The time evolution of the temperature of an object follows the Newton's cooling lawsdTdx=-k(T - Ts),where the term k = 2.2 (1/s) is the heat transfer constant, and Tg = 25.6° C is the ambient temperature.The initial temperature of the object at time t = = 0 is T(t = 0) = 200°C.°CUse the Euler's method, and a time step of h=0.2s, calculate:When t = = 0.2s, T =°CWhen t 1s, T =

Newtons Cooling Law is given as, dTdX=-k (T-Ts) K= 2.2 1/s Ts =25.6 °C t=0 T(t=0) = 200 °C h=…

The time evolution of the temperature of an object follows the Newton's cooling laws dT dx where the term k = = 2.2 (1/s) is the heat transfer constant, and T = 25.6° C is the ambient tem The initial temperature of the object at time t = = 0 is T(t = 0) 200°C. -k(T - Ts), Use the Euler's method, and a time step of h=0.2s, calculate: When t = 0.2s, T = °C -

The time evolution of the temperature of an object follows the Newton's cooling laws dT dx where the term k = = 2.2 (1/s) is the heat transfer constant, and T = 25.6° C is the ambient tem The initial temperature of the object at time t = = 0 is T(t = 0) 200°C. -k(T - Ts), Use the Euler's method, and a time step of h=0.2s, calculate: When t = 0.2s, T = °C -

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.5P: To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the...

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To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the material is subjected to a uniform heat flux of 2500 W/m2 while thermocouples embedded in the wall at 2.5 cm. intervals are read over a period of time. After the system had reached equilibrium, an operator recorded the thermocouple readings shown below for two different environmental conditions: Distance from the Surface (cm) Temperature (C) Test 1 0 40 5 65 10 97 15 132 Test 2 0 95 5 130 10 168 15 208 From these data, determine an approximate expression for the thermal conductivity as a function of temperature between 40 and 208C.
Newtons laws of cooling proposes that the rate of change of temperature is proportional to the temperature difference to the ambient (room) temperature. And can be modelled using the equation: dT/dt = -k (T-Ta)It can also be written as dT/T-Ta = -k dtWhere:T = Temperature of materialTa = Ambient (room) temperaturek = A cooling constanta) integrate both sides of the equation and show that the temperature difference is given by:(T-Ta) = CoE^-kt(Co is a constant for this problem)B) calculate Co if the initial temperature is 70 degrees C and Ta = 20 degrees C?
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 20C 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?
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 13mm and thickness is 0.3mm. Find the time constant of the sheath. Material QU(kg/m)s(J/Kg - °c) 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 compound3210 800 Time constant of the bare material is, T=
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The initial temperature distribution of a 5 cm long stick is given by the following function. The circumference of the rod in question is completely insulated, but both ends are kept at a temperature of 0 °C. Obtain the heat conduction along the rod as a function of time and position ? (x = 1.752 cm²/s for the bar in question) 100 A) T(x1) = 1 Sin ().e(-1,752 (³¹)+(sin().e (-1,752 (²) ₁ + 1 3π TC3 .....) 100 t + ··· ....... 13) T(x,t) = 200 Sin ().e(-1,752 (²t) + (sin (3). e (-1,752 (7) ²) t B) 3/3 t + …............) C) T(x.t) = 200 Sin ().e(-1,752 (²t) (sin().e(-1,752 (7) ²) t – D) T(x,t) = 200 Sin ().e(-1,752 (²)-(sin().e (-1,752 (²7) ²) t E) T(x.t)=(Sin().e(-1,752 (²t)-(sin().e(-1,752 (²) t+ t + ··· .........) t +.... t + ··· .........) …..)
An unmanned submarine is equipped with temperature and depth measuring instruments and has radio 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 readings in steady state. The depth measuring instrument is approximately zero order and the temperature transducer first order with a time constant of 50 seconds. The water temperature on the sea surface, , is 20 °C and the temperature at a depth of x meters is given by the relation: If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5 meters / second, draw a table showing the temperature and depth measurements reported at intervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error in each temperature reading.What temperature does the submarine report at a depth of 1000 meters?
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A solid steel cube is stored in a freezer, where the temperature is −20.0 ̊C. While the cube is in the freezer, you measure its side length (L) to be 1.75050 meters. The cube is then placed outside for a long time, so that the temperature of the cube reaches the temperature of the air outside. As a result, the side length increases to 1.75170 meters due to thermal expansion. The coefficient of linear expansion for steel is 12.0×10−6 ̊C−1. (a) What is the temperature of the air outside? Give your answer in degrees Celsius ( ̊C). (b) What is the volume of the cube when its temperature is 20.0 ̊C? Give your answer in cubic meters (m3).
The wall (thickness L) of a furnace is comprised of brick material (thermal conductivity, k = 0.2 Wm¯' K'). Given that the atmospheric temperature is 0°C at both sides of wall, the density (p) and heat capacity (c) of the brick material are 1.6 gm cm³ and 5.0 J kg K¯l respectively. du Solve pc = k- subject to initial conditions as u(x,0) = x²(L – x). ốt Consider the case 2=- p² only.