**Assignment 1**

**1.**What is Thermal Conductivity? Write in brief on its variation with temperature.

**2.**What is lumped capacity? Give the assumptions for lumped capacity analysis.

**3.**Derive the general heat conduction equation for three dimensions in Cartesian coordinates? State equations in cylindrical and spherical coordinates?

**4.**Derive the expression for temperature distribution along the fin with insulated end.

**5.**The wall of a furnace comprises three layers, the first layer is refractory (whose maximum allowable temperature is 1400^{o}C) while the second layer is insulation (whose maximum allowable temperature is 1093^{o}C). The third layer is a plate of 6.35 mm thickness of steel [thermal conductivity = 45 W/(m K)]. Assume the layers to be in very good thermal contact. The temperature *T*_{0} on the inside of the refractory is 1370^{o}C, while the temperature *T*_{3} on the outside of the steel plate is 37.8^{o} The heat loss through the furnace wall is expected to be 15800 W/m^{2}. Determine the thickness of refractory and insulation that results in the minimum total thickness of the wall.

Given thermal conductivities in W/(m K):

Layer | k at 37.8^{o}C |
k at 1093^{o}C |

Refractory | 3.12 | 6.23 |

Insulation | 1.56 | 3.12 |

**6.**Calculate heat loss per meter of length of a pipe from an insulated pipe carrying hot fluid

Inner diameter =100 mm Outer diameter = 120 mm

Temp. of fluid = 358 K Temp. of surrounding = 298 K

Thickness of insulation = 30 mm

K for pipe material = 58 W/m K K for insulating material = 0.2 W/m K

Inside heat transfer coefficient = 720 W/m^{2} K Outside heat transfer coefficient = 9 W/m^{2} K

**Assignment 2**

**1.**Explain in detail different types of heat exchangers with diagram

**2.**Explain multiple effect evaporators with different feed arrangements.

**3.**Derive the expression for effectiveness of heat exchanger for parallel flow arrangement.

**4.**What is boiling? Draw pool boiling curve and explain different boiling zones.

**5.**Air at 30ºC is flowing across a tube with a velocity of 25 m/s. The tube could be either a square with 5 cm or a circular cylinder of diameter 5 cm. The tube surface temperature is 124ºC. Compare the rates of heat flow in each case.

Use, Nu_{D} = 0.027 (ReD)^{0.805} (Pr)^{0.33} for circular tube

Nu_{D} = 0.102 (ReD)^{0.675} (Pr)^{0.33} for square tube

At 77 ºC, the properties of air are :

ν=20.92 x 10^{-6 } m^{2} / sec, K = 3×10^{–2} W/m-K, Pr = 0.7.

**Tutorial No-1**

**1.**Give the physical significance of the following numbers

**(i)** Prandtl number

**(ii)** Nusselt number

**(iii)** Grashoff number

**(iv)** Stanton number

**(v)** Reynolds’ number

**2.**Derive the necessary expression for the Critical thickness of insulation for cylinder with neat diagram.

**3.**Air at 300°C and atmospheric pressure is heated as it flows through a tube with a diameter of 25 mm at a velocity of 12 m/sec. Calculate the heat transfer rate per unit length of tube if a constant heat flux condition is maintained at the wall which is at 32°C above the air temperature, over entire length of the tube. Calculate the rise in bulk temperature over a 3.3 m length of the tube. Properties of air are:

**i)** Dynamic viscosity = 29.7 × 10–6 kg/m.sec

**(ii)** Thermal conductivity = 0.0461 W/m°K

**(iii)** Prandtl number = 0.674

**(iv)** Cp = 1.047 kJ/kg°K

**(v)** Density = 0.615 kg/m3.

**4.**Consider a plane wall 100mm thick and of thermal conductivity 100 W/m.K*. *Steady state conditions are known to exist with *T _{1}= *400 K and

*T*600 K . Determine the heat flux and the temperature gradient

_{2}=*dT/dx*for the coordinate systems shown.

**Tutorial No-2**

**1.**What is LMTD? Derive the equation for ΔTlm for counter flow heat exchanger.

**2.**What is Wien’s law of displacement? Derive the expression.

**3.**Explain vacuum evaporation and boiling point elevation.

**4.**It is observed that the value of the radiation emitted by the sun is maximum at a wavelength of 0.58 microns. Estimate the temperature of surface of sun and emissive power. Consider sun to be a black body.

**5.**1000 kg/hr. of a dilute solution of sodium hydroxide containing 10% NaOH is to be concentrated to 40% NaOH by weight in a single effect evaporator. The feed is available at 25°C. Boiling point of the solution may be considered as 100°C. Specific heat of dilute solution is 4180 J/kgK. Latent heat of vaporization of water is 2239 kJ/kg. Saturated steam corresponding to 1.8 bar pressure and 117°C is available for heating purpose. Latent heat of condensation of steam is 2212 kJ/kg. If the overall heat transfer coefficient for the system is 850 W/m^{2} K, calculate :

**(i)** The quantity of water evaporated;

**(ii)** Steam consumed and steam economy;

**(iii)** Surface area of the evaporator.

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