The degree of the differential equation: In dz² 20
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- Consider a flat plate or a plane wall with a thickness L and a long cylinder of radius r0. Both of these are made of materials such that they can be treated as lumped capacitances (Bi0.1). Show that in each case, the characteristic length lc, defined lc=(V/As), can be approximated as (L/2) and (ro/2), respectively.The subject is differential equationsThe block in the drawing has dimensions L0×2L0×3L0,where L0 =0.5 m. The block has a thermal conductivity of 300 J/(s·m·C˚). In drawings A, B, and C, heat is conducted through the block in three different directions; in each case the temperature of the warmer surface is 36 ˚C and that of the cooler surface is 6 ˚C Determine the heat that flows in 6 s for each case.
- Find the particular solution of the following differential equation: 100 V' = 200 - 10 V where V is the dependent and t is independent. Given that when t= 0 , V = 0. Find V at 2 seconds.Solve the following first order differential equations: dy/dx+ytanx=y^3sec^4xThe surface area of an unclothed person is 1.5m ^2 and thier skin tempature is 33 degree celcius. This ideal person is located in a room with a tempature of 65 dregrees F. and has an emissivity of e=0.95 suppose the room has dimensions 4mx9mx18m a) suppose you and your closest 10 friends come into this room and heat it up. suppose your clothes are in equilibium with your skin and have the same tempature and emissivity. Further suppose that your net power into the room remains constant . How long does it take before the room to get to hot say 95 degrees
- Newton's law of cooling states that dT/dt = k(T−t0), where T(t) is the temperature of the body that is cooling, T0 is the temperature of the surrounding medium and k is constant. Solve the differential equation.Unit of thermal conductivity in S.I. units is(A) J/m² sec(B) J/m °K sec(C) W/m °K(D) Option B and C above.The image shows a plane wall of thicknessΔx = 21 cm with a thermal conductivity k=0.7 W/(mK). Given that the temperature at point 2 is 283 K and that the heat flux from points 1 to 2 is 154 W/m2 calculate the temperature at point 1 in Kelvin to 1dp (decimal place
- A parachutist has a terminal velocity of -176 feet per second. That is, no matter how long a person falls, his or her speed will not exceed 176 feet per second, but it will get arbitrarily close to that value. The velocity in feet per second, v(t), after t seconds satisfies the differential equation v′(t) = 32 - k *v(t). What is the value of k?Give definition of unreliability F(t)of a component as function of time.Model the problem in terms of a differential equation