Advance Heat Transfer(Department Elective - I) — Winter 2020

Define fin effectiveness and the fin efficiency

Define Biot number. Discuss physical significance of Biot number.

Adiecast component has a mass of 1.2 kg and density 7150 kg/m3 with surface area of 0.075 m2. The thermal conductivity of the material is 95 W/mK and the specific heat is 385 J/kg K. It comes out of the machine at 345°Cand is exposed to air at 20°Cwith a convective heat transfer coefficient of 56.8 W/m2K. Determine i. The temperature of the part after 5 minutes. ii. The time required to reach 50°C. iii. The time constant. iv. The value of convective heat transfer coefficient upto which the lumped parameter model can be used. v. The volume/area ratio upto which the lumped parameter model can be used.

Derive temperature distribution and heat transfer rate expression, under one dimensional steady state, uniform volumetric heat generation rate in plane wall having same temperature at both end surface. (Assume constant cross sectional area and constant thermal conductivity.)

Define: Nusselt Number, Reynolds Number, Prandtl Number

Differentiate nucleate boiling and film boiling.

Express conventional generalised basic equation for forced convection parallel flow over a flat plate for local and average skin friction heat transfer convection coefficient using Nusselt Number, Reynolds Number, Prandtl Number.

Define: Grashof number. Tell physical significance of Grashof number.

Derive differential equation, under one dimensional steady state heat conduction in straight infinite long fin of rectangular profile for following cases: i. Pure convection heat transfer through fin surface. ii. Pure radiation heat transfer through fin surface. iii. Convection and radiation heat transfer through fin surface. (Assume constant cross sectional area and constant thermal conductivity.)

Explain radial fins of rectangular and parabolic profiles.

Tell physical significance of Nusselt number and Prandtl number.

State governing equation and boundary condition for 1-Dflow for transient heat conduction in semi-infinite solids.1 Asteel ingot (large in size) heated uniformly to 745°Cis hardened by quenching it in an oil bath maintained at 20°C. Determine the length of time required for the temperature to reach 595°Cat the depth of 12 mm. The ingot may be approximated as a flat plate. For steel ingot, thermal diffusivity = 1.2 x 10-5 m2/s.

Distinguish between natural and forced convection heat transfer.

Define emissivity correction factor and pressure correction factor. Express equation for gas and gas mixture which correlate both above factor.

Along 10-cm-diameter steam pipe whose external surface temperature is 110°Cpasses through some open area that is not protected against the winds (Fig. 2). Determine the rate of heat loss from the pipe per unit of its length when the air is at 1 atm pressure and 10°Cand the wind is blowing across the pipe at a velocity of 8 m/s. Assumptions: 1 Steady operating condition exists. 2 Radiation effects are negligible. 3 Air is an ideal gas. The Nusselt number can be determined from 4/5 0.62Re1/2 Pr1/3   Re  5/8 Nu  0.3 1     1  0.4/ Pr 2/3 1/4   282000   The properties of air at the average film temperature of T = (T + T )/2 f s ∞ = (110 + 10)/2 = 60°Cand 1 atm pressure are k = 0.02808 W/m · °C, Pr = 0.7202, ν = 1.896 x 10-5 m2/s.

Differentiate film wise condensation and drop wise condensation.

Define terms: i. Spectral Transmissivity ii. Spectral absorptivity iii. Spectral emissivity

Avolume of 5 cm3 is available for a circular pin fin. Determine the optimum diameter. Conductivity = 200 W/mK, convection coefficient = 200 W/m2K. Assume fin end is insulated.

Saturated steam at atmospheric pressure condenses on a 2-m-high and 3- m wide vertical plate that is maintained at 80°Cby circulating cooling water through the other side. When plate is vertical, then the condensation heat transfer coefficient is 5848 W/m2 0C. Determine the rate of heat transfer by condensation to the plate if the plate were tilted 30° from the vertical, as shown in Figure 3.

State types of heat loss from human body.

Fluid motion over a vertical flat plate is steady, laminar, two- dimensional and the fluid to be Newtonian with constant properties. Prove that governing equation for natural convection flow is2 u u  u   u v v  gT T .  x y y Draw velocity and temperature profiles for natural convection flow over a hot vertical plate at temperature Tinserted in a fluid at temperature T . s ∞2 (Hint: Apply newton’s second law of motion in x direction, momentum principle in x direction)

Define boiling. Explain various regimes of boiling. Fig. 1, Q-4 (c) Fig. 2, Q-5(c) Fig. 3, Q-7 (b)3

State assumption used in Nusselt theory, laminar film condensation over vertical plate.

Explain radiation effect on temperature measurements. Derive expression for actual temperature of fluid.