The ‘tog’ is a unit of thermal resistance commonly used by the textile industry. Doonas and blankets are sometimes sold with a tog rating. 1 tog 0.1 m2K/W For this definition of thermal resistance Typical blanket values are given below: Lightweight summer doona Spring/Autumn weight doona Winter weight doona: 3.0 – 4.5 tog 7.5 – 10.5 tog 12.0 – 13.5 tog Consider a double bed consisting of a mattress with an insulated bottom surface, an electric blanket, a sheet and a doona. Heat is lost at the surface of the doona by natural convection. The configuration is shown beloW: Heat loss Doona Sheet Electric blanket Mattress with insulated base The electric blanket is switched on and left for a long time to reach a steady state The bed is in a very large room (such that the ambient temperature does not change), with an ambient temperature of 20°C. The temperature difference between the ambient air and the top surface of the doona is 0.1°C Assume that a steady state has been reached, and no heat transfers through the base of the mattress. For this question, disregard heat transfer from any vertical surfaces. Assume both the electric blanket and the sheet are thin and add negligible thermal resistance. A double mattress measures 138cm by 188 cm. 4 marks [5 marks] 4 marksl [5 marks]

(i)Show that the thermal expansion coefficient (B) of an ideal gas is 1/T.

(ii)Determine the Rayleigh number associated with natural convection at the top surface of the

(iii) Determine the heat loss from natural convection at the top surface of the doona [This is

(iv) Determine the temperature of the sheet if a 12 tog doona is used. What about if a six tog doona equivalent to the heat supplied by the electric blanket] doona is used?


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