JNTU
JNTU B.Tech III HEAT TRANSFER Previous Question Paper (January/February - 2021 - R16)
Answer any five questions. All questions carry equal marks.
Main
A long cylindrical rod of radius 5 cm and K = 10 W/m K contains radioactive material which generates heat uniformly within the cylinder at a constant rate of 3 MW/m3. The rod is cooled by convection from its cylindrical surface into ambient air at 50°C with heat transfer coefficient of 60 W/m2 K. Calculate the temperature at the centre and outer surface of the cylindrical rod.
Answer
For a long cylinder with uniform heat generation, the temperature distribution is governed by the steady-state heat conduction equation in cylindrical coordinates. The heat generation rate is q̇ = 3 × 106 W/m3, thermal conductivity k = 10 W/m K, radius R = 0.05 m, ambient temperature T∞ = 50°C, and heat transfer coefficient h = 60 W/m2 K.
First, determine the outer surface temperature (Ts) using the energy balance at the surface, where heat generated equals heat dissipated by convection:
Rearranging for Ts:
Substituting the values:
Next, determine the centre temperature (T0) using the standard temperature distribution formula for a solid cylinder with uniform heat generation:
At the centre (r = 0):
Substituting the values:
The temperature at the outer surface is 1300°C and the temperature at the centre is 1487.5°C.
A 0.75 m high and 1.25 m wide double pane window consists of two 3 mm thick layers of glass (85 W/m K) separated by a 10 mm wide stagnant air space (0.022 W/m K). Determine the rate of heat transfer through this window and the temperature of the inner surface, when the room is maintained at 24°C. Take the convective heat transfer coefficients on the inside and the outside surfaces of the window as 15 and 50 W/m2K respectively.
Answer
To determine the rate of heat transfer, we calculate the total thermal resistance of the window system. The system consists of five resistances in series: inside convection, first glass layer, stagnant air space, second glass layer, and outside convection.
Given data: Height H = 0.75 m, Width W = 1.25 m, Area A = 0.9375 m2. Thicknesses: tglass = 0.003 m, tair = 0.01 m. Thermal conductivities: kglass = 0.85 W/mK, kair = 0.022 W/mK. Convection coefficients: hin = 15 W/m2K, hout = 50 W/m2K. Temperatures: T∞,in = 24°C, T∞,out = -10°C (assuming standard winter conditions if not specified, or leave as variables).
The thermal resistances are:
- Rconv,in = 1 / (hin × A) = 1 / (15 × 0.9375) = 0.0711 K/W
- Rglass = tglass / (kglass × A) = 0.003 / (0.85 × 0.9375) = 0.00376 K/W
- Rair = tair / (kair × A) = 0.01 / (0.022 × 0.9375) = 0.4848 K/W
- Rconv,out = 1 / (hout × A) = 1 / (50 × 0.9375) = 0.0213 K/W
Total resistance Rtotal = Rconv,in + 2 × Rglass + Rair + Rconv,out = 0.0711 + 0.00752 + 0.4848 + 0.0213 = 0.5847 K/W.
Assuming an outside temperature of -10°C, the rate of heat transfer is:
The inner surface temperature Ts,in is calculated using the inside convection resistance:
A thin copper rod (K= 95 W/m K) is 12 mm in diameter and spans between two plates 150 mm apart. Air flows over the plates providing the convective heat transfer coefficient equal to 50 W/m2 K. If the surface temperature of the plates exceeds the air temperature by 45°C, calculate excess temperature at mid length of the rod over that of air and the heat loss from the rod.
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State and explain Buckingham Pi theorem and apply the same for natural convection heat transfer.
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What is the significance of Reynolds number and Nusselt number in forced convection heat transfer? Explain.
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Air at 2 bar and 40°C is heated as it flows through a 30 mm diameter tube at a velocity of 10 m/sec. If the wall temperature is maintained at 100°C all along the length of tube, make calculations for the heat transfer per unit length of the tube.
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Draw the velocity profile on vertical flat plate for natural convection and discuss the importance in evaluating the heat transfer coefficient.
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In a counter flow double pipe heat exchanger water is heated from 25°C to 65°C by oil with a specific heat of 1.45 kJ/kg K and the mean flow rate of 0.9 kg/s. The oil is cooled from 230°C to 160°C. If the overall heat transfer coefficient is 420 W/m2 K. Calculate a) rate of heat transfer, b) mean flow rate of water and c) surface area of the heat exchanger.
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A square room 4 m × 4 m and height 3 m has all its walls perfectly insulated. The floor and ceiling are maintained at 300 K and 280 K respectively. Assuming an emissivity value 0.75 for all surfaces, determine the wall temperature and the net heat interchange between the floor and the ceiling. Take floor to ceiling shape factor as 0.28.
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What is the need of radiation shields? Explain the significance and their applications.
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