Consider the following partial differential equation
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- NSLOM using Differential EquationsThe same engineer decides to look into rates of cooling for liquids toexperiment with different cooling solutions for servers. She finds thatthe rate of cooling for one liquid can be modelled by the equation:y = 48 × 0.99t(0 ≤ t ≤ 80)where y is the temperature of the liquid in degrees Celsius and t is thetime in minutes.(i) State whether the type of reduction for this model is linear orexponential. Describe how reduction rate differs between linear andexponential functions. (ii) Calculate the temperature when t = 20. [3](iii) Write down the scale factor and use this to find the percentagedecrease in the temperature per minute. (iv) Use the method shown in Subsection 5.2 of Unit 13 to find the timeat which the temperature is 30◦(v) Determine the halving time of the temperature.Describe comprehensively in essay form the role and significance of Partial Differential Equation (PDE) in CFD in engineering modeling and design. Please answer my question. Please. I'm begging you :((
- 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?Step 2 of the solution is incorrect for the answer.calculations does not add upThe outlet temperature will be: →T2=m˙1×T1+m˙3×T3m˙1+m˙3 =10×372.78+5×120010+5 =3727.8+600015=648.52 K ..................answerDerive the differential equation
- Describe Lagrangian Approach hence show that Lagrangian's equation is given as d/dt dL/dqj - dL/dqj = 0Complete the following table for refrigerant-134a. Show your work and explain how you got your values. T (oF) P psia) h (Btu/Ibm) X Phase description 80 78 15 0.6 10 70 180 129.46 110 1.0Problem: 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.
- for the following differential equation, determine (a) order, (b)degree, (c) linearity, (d) unknown function, and (e) independent variablesThe Derivative and DifferentiationQ5Two 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?