Heat Transfer T...

Under which of the following conditions stated with respect to internal and external resistance of a body is lumped system analysis applicable?

A cube of side 50 mm is left in a furnace. Calculate the Fourier number after 20 seconds if the thermal diffusivity (α) is given as 42.2 × 10^-6 m²/s.

In a particular case of lumped analysis, the temperature distribution was found to be T = α + βe^-γτ, where τ = time (in seconds) and α, β and γ are constants. What is the time constant corresponding to the above relation?

A steel ball of diameter 60 mm is at 950°C. It is allowed to cool by submerging it in oil of 50℃, with convective heat transfer coefficient h = 20 W/m²K.

The thermophysical properties of steel are:

Density ρ = 7800 kg/m³, conductivity k = 40 W/mK, specific heat C = 600 J/kgK.

Find the time (seconds) required to reach the temperature difference between ball and oil to 36.7% of initial temperature difference.

The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1mm diameter sphere. The properties of the junction are k = 35 W/m°C, ρ = 8500 kg/m³ and C_p = 320 J/kg°C and the convection heat transfer coefficient between the junction and the gas is h = 210 W/m²°C. Determine how long (in sec) it will take for the thermocouple to read 99 percent of the initial temperature difference.

A steel plate (α = 1.2 × 10^-5 m²/s, k = 43 W/mK) is of thickness 10 cm. The plate is initially at a temperature of 250°C  and is suddenly immersed in an oil bath of temperature 45°C. Convective heat transfer coefficient if 700 W/mK and the value of Fourier number from Heisler chart corresponding to Bi^-1 = 1.229 and θ₀ = 0.268 is 2.4. Calculate the time taken (s) for the plate to cool down to 100°C at the center.

 A very long thin glass walled, 0.3 cm diameter, mercury thermometer is placed in a stream of air with convective coefficient of 60 W/m².K for measuring transient temperature of air. Consider cylindrical thermometer bulb consists of mercury only. For which k = 8.9 W/mK and α = 0.016 m²/hour. Calculate the time required (in seconds) for the temperature change to reach half of its initial value.

A steel ball (density = 7800 kg/m³) of 10 mm diameter at 800 K is required to be cooled to 350 K by immersing it in the water at 300 K. The convective heat transfer coefficient is 1000 W/m².K. The thermal conductivity of steel is 40 W/m.K, specific heat c = 600 J/kg.K. The time constant for the cooling process τ is 16 s. Find total energy transferred at t = 8 seconds.

A small metal bead (radius 0.5 mm), initially at 100°C, when placed in a stream of fluid at 20°C, attains a temperature of 28°C in 4.35 seconds. The density and specific heat of the metal are 8500 kg/m³ and 400 J/kgK respectively. If the bead is considered as a lumped system, the convective heat transfer coefficient (in W/m².K) between the metal bead and the fluid stream is