JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV Year HEAT TRANSFER Previous Question Paper (September - 2021 - R16)
Answer any five questions. All questions carry equal marks.
Main
With relevant examples explain mechanism of conduction, convection and radiation.
Answer
Heat transfer occurs through three primary mechanisms:
- Conduction: The transfer of thermal energy through stationary matter by physical contact or atomic vibrations. It occurs due to a temperature gradient in solids or stagnant fluids. Example: Heat flowing through a metal rod when one end is placed in a flame.
- Convection: The transfer of heat by the actual movement of fluid particles (liquid or gas). It is categorized into natural convection (driven by buoyancy forces due to density differences) and forced convection (driven by external means like a fan or pump). Example: Cooling of a hot surface by a blowing fan.
- Radiation: The transfer of energy via electromagnetic waves, requiring no physical medium. All matter above absolute zero emits radiation. Example: The heat felt from the sun or a glowing electric heater element.
Derive the 1-D heat conduction under steady state condition.
Answer
For 1-D steady-state heat conduction in a plane wall of thickness L, thermal conductivity k, and surface temperatures T1 and T2, we apply Fourier's Law of Heat Conduction:
Under steady-state conditions, the temperature does not change with time, and the heat flow rate q is constant through any cross-section. Separating variables and integrating across the thickness:
Integrating from x = 0 to L and T = T1 to T2:
Rearranging for the heat transfer rate:
This expression represents the 1-D steady-state heat conduction equation, where the heat flux is proportional to the temperature difference and inversely proportional to the thickness of the material.
A stainless steel plate is of 2 cm thick is maintained at a temperature of 550°C at one face and 50°C on the other. The thermal conductivity of stainless steel at 300°C is 19.1 W/m K. Calculate the heat transferred through the material per unit area.
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In what way is the science of heat transfer different from thermodynamics? Explain.
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Explain why the conductivity of metals decreases and conductivity of insulating material increases with increases in temperature.
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A metallic plate, 3 cm thick is maintained at 400°C on one side and 100°C on the other side. How much heat is transferred through the plate? Take k for the metallic plate as k=370 W/m-K.
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Discuss briefly thermal and hydrodynamic boundary layer and obtain Reynold’s analogy in forced convection.
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A plate 20 cm height and 1 m wide is placed in air at 20°C. If the surface of the plate is maintained at 100°C calculate the boundary layer thickness and local heat transfer coefficient at 10cm from the leading edge. Also calculate the average heat transfer coefficient over the entire length of the plate.
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Describe Buckingham’s method of π-terms to formulate a dimensionally homogenous equation.
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A flat plate 1m wide and 1.5 m long is to be maintained at 90°C in air when free stream temperature is 10°C. Determine the velocity at which air must flow over the plate so that the rate of energy dissipation from the plate is 3.75 kW.
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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 cm and 40 cm from the leading edge of the plate. Calculate the mass flow which enters the boundary layer between x = 20 cm and x = 40 cm. 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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A flat electrical heater of 0.4 m × 0.4 m size is placed vertically in still air at 20°C. The heat generated is 1200 W/m². Determine the value of convective heat transfer co-efficient and the average plate temperature.
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Explain Grashoff number significance in natural convective heat transfer.
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Distinguish between a black body and grey body. Prove that intensity of radiation is given by Ib = Eb/π
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State and explain Kirchoff’s identity? What are the conditions under which it is applicable?
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