Jawaharlal Nehru Technological University Hyderabad B.Tech IV HEAT TRANSFER Previous Question Paper (July/August - 2023 - R16)

Derive an expression for general three dimensional heat conduction equation in cylindrical coordinate system.

A hollow sphere of pure iron contains a liquid mixture which releases 8000 watts inside diameter of the sphere is 120mm and outside diameter of the sphere is 240mm. Steady state conditions prevail and outside surface temperature of the sphere is 60°C. Determine the temperature at a location 30mm from the outside surface of the sphere. Assume material of sphere has a thermal conductivity of 75W/m-k and the heat released by chemical mixture is constant.

A composite wall is made of fire clay brick of (K=1.5W/m-K) and magnesia insulation (K=0.04 W/m-K). The temperature of exposed surface of the fire clay brick is 3800 °C and that of the external surface of the insulation is 45 °C. Determine the insulation thickness required to provide a temperature of the interface not to exceed 300 °C. Determine also the interface temperature if the insulation thickness is doubled.

Derive the equation for critical radius of the insulation for the cylinder.

Derive an expression for the temperature distribution and rate of heat transfer from a fin of uniform Cross section. Neglect the heat transfers from the fin.

A 0.5 cm thick and 4 cm long fin has its base on a plane plate which is maintained at 110°C. The ambient air temperature is 20°C. The conductivity of the fin material is 60 W/m-K and the heat transfer coefficient h = 150 W/m²-K. Assume that the tip of the fin is insulated. Determine: (i) Temperature at the end of the fin (ii) Temperature at the middle of the fin (iii) Total heat dissipated by the fin.

Derive an expression for instantaneous temperature and heat transfer rate for a body subjected to heating or cooling in terms of Biot and Fourier number.

A hot cylinder ingot of 50mm and 200mm long is taken out from the furnace at 800°C and dipped in water till its temperature falls to 500°C. Then it is directly exposed to air till its temperature falls to 100°C. Find the total time required for the ingot to reach the temperature from 800°C to 100°C. Take the following for ingot: k = 60W/m°C, C = 200J/m°C, ρ = 800kg/m³, heat transfer coefficient in water = 200W/m²°C, heat transfer coefficient in air = 20W/m²°C, Temperature of air or water = 30°C.

Explain the concept of boundary layer for flow over flat plate showing different regimes of fluid flow.

Oil at 25°C is heated in a horizontal tube 15 m long having a surface temperature of 50°C. The pipe has an inner diameter of 0.05 m. The oil flow rate is 1 kg/s at inlet temperature. What will be the oil temperature as it leaves the tubes? What is the average heat transfer coefficient? The flow rate is in the laminar region. The properties of the oil are: Specific gravity 0.8: Thermal conductivity 0.125 W/m-K: Specific heat 3.14 kJ/kg-K. Viscosity at 50°C is 0.025 kg/m-s; Viscosity at 25°C is 0.015 kg/m-s.

Obtain an expression for the effectiveness of a counter flow heat exchanger in terms of NTU and the capacity ratio C.

8000kg/hr of air at 100°C is cooled by passing it through a single pass cross flow heat exchanger. To what temperature is the air cooled, if water entering at 15°C flows through the tubes un mixed at the rate of 7500 kg/hr. Take U = 500 kJ/hr m², A= 20m², Cp of air = 1 kJ/kg°C, Cp of water = 4.2 kJ/kg°C.

With the help of typical experimental boiling curve explain the different regimes of pool boiling.

Air free saturated steam at a temperature of 65°C (p = 25.03 kPa) condenses on a vertical outer surface of a 3m long vertical tube maintained at a uniform temperature of 35°C. Assuming film condensation, calculate the average heat transfer coefficient over the entire length of the surface and the rate of condensate flow.

State and Prove Kirchhoff’s law of radiation.

Calculate the net radiant heat exchange per unit area for two parallel plates at temperatures of 427°C and 27°C respectively. ε (hot plate) is 0.9 and ε(cold plate) is 0.6. A polished aluminum shield is placed between them, find the percentage reduction in heat transfer. ε(Shield) is 0.4.