Explanation Given: The temperature of the room is T 1 = 30 °C . The diameter of the glass bed is D = 10 mm . The initial temperature of the glass bed is T i = 400 °C . The convection heat transfer coefficient of the glass bed is q c o n v = 28 W / m 2 ⋅ K . The density of the glass bed is ρ = 2800 kg / m 3 . The specific heat of glass bed is c p = 750 J / kg ⋅ K The thermal conductivity of the glass bed is k = 0.7 W / m ⋅ K . Formula used: The Biot numberis givenas, B i = h L c k Here, L c is the characteristic length, h is heat transfer coefficient and k is the thermal conductivity. Characteristic length L c is givenas, L c = r o Here, r o radius of outer diameter. Thermal diffusivity is given as, α = k ρ C p Here, k is the thermal conductivity. C p is the specific heat, and ρ is the density. TheFourier number is given as, τ = α t r o 2 Here α is the thermal diffusivity, t is the characteristics time, and l is the characteristic length. The one term approximation method for spherical is given as, θ ( 0 , s p h ) = ( A 1 e − λ 2 τ ) Here, λ 1 and A 1 are the functions of the Biot number. Calculation Characteristic length L c can be calculated as, L c = r o L c = 0.005 m The Biot number can be calculated as, Bi = h L c k Bi = 28 W / m 2 ⋅ K × 0.005 m 0.7 W / m ⋅ K = 0

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Chapter 4, Problem 154P

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Chapter 4, Problem 153P

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The temperature at the center of the glass bead.

Solution Summary: The author explains the temperature at the center of the glass bead, the convection heat transfer coefficient, and the thermal conductivity.

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