JNTU
JNTU B.Tech IV Year HEAT TRANSFER Previous Question Paper (March - 2021 - R16)
Answer any Five Questions. All Questions Carry Equal Marks.
Main
Describe different modes of heat transfer along with their basic laws and discuss different applications.
Answer
Heat transfer occurs through three primary modes:
- Conduction: The transfer of energy through direct molecular interaction in solids or stationary fluids. It is governed by Fourier's Law of Heat Conduction: Q = -kA(dT/dx), where Q is the heat transfer rate, k is thermal conductivity, A is area, and dT/dx is the temperature gradient. Applications include heat loss through furnace walls and heat sinks in electronics.
- Convection: The transfer of energy between a solid surface and a moving fluid. It is governed by Newton's Law of Cooling: Q = hA(Ts - T∞), where h is the convective heat transfer coefficient, Ts is the surface temperature, and T∞ is the fluid temperature. Applications include cooling of engines and heat exchangers.
- Radiation: The transfer of energy via electromagnetic waves, requiring no medium. It is governed by the Stefan-Boltzmann Law: Q = εσA(Ts4 - Tsur4), where ε is emissivity, σ is the Stefan-Boltzmann constant, and Tsur is the surroundings temperature. Applications include solar energy collectors and space heating.
A long Cylindrical rod of radius 5 cm and K=10 W/m K, contains radio-active 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
Given: Radius R = 0.05 m, Thermal conductivity k = 10 W/m K, Heat generation q = 3 × 106 W/m3, Ambient temperature T∞ = 50°C, Convection coefficient h = 60 W/m2 K.
First, calculate the outer surface temperature (Ts) using the energy balance: Heat generated = Heat dissipated by convection.
Next, calculate the center temperature (T0) using the temperature distribution formula for a cylinder with uniform heat generation:
The temperature at the outer surface is 1300°C and the temperature at the center is 1487.5°C.
What is critical radius of insulation? Derive the equation in spherical coordinate system.
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Derive the equation for heat transfer rate and temperature distribution for a circular fin with insulated tip.
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How do the fluid properties influence the convective heat transfer? Explain the significance of convective heat transfer.
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What are different non dimensional parameters influence the forced convection? Explain in detail about the non dimensional parameters.
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Explain Von Karman integral momentum equation over a flat plate for the given velocity profile.
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Draw the velocity and pressure profile over the cylinder for different Reynolds number and explain the significance.
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What is meant by fouling factor of heat exchangers? Explain its effect on heat exchanger design.
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Determine the heat loss by radiation per meter length of 8 cm diameter pipe at 300°C if it is located in a large room with red brick walls at a temperature of 27°C. Emissivity of pipe is 0.79 and of brick is 0.93.
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Explain the phenomenon film condensation over vertical cylinder and explain the salient features.
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