1. A motor coil can be modeled as a hollow copper cylinder with an outer diameter of 50 mm, an inner diameter of 40 mm, and a length of 60 mm. The motor stalls at time t = 0 and, at this point, the copper experiences a step input in electrical heating of Po⚫u(t), where Po is 350 W. Assume that there is little time for significant heat loss to the environment so that the copper cylinder can be considered to be insulated. If the initial temperature is 30 °C, find the temperature as a function of time, T(t), analytically using Laplace transforms. Calculate the time required to reach the breakdown temperature of the wire insulation, which is approximately 250 °C. Write a script file in MATLAB® to: (a) determine the time for the copper to reach 250 °C using the command find; and (b) plot T(t) over this time interval. Copper has a density of 8960 kg/m³ and a specific heat of 390 J/kg-°C.

Your factory produces cryogenic refrigerators, and your task is to design a control system for the fridge, but, using the same sensor, you must also supply the end-user with temperature monitoring. The cryogenic freezer is controlled in a tight band around minus 85°C, therefore in controlling the fridge you need to have the most accurate information available regarding the operating range of the fridge (nominally at -85°C, but it can be colder and it can defrost if faulty and reach a maximum ambient temperature of say 50°C to be safe).   Due to the economy of RTD sensors, it is decided by management to use a PT100 RTD sensor (range -400°F to 1200°F) with a smart transmitter which needs to be set up correctly to a 4-20mA input on the PLC controlling the fridge. Taking the above conditions into account, the measuring range should be -100°C to 50°C (which should cater for the worst ambient temperature).   a)      Make sure the RTD is the correct choice  b)      Set the smart transmitter…

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

In this question, we are concerned with the evolution of the temperature u(x, t) in a homogeneous thin heat conducting rod of length L = 1. We can consider that the rod is laterally insulated as to have a one-dimensional problem. The evolution of the temperature is governed by the one-dimensional heat equation ди 0 0 = K Ət Əx2' Assume that this equation is subject to the following initial conditions u(x,0) = f(x) and boundary conditions (0, t) = 0 and ди (1,t) + и(1,t) — 0 (i) Discuss briefly the physical meaning of the boundary conditions.

Please answer question with as much detail as possible Please Use the “NCEES FE Reference Handbook 10.0.1” which can be downloaded for Free from https://ncees.org/ as your Reference for tables and formulas

Can I please get assistance with the transition from equation (3.72) through equation (3.73)? Step by Step. ***This is an example from my text book and not a homework problem.

**19. ssm Two cylindrical rods are identical, except that one has a thermal conductivity k and the other has a thermal conductivity k2. As the drawing shows, they are placed between two walls that are maintained at different temperatures Tw (warmer) and Te (cooler). When the rods are arranged as in part a of the drawing, a total heat Q' flows from the warmer to the cooler wall, but when the rods are arranged as in part b, the total heat flow is Q. Assuming that the conductivity k, is twice as great as k, and that heat flows only along the lengths of the rods, determine the ratio Q'/Q. k1 k2 Tw k2 Tc Tw Tc (a) (b)

An external wall of a building has a U value of 0.50 W/m^2K. The indoor temperature is21 degrees C and the outdoor temperature is -2.0 degrees C The steady-state heat loss is calculated to be 11.5W/m^2 The wall contains a layer of insulation 40 mm thick with a conductivity of0.035 W/mK. What would the insulation thickness need to be in order toreduce the steady state heat loss by 50%? answer = 0.11m ​​​​​​​please show all working

please i need solution in 20 mins help me . i will give positive feedback

Steady state temperatures at three nodes are given in K. This object generates heat itself at rate of q = 5×107 W/m³ and has a thermal conductivity of 20 W/m K. Two of its sides are maintained at a constant temperature of 300 K, while the others are insulated. Find temperatures at nodes 1, 2 and 3 in K. 5 mm 2 398.0 348.5 3 374.6 - Uniform temperature, 300 K 5 mm