JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year HEAT TRANSFER Previous Question Paper (August - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Derive the general heat conduction equation in Cartesian Coordinate system.
Answer
Consider an elemental control volume of dimensions dx, dy, and dz in a Cartesian coordinate system. Applying the first law of thermodynamics (energy balance): Energy conducted in + Energy generated = Energy conducted out + Energy stored.
For the x-direction, the net heat conduction is:
Using Fourier's Law, qx = -k(dy dz)(∂T/∂x). Substituting this, the net heat flow in the x-direction is (∂/∂x)(k ∂T/∂x)dx dy dz. Repeating this for y and z directions and adding internal heat generation (q̇ dx dy dz) and energy storage (ρ cp (∂T/∂t) dx dy dz), we obtain the general heat conduction equation:
For constant thermal conductivity k, this simplifies to:
A furnace wall consists of 200 mm layer of refractory bricks, 6 mm layer of steel plate and a 100 mm layer of insulation bricks. The maximum temperature of the wall is 1150°C on the furnace side and the minimum temperature is 40°C on the outermost of the wall. An accurate energy balance over the furnace shows that the heat loss from the wall is 400 W/m² . It is known that there is a thin layer of air between the layers of refractory bricks and steel plate. Thermal conductivities for the three layers are 1.52, 45 and 0.138 W/mK respectively. Find:
i) How many millimeters of insulation brick is the air layer equivalent?
ii) What is the temperature of the outer surface of the steel plate?
Answer
Given: q/A = 400 W/m2, T1 = 1150°C, T4 = 40°C. Thicknesses: L1 = 0.2 m, L2 = 0.006 m, L3 = 0.1 m. Conductivities: k1 = 1.52, k2 = 45, k3 = 0.138 W/mK.
i) The total thermal resistance is Rtotal = (T1 - T4) / (q/A) = (1150 - 40) / 400 = 2.775 m2K/W. The sum of individual resistances is R1 + R2 + R3 = (0.2/1.52) + (0.006/45) + (0.1/0.138) = 0.13158 + 0.00013 + 0.72464 = 0.85635 m2K/W. The resistance of the air gap Rair = Rtotal - (R1 + R2 + R3) = 2.775 - 0.85635 = 1.91865 m2K/W. Assuming the air gap has the same conductivity as the insulation (k3 = 0.138), the equivalent thickness Leq = Rair × k3 = 1.91865 × 0.138 = 0.26477 m, which is 264.77 mm.
ii) To find the temperature of the outer surface of the steel plate (T3), we calculate the temperature drop across the insulation layer: T3 - T4 = (q/A) × R3 = 400 × (0.1/0.138) = 289.85°C. Thus, T3 = 40 + 289.85 = 329.85°C.
Derive the expression for temperature distribution under one dimensional steady state heat conduction through composite cylinder.
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Define thermal conductivity, thermal diffusivity and thermal resistance and write their equations.
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Derive an expression for temperature distribution and heat transfer rate through fin insulated at the tip.
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What are the assumptions for lumped capacity analysis? Discuss.
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Aluminum fins of rectangular profile are attached on a plane wall with 5 mm spacing. The fins have thickness y = 1 mm, L = 10 mm, and the thermal conductivity K = 200 W/mK. The wall is maintained at a temperature 200°C, and the fins dissipate heat by convection into the ambient air at 40°C, with heat transfer coefficient h = 50 W/m²K. Determine the heat loss.
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Explain the Reynold and Colburn Analogy.
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A plate of length 750 mm and width 250 mm has been placed longitudinally in a stream of crude oil which flows with a velocity of 5 m/s. If the oil has a specific gravity of 0.8 and kinematic viscosity of 1 stoke, calculate:
i) Boundary layer thickness at the middle of the plate.
ii) Shear stress at the middle of plate and
iii) Friction drag on one side of the plate.
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Show by dimensional analysis for free convection, Nusselts number is a function of Prandtl number and Grasshoff number.
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What are the advantages and limitations of dimensional analysis? Explain.
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Derive expression for effectiveness by NTU method for parallel flow heat exchanger.
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Steam at atmospheric pressure enters the shell of a surface condenser in which the water flows through a bundle of tubes of diameter 25 mm at the rate of 0.05 Kg/s. The inlet and outlet temperatures of water are 15°C and 70°C respectively. The condensation of steam takes place on the outside surface of the tube. If the overall heat transfer coefficient is 230 W/m²K, calculate the following using NTU method:
i) The effectiveness of the heat exchanger
ii) The length of the tube
iii) The rate of steam condensation
Take the latent heat of vaporization at 100°C is 2257 kJ/kg.
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Explain briefly the various regimes of saturated pool boiling by drawing the diagram.
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What is a black body? How does it differ from a gray body? Discuss in detail.
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