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Answer:
a) What is the surface temperature, in °C, after 400 s?
T (0,400 sec) = 800°C
b) Yes, the surface temperature is greater than the ignition temperature of oak (400°C) after 400 s
c) What is the temperature, in °C, 1 mm from the surface after 400 s?
T (1 mm, 400 sec) = 798.35°C
Explanation:
oak initial Temperature = 25°C = 298 K
oak exposed to gas of temp = 800°C = 1073 K
h = 20 W/m².K
From the book, Oak properties are e=545kg/m³ k=0.19w/m.k Cp=2385J/kg.k
Assume: Volume = 1 m³, and from energy balance the heat transfer is an unsteady state.
From energy balance:
Initial temperature wall =
Surface temperature = T
Gas exposed temperature =
Answer:
c = 18.0569 mm
Explanation:
Strategy
We will find required diameter based on angle of twist and based on shearing stress. The larger value will govern.
Given Data
Applied Torque
T = 750 N.m
Length of shaft
L = 1.2 m
Modulus of Rigidity
G = 77.2 GPa
Allowable Stress
г = 90 MPa
Maximum Angle of twist
∅=4°
∅=4*/180
∅=69.813 *10^-3 rad
Required Diameter based on angle of twist
∅=TL/GJ
∅=TL/G*/2*c^4
∅=2TL/G**c^4
c=∅
c=18.0869 *10^-3 rad
Required Diameter based on shearing stress
г = T/J*c
г = [T/(J*/2*c^4)]*c
г =[2T/(J**c^4)]*c
c=17.441*10^-3 rad
Minimum Radius Required
We will use larger of the two values
c= 18.0569 x 10^-3 m
c = 18.0569 mm