Chapter 3, Problem 3.19P

cylindrical fuel element for a gas-cooled nuclear reactor, the heat generation rate within the fuel element due to fission can be approximated by the relation: q(r) = q_0 [1 - (r/a)^2] W/m^3 where a is the radius of the fuel element and q_0 is constant. The boundary surface at r = a is maintained at a uniform temperature T_0. Assuming one-dimensional, steady-state heat flow, develop a relation for the temperature drop from the centerline to the surface of the fuel element. For radius a= 30mm, the thermal conductivity k = 10 W/m middot K and q_0 = 2 times 10^7 W/m^3, calculate the temperature drop from the centerline to the surface.

Hab. Tiruneh, [4/2/2023 1:23 AM]A solar flux q ^ * falls on a unit length of a very thin tube of diameter d. Inside the tube is a stationary water with initial temperature T_{i} (same as ambient and no gradient inside at any time) and absorbs some of the heat while the rest leaves by convection from the surface to the ambient at T_{m} Develop an equation that can help to determine the temperature of the water at any time. Plot the temperature of the water against time. For a long elapsed time what will be the temperature? To simplify the analysis use theta = T*T_{e} * d*theta = dT theta_{i} = T_{i}*T_{o} (initial condition. Hab. Tiruneh, [4/2/2023 11:53 AM]A flat wall is exposed to an environmental temperature of 38°C. The wall is covered with a layer of insulation 2.5 cm thick whose thermal conductivity is 1.4W / (m ^2 *` C and the temperature of the wall on the inside of the insulation is 315°C. The wall loses heat to the environment by convection. Compute the value of the convection…

Q2/ cylindrical electrical heating element (dissipated 1000 W/m) of diameter D=10 mm, thermal conductivity k=240 W/m K, density 2700 kg/m3, and specific heat cp = 900 J/kg K is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 27°C and 10 m/s, respectively. calculate the surface temperature per unit length of the heater.

Heat transfer to and from a reaction flask is often a critical factor in controlling reaction rate. The heat transferred (q) depends on a heat transfer coefficient (h) for the flask material, the temperature difference (∆T) across the flask wall, and the commonly “wetted” area (A) of the flask and bath, q = hA∆T. When an exothermic reaction is run at a given T, there is a bath temperature at which the reaction can no longer be controlled, and the reaction “runs away” suddenly. A similar problem is often seen when a reaction is “scaled up” from, say, a half-filled small flask to a half-filled large flask. Explain these behaviors.

Air at atmospheric pressure and 27 degree celsius is blown across a long 4.0-cm diameter tube at a velocity of 20 m/s. Determine the heat transfer rate per unit length. Assume that wall temperature is 60 degree celsius

A 1.2 m long vertical pipe, with a diameter 0.05 m, carrying a mixture of liquid water and vapor at atmospheric pressure is used to heat a very large liquid water tank, with water temperature maintained at 40 C. Calculate how much is the heat rate transferred from the pipe to the surrounding water at steady-state. (Consider the water in the tank at atmospheric pressure.)

Air at atmospheric pressure and 27oC is blown across a long 4.0-cm diameter tube at a velocity of20 m/s. Determine the heat transfer rate per unit length. Assume that the temperature of the wall is 60oC.