Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech III HEAT TRANSFER Previous Question Paper (May - 2019 - R16)
Note: Part A is compulsory (25 marks). Part B consists of 5 Units. Answer any one full question from each unit (10 marks each).
Part A
Define Newton's law of cooling.
Answer
Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its surroundings, provided the temperature difference is small and the nature of the surface remains constant. Mathematically, this is expressed as:
Where:
- Q is the rate of heat transfer (W)
- h is the convective heat transfer coefficient (W/m²·K)
- A is the surface area of the body (m²)
- Ts is the surface temperature of the body (K or °C)
- T∞ is the ambient or surrounding fluid temperature (K or °C)
Explain the term boundary conditions.
Answer
In the study of heat conduction, boundary conditions are the mathematical constraints applied to the governing heat diffusion equation to determine a unique solution for the temperature distribution within a physical system. Since the heat equation is a second-order partial differential equation in space, the solution involves constants of integration that must be evaluated using the physical conditions existing at the boundaries of the domain.
There are three primary types of boundary conditions:
- Dirichlet Boundary Condition (Prescribed Temperature): The temperature at the boundary surface is specified as a constant or a known function of time. This is expressed as: T(x, t) = T_s
- Neumann Boundary Condition (Prescribed Heat Flux): The heat flux at the boundary surface is specified, often representing an insulated surface where the gradient is zero. This is expressed as: -k(∂T/∂x) = q''_s
- Robin Boundary Condition (Convection Condition): The heat flux at the boundary is equated to the heat transfer by convection between the surface and the surrounding fluid. This is expressed as: -k(∂T/∂x) = h(T_s - T_∞)
Without these conditions, the general solution to the heat equation remains an indefinite family of curves; boundary conditions effectively 'anchor' the solution to the specific physical reality of the problem.
Discuss the physical interpretation of thermal diffusivity.
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How does the fin efficiency differ from fin effectiveness?
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What is the difference between local and average convection heat transfer?
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Draw a neat sketch showing laminar and turbulent regions of the boundary layer during flow over a flat plate.
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Define Reynolds analogy.
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List out the assumptions made during derivation of expression for LMTD.
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State and explain the Wien – Displacement Law.
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Differentiate between film wise and drop wise condensation.
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Part B
What is meant by thermal resistance? Explain the electrical analogy for solving heat transfer problem.
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A mild steel tank of wall thickness 10mm contains water at 90°C. Calculate the rate of heat loss per m² of tank surface area when the atmospheric temperature is 15°C. The thermal conductivity of mild steel is 50 W/m K and the heat transfer co-efficient for inside and outside the tank is 2800 and 11 W/m²K respectively. Calculate also the temperature of the outside surface of the tank.
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What is the critical thickness of insulation on a small diameter wire or pipe. Explain its physical significance and derive the expression for same.
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The wall of a cold room is composed of three layers. The outer layer is brick 30cm thick, the middle layer is cork 20 cm thick, the inside layer is cement 15 cm thick. The temperatures of the outside air is 25°C and on the inside air is -20°C. The film co-efficient for outside air and brick is 55.4 W/m²K. Film co-efficient for inside air and cement is 17 W/m²K. Find heat flow rate. Assume k(brick) = 2.5 W/mK, k(cork) = 0.05 W/mK, k(cement) = 0.28 W/mK.
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A 12 cm diameter cylindrical bar initially at a uniform temperature of 40°C is placed in a medium at 650°C with a convective heat transfer coefficient of 22 W/m²K. Determine the time required for centre to reach 255°C. Also calculate the temp of the surface. Take k=0.2 W/mK, ρ=580 kg/m³, Cp=1050 kJ/kg.
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Develop an expression for temperature distribution in a slab made of single material.
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Sheets of brass and steel, each of thickness 1cm, are placed in contact. The outer surface of brass is kept at 100°C and the outer surface of steel is kept at 0°C. What is the temperature of the common interface? The thermal conductivities of brass and steel are in the ratio of 2:1.
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Explain the Raleigh’s method of dimensional analysis giving an example.
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How do you determine Grasshof number? State its physical significance.
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What do you understand by hydrodynamic and thermal boundary layers? Illustrate with reference to flow over a heated flat plate. How is the boundary layer thickness defined?
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A water heater is fabricated by a resistance wire wound uniformly over a 10 mm diameter and 4m long tube. The resistance element maintains a uniform heat flux of 1000 W/m². The mass flow rate of water is 12kg/hr and its inlet temperature is 10°C. Estimate the surface temperature of tube at the exit.
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Discuss how the geometric parameter of the pipe, physical properties of the fluid and its velocity influence the heat transfer coefficient in the fluid flow in a pipe.
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Water at 30°C is flowing through a pipe of 25 mm inner diameter at a rate of 1 m³/hr. Find the heat transfer coefficient in water if the length of the pipe is 50 cm. The thermal conductivity, density and kinematic viscosity of water are 0.63 W/mK, 980 Kg/m³, and 0.6 × 10⊃-6 m²/s respectively.
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In a heat exchanger, water flows through a 0.02 m inner diameter copper tube at a velocity of 1.5 m/s. The water entering the tube at 15°C is heated by steam condensing at 100°C on the outside surface of the tube. What would be heat transfer coefficient for water if it is to leave the pipe at 45°C? The physical properties of water at the bulk temperature 30°C are: k = 0.6172 W/(m.K), ν = 0.805 × 10⊃-6 m²/s, ρ = 995 kg/m³, Cp = 4171 J/(kg.K).
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A black body is kept at a temperature of 1000K. Determine the fraction of thermal radiation emitted by the surface in the wavelength band 1.0 to 6.0μm.
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Estimate the rate of solar radiation on a plate normal to the sun rays. Assume the sun to be a black body at a temperature of 5527°C. The diameter of the sun is 1.39 × 10⊃6 km and its distance from the earth is 1.5 × 10⊃8 km.
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Define the terms (i) Absorptivity (ii) Reflectivity and (iii) Transmissivity.
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Differentiate between specular and diffuse reactions.
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Derive Stefan-Boltzmann's law from Plank's law.
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