Section B 3. (a) State Fourier's law of Thermal Conduction (4 marks) (b) A rectangular swimming pool is to be constructed to the following specifications: Internal Pool Dimensions: length 5 m; breath 5 m; depth 4 m Base of pool: concrete layer 26 cm thick Walls of pool: an inner limestone wall 21 cm wide, a concrete wall 28 cm wide and an outer limestone wall 18 cm wide. A water heater will be installed to maintain a constant pool water temperature of 25C day and night. To minimise energy consumption, it is agreed that the water heater rating should not exceed 8.5kW. It is estimated that during daytime, the water in the pool will receive an average solar radiation intensity equal to 500 W/m. To improve insulation, an air gap will be introduced between the concrete wall and outer limestone wall. Estimate the required width for the air gap if the stated water heater rating is not to be exceeded. (26 marks) Notes: Assume an ambient temperature of 15C. Take the temperature of the earth in which the pool is built as constant at 10C. Assume that the heat transfer coefficient for the base and wall surfaces in contact with the water as 10W/mK while the heat transfer coefficient for the free water surface as 8W/mK. Thermal conductivities: Concrete: 0.9 W/mK; Limestone: 1.8 W/mK; Air: 0.024 W/mK Ignore any losses due to thermal radiation.