steady-state temperature profile
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- A rod length l with the thermally insulated lateral surface is made of a material whose thermal conductivity varies as K = α sin (ln T), where α is a constant. The ends of the rod are kept at temperatures T1 and T2. Find the temperature T(x), where x is the distance from the end whose temperature is T1, and also find the heat flowing per second per unit cross-sectional area.Air with uniform velocity of U is flowing over flat square-shape plates with different arrangements given in figure below. One plate is used in arrangement (a), whereas four square plates are used in the arrangement (b). All the plates are the same size. What is the frictional forces ratio (Fp/Fa)? (Note: Assume laminar boundary layer condition along the plate arrangements) (a) (b)A// For laminar flow over a flat plate, the local heat transfer coefficient h, is known to -1/5 vary as x where x is the distance from the leading edge (x =0) of the plate. What is 3 the ratio of the average coefficient between the leading edge and some location x on the plate to the local coefficient at x? for velocity equation u 2-0.43x+x² Plot the local heat transfer coefficient over a 0.8 cm length(take T-35c)
- 4. The faces of the thin square plate in the below figure with side a = 21 are perfectly insulated. The upper side is kept at 100°C and the other sides are kept at 0°C. Find the steady-state temperature u(x, y) in the plate. y a a xA prismatic bar 50°F is imbedded in a rigid concrete wall. The bar is 40 in long and has a cross-sectional area of 4 in?. What is the axial force in the bar if its temperature is raised to 100°F? Assume cocfficient of thermal expansion is 5x10%F and modulus of clectricity is 32x10° psi.Consider the thermal system shown below. The temperature of the inflow liquid is kept constant, and the liquid inflow rate G kg/s is also kept constant. For t <0 the system is at steady state, wherein the heat input from the heater is U kcal/s and the temperature of the liquid in tank 2 is 0,°C. At t 0 the heat input is changed from U to U + u where u is small. This change will cause the temperature of the liquid in tank 2 to change from 02 to 02 +82. Taking the change in the heat input from the heater to be the input to the system and the change in the temperature of the liquid in tank 2 to be the output, obtain the transfer function 02(s)/U(s). Assume that the thermal capacitances of tanks 1 and 2 are Ci kcal/°C and C2 kcal/C, respectively, and that the specific heat of the liquid is c kcal/kg°C. The steady-state heat flow rates from tanks 1 and 2 are the same, Q kcal/s. The changes in and heat flow rates from tanks 1 and 2 are q2, respectively. U +u G Tank 1 O+ 0, O+ 0, O+ 42 Tank 2
- 3. The power P dissipated in a resistor is given by P = . If E=200 volts and R = 8 ohms, find the change in P resulting from a drop of 5 volts in E and an increase of 0-2 ohm in R.A U-tube is rotating at a constant angular velocity of w. The liquid (glycerin) rises to the level shown below. Obtain a relation for w in terms of g, ℎ, and L.Q5) A solid copper rod is of cross-sectional area 15 mm2 and length 2m. Calculate: a)its change in length when its temperature rises by 30oC b)the force needed to prevent it from expanding by the amount in (a). (given: for steel, the coefficient of linear expansion, α = 12 x 10-6 k-1 and young’s modulus is 2 x 1011 Pa) Assume that the proportional limit is not exceeded.
- 2.Turbulent flow is defined as the fluid moves in layers.one layer gliding smoothly over adjacent layer true O False1. When the force of 3 mN is applied to the plate the line AB in the liquid remains straight and has a velocity of 0.6x10-3 m/s. If the surface area of the plate in contact with the liquid is 0.6 m2, determine the approximate viscosity of the liquid. В B' 3 mN 4 mm ANo. 1. (10 Pts) An aluminum pipe with a length of 60 m at a temperature of 10°C rests freely on the ground. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe. (a) At what temperature (degrees Celsius) will the aluminum pipe be 15 mm longer than the steel pipe? (Assume that the coefficients of thermal expansion of aluminum and steel are aa=23x10-6/"C and as=12x10-6/ c, respectively.) (b) What is the axial stress developed in the aluminum pipe when the temperature was increased? 5 mm Aluminun Steel Figure No. 1