JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV HEAT TRANSFER Previous Question Paper (October/November - 2020 - R16)
Answer any Five Questions. All Questions Carry Equal Marks.
Main
Derive general heat conduction equation in Cartesian coordinates.
Answer
Consider a small differential control volume element of dimensions dx, dy, and dz in Cartesian coordinates. Applying the first law of thermodynamics (energy balance): Rate of energy storage = Rate of energy inflow - Rate of energy outflow + Rate of energy generation. For the x-direction, the net heat conduction rate is given by Q_x - Q_(x+dx) = -[∂Q_x/∂x]dx. Using Fourier's Law of Conduction, Q_x = -k(dy dz)(∂T/∂x). Substituting this into the balance equation for all three dimensions and including internal heat generation q_g, we obtain:
Assuming constant thermal conductivity k, the equation simplifies to the general heat conduction equation:
where α = k/(ρc_p) is the thermal diffusivity.
Discuss some applications of heat transfer.
Answer
Heat transfer principles are fundamental to engineering design and analysis. Key applications include:
- Heat Exchangers: Essential in power plants, chemical processing, and HVAC systems to transfer heat between fluids, such as condensers, evaporators, and radiators.
- Electronic Cooling: Managing heat dissipation in microprocessors and power electronics using heat sinks, fans, and heat pipes to prevent thermal failure.
- Thermal Insulation: Used in building construction and cryogenic storage to minimize heat loss or gain, thereby improving energy efficiency.
- Manufacturing Processes: Critical in metal casting, welding, heat treatment, and plastic molding where precise temperature control determines material properties.
- Aerospace and Automotive: Designing thermal protection systems for re-entry vehicles and managing engine cooling and exhaust systems to ensure structural integrity.
- Energy Conversion: Optimizing boiler performance, solar thermal collectors, and fuel cells to maximize thermal efficiency.
Derive an equation for temperature distribution in a hollow sphere.
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Hot gas at a constant temperature of 400°C is contained in a spherical shell (2000 mm ID, 50mm thick) made of steel. Mineral wool insulation (k=0.06 W/m-K) of thickness 100mm is wrapped all around it. Calculate the steady rate at which heat will flow out if the outside air is at a temperature of 30°C. HTC on the inner surface of the steel shell and on the outer surface of the insulation is 15 W/m²K.
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A tube 2 cm O.D maintained at uniform temperature of Ti is covered with insulation (k=0.20 W/m K) to reduce heat loss to the ambient air Tα with ha=15W/m²K. Find:
the critical thickness rc of insulation
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the ratio of heat loss from the tube with insulation to that without insulation, if the thickness of insulation is equal to rc.
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A stainless steel fin (k=20W/m K) having a diameter of 20 mm and a length of 0.1 m is attached to a wall at 300°C. The ambient temperature is 50°C and the heat transfer coefficient is 10 W/m²K. The fin tip is insulated. Determine:
the rate of heat dissipation from the fin,
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the temperature at the fin tip,
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the rate of heat transfer from the wall area covered by the fin was not used and
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the heat transfer rate from the same fin geometry if the stainless steel fin is replaced by a fictitious fin with infinite thermal conductivity.
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Air at 27°C and 1 atm flows over a flat plate at a speed of 2 m/s. Calculate the boundary layer thickness at a distance of 20 and 40 cm from the leading edge of the plate. Calculate the mass flow which enters the boundary layer between x= 20 cms and x = 40 cms. The viscosity of the air is at 27°C is 1.85 × 10^-5 kg/m s. Assume the unit depth in the z- direction.
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Liquid bismuth flows at a rate of 4.5 kg/s through a 5 cm diameter stainless steel tube. The bismuth enters at 415°C and is heated to 440°C as it passes through the tube. If a constant heat flux is maintained at along the tube and the tube wall is at a temperature 20°C higher than bismuth bulb temperature, calculate the length of the tube required to affect the heat transfer.
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Air at 20°C and 1 atmosphere flows over a flat plate at 35 m/s. The plate is 75 cm long and is maintained at 60°C. Calculate the heat transfer from the plate per unit width of the plate. Also calculate the turbulent boundary layer thickness at the end of the plate assuming it to develop from the leading edge of the plate.
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Distinguish between bulk mean temperature and film temperature.
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Define irradiation and radiosity. What does radiation shape factor mean?
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Two large parallel planes having emissivities 0.3 and 0.5 are maintained at temperatures of 900°C and 400°C respectively. A radiation shield having an emissivity of 0.05 is placed between the two planes. Estimate: i) Heat exchange per m² of area if the shield were not present, ii) Temperature of the shield, and iii) Heat exchange per m² area when the shield is present.
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