath material used is SS316. The length of the sheath is 10mm and thickness is 0.2mm. Find the time constant of the sheath. Material Q(kg/m3) s(J/Kg - oc) K(W/m-k) Platinum 21450 130 71.6 SS304 8030 500 21.4 SS316 7990 500 21.4 SS410 7750 460 24.9 Air 1.20 1005 0.025 MgO Powder 3580 877 26.8 Silicon compound 3210 800 3 Time constant of the bare material is, T= Answer