HEAT AND MASS TRANSFER (RME-502 / RME-502A)
B.Tech (SEM-V) – AKTU
SECTION A
(Attempt all questions – 2 × 7 = 14 marks)
Q1 (a) What is thermal contact resistance? How is it related to thermal contact conductance?
Thermal contact resistance is the resistance to heat flow at the interface of two solid surfaces in contact due to surface roughness and air gaps. It reduces heat transfer across the interface. Thermal contact conductance is the reciprocal of thermal contact resistance and represents the ability of heat to flow across the contact surface.
Q1 (b) What is lumped system analysis? When is it applicable?
Lumped system analysis assumes uniform temperature throughout a body during heat transfer. It is applicable when internal thermal resistance is much smaller than surface resistance, that is when the Biot number is less than 0.1.
Q1 (c) Define Prandtl number and Grashof number.
Prandtl number is the ratio of momentum diffusivity to thermal diffusivity and indicates the relative thickness of velocity and thermal boundary layers.
Grashof number is the ratio of buoyancy force to viscous force in natural convection and indicates the strength of free convection.
Q1 (d) Define reflectivity, transmissivity, and absorptivity.
Reflectivity is the fraction of incident radiation reflected by a surface.
Transmissivity is the fraction of radiation transmitted through a material.
Absorptivity is the fraction of radiation absorbed by a surface.
Q1 (e) What are the common approximations made in heat exchanger analysis?
Common approximations include steady-state operation, negligible heat loss to surroundings, constant physical properties, and uniform overall heat transfer coefficient.
Q1 (f) What is the difference between sub-cooled boiling and saturated boiling?
Sub-cooled boiling occurs when liquid temperature is below saturation temperature but boiling occurs at the surface. Saturated boiling occurs when the liquid temperature is equal to saturation temperature and vapor bubbles form throughout the liquid.
Q1 (g) Define Fick’s law of mass diffusion.
Fick’s law states that the rate of mass diffusion is proportional to the negative concentration gradient. It describes how mass transfers from a region of high concentration to low concentration.
SECTION B
(Attempt any three – 7 × 3 = 21 marks)
Q2 (a) Derive the general heat conduction equation in Cartesian coordinate system.
The general heat conduction equation is derived by applying energy balance to a differential control volume. It accounts for conduction in three directions, internal heat generation, and transient effects. The final form relates temperature variation with space and time coordinates.
Q2 (b) One end of a long rod is inserted into a furnace. Explain heat transfer mechanism involved.
Heat is transferred from the furnace to the rod by conduction. Along the length of the rod, heat is lost by convection and radiation to the surrounding air. At steady state, heat conducted along the rod balances heat lost to surroundings.
Q2 (c) Explain critical radius of insulation.
Critical radius of insulation is the radius at which heat loss from a cylindrical or spherical surface is maximum. Beyond this radius, adding insulation reduces heat loss. It depends on thermal conductivity of insulation and convective heat transfer coefficient.
SECTION C
(Attempt any two – one from each unit, 7 × 2 = 14 marks)
Q4 (a) Derive an expression for temperature distribution for a very long fin.
For a very long fin, the temperature approaches ambient temperature at infinite length. Using fin equation and applying boundary conditions, the temperature distribution is obtained as an exponential decay function along the fin length.
Q4 (b) Estimate the time of death using Newton’s law of cooling.
Newton’s law of cooling relates body temperature change to ambient temperature and heat transfer coefficient. By substituting given data and solving the equation, the time of death is estimated based on temperature difference.
Q5 (a) Explain forced convection over a flat plate.
In forced convection over a flat plate, fluid motion is caused by external means. A velocity boundary layer develops along the plate and heat is transferred by convection. Heat transfer coefficient depends on Reynolds number and Prandtl number.
Q5 (b) Explain heat loss from a steam pipe with insulation.
Heat loss occurs due to conduction through insulation followed by convection and radiation from the outer surface. Overall heat transfer coefficient is calculated considering all resistances in series.
