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A plane slab of thickness 60 cm is made of a material of thermal conductivity k = 17.45 W/m K. Let us assume that one side of the slab absorbs a net amount of radiant energy at the rate q = 530.5 watt/m2. If the other face of the slab is at a constant temperature t2 = 38 degree Celsius. Comment on the temperature with respect to the slab?

Correct Answer: 47.08 degree Celsius
Heat flux, q = k (t s – t f) / Thickness. So, t s = 56.17 degree Celsius. Now, t = t s + (t f – t s) x/Thickness.

A 2 cm thick steel slab heated to 525 degree Celsius is held in air stream having a mean temperature of 25 degree Celsius. Estimate the time interval when the slab temperature would not depart from the mean value of 25 degree Celsius by more than 0.5 degree Celsius at any point in the slab. The steel plate has the following thermal physical properties Density = 7950 kg/m3 C P = 455 J/kg K K = 46 W/m K

A flat wall of fire clay, 50 cm thick and initially at 25 degree Celsius, has one of its faces suddenly exposed to a hot gas at 950 degree Celsius. If the heat transfer coefficient on the hot side is 7.5 W/m2 K and the other face of the wall is insulated so that no heat passes out of that face, determine the time necessary to raise the center of the wall to 350 degree Celsius. For fire clay brick Thermal conductivity = 1.12 W/m K Thermal diffusivity = 5.16 * 10 -7 m2/s

The rear window of an automobile is made of thick glass i.e. AB = 5 mm and thermal conductivity is 0.8 W/m degree. To defrost this window, a thin transparent film type heating element has been fixed to its inner surface. For the conditions given below, determine the electric power that must be provided per unit area of window if a temperature 5 degree Celsius is maintained at its outer surface. Interior air temperature and the corresponding surface coefficient are 20 degree Celsius and 12 W/m2 degree. Surrounding air temperature and the corresponding surface coefficient are – 15 degree Celsius and 70 W/m2 degree. Electric heater provides uniform heat flux

A centrifugal pump which circulates a hot liquid metal at 500 degree Celsius is driven by a 3600 rpm electric motor. The motor is coupled to the pump impeller by a horizontal steel shaft of dia 25 mm. Let us assume the motor temperature as 60 degree Celsius with the ambient air at 25 degree Celsius, what length of shaft should be specified between the motor and the pump? It may be presumed that the thermal conductivity of the shaft material is 35W/m K and that the convective film coefficient between the steel shaft and the ambient air is 15.7W/square m K

A water line is buried underground in dry soil that has an assumed initial temperature of 4.5 degree Celsius. The pipe may have no flow through it for long period of time, yet it will not be drained in order that no freezing occurs, the pipe must be kept at a temperature not lower than 0 degree Celsius. The pipe is to be designed for a 30 hour period at the beginning of which the soil surface temperature suddenly drops to – 17 degree Celsius. Workout the minimum earth covering needed above the water pipe so as to prevent the possibility of freezing during 36 hour cold spell. The soil in which the pipe is buried has the following properties Density = 640 kg/m3 Specific heat = 1843J/kg degree Thermal conductivity = 0.345 W/m degree

Two rods A and B of the same length and diameter protrude from a surface at 120 degree Celsius and are exposed at air at 25 degree Celsius. The temperatures measured at the end of the rods are 50 degree Celsius and 75 degree Celsius. If thermal conductivity of material A is 20W/ m K, calculate it for B

A composite slab consists of 5 cm thick layer of steel (k = 146 kJ/m hr degree) on the left side and a 6 cm thick layer of brass (k = 276 kJ/m hr degree) on the right hand side. The outer surfaces of the steel and brass are maintained at 100 degree Celsius and 50 degree Celsius. The contact between the two slabs is perfect and heat is generated at the rate of 4.2 * 10 5 k J/m2 hr at the plane of contact. The heat thus generated is dissipated from both sides of composite slab for steady state conditions. Calculate the temperature at the interface

What maximum thickness of concrete can be poured without causing the temperature gradient to exceed 98.5 degree Celsius per meter anywhere in the slab? Consider a 1.2 m thick slab of poured concrete (k = 1.148 W/m degree) with both of side surfaces maintained at a temperature of 20 degree Celsius. During its curing, chemical energy is released at the rate of 80 W/m3. Workout the maximum temperature of concrete

The handle of a saucepan, 30 cm long and 2 cm in diameter, is subjected to 100 degree Celsius temperature during a certain cooking operation. The average unit surface conductance over the handle surface is 7.35 W/m2 degree in the kitchen air at 24 degree Celsius. The cook is likely to grasp the last 10 cm of the handle and hence the temperature in this region should not exceed 38 degree Celsius. What should be the thermal conductivity of the handle material to accomplish it? The handle may be treated as a fin insulated at the tip

During heat treatment, cylindrical pieces of 25 mm diameter, 30 mm height and at 30 degree Celsius are placed in a furnace at 750 degree Celsius with convective coefficient 80 W/m2 degree. Calculate the time required to heat the pieces to 600 degree Celsius. Assume the following property values Density = 7850 kg /m3 Specific heat = 480 J/kg K Conductivity = 40 W/m degree