) An insulating cork table mat is placed on a wooden tabletop of thickness 4 cm. A wok is placed on the mat and allowed to stand until steady-state conditions

are reached. If the surface of the mat in contact with the wok is at a temperature of 450 °F and the lower surface of the table is at 68 °F, the table would be damaged if the temperature exceeded 345.6 °F, ignoring any lateral heat flow, would a 5 mm thick mat be sufficient to prevent damage to the table? (The thermal conductivities of the cork and the wood are 0.05 Wm-1K1 and 0.15 Wm1K1 respectively). b) An alloy is cast into an ingot with a height of 40 mm. The mould is heated underneath to 1500 °C with the top surface is at a temperature of 700 °C. The mould is cooled slowly with both temperatures changing at the same rate. i)Using the Rayleigh number show that convection currents are likely to form within the molten alloy during cooling.[3] one method to prevent convection currents is to heat the top surface. What temperature would the mould need to be heated to prevent the formation of convection currents[2] coefficient of thermal expansion = 3.15 x 103 mK1 acceleration due to gravity = 9.81 m s2 Kinematic viscosity 0.1 cm2 s1 Thermal diffusivity = 3.31 x 105 m² s1 No convective motion occurs at a Rayleigh number less than 1708