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MECHANISM OF HEAT TRANSFER Mode of Heat transfer • Conduction • Convection • Radiation CONDUCTION Heat transfer between two bodies in contact or from one point of a body to another point of the same body. Atoms in hotter regions have more kinetic energy which they transfer to neighboring atoms. Consider a conductor of length L and cross-section A. If one end of the conductor is at high temperature TH and the other end at a lower temperature Tc, then the heat current H, is defined as the rate of heat flow through the conductor RADIATION Heat transfer by electromagnetic radiation (through empty space). A - surface area of the object, m2 e - emissivity (ranges from 0 to 1) H - Heat Current (rate at which an object radiates or emits radiant energy (J/s or W) T – Absolute temperature (K) ΔH = Aeσ(T4body-T4S) A - surface area of the object, m2 e - emissivity (ranges from 0 to 1 ΔH - Net Rate of Heat loss or gain of energy by radiation(J/s or W) Tbody – Absolute temperature of the radiating body TS – Absolute temperature of surroundings SAMPLE PROBLEM 1) The rod is made of copper is 45 cm long and has a cross sectional area of 1.25 cm2. Let TH = 100oC and TC = 0oC. (Use thermal conductivity of copper = 385W/m.k) a) What is the final steady-state temperature gradient along the rod? b) What is the heat current in the rod in the final steady state? c) What is the final steady-state temperature at a point in the rod 12 cm from its left end? 2) One end of the insulated metal rod is maintained at 100oC, and the other end is maintained at 0oC by an icewater mixture. The rod is 60 cm long and has crosssectional area of 1.25 cm2. The heat conducted by the rod melts 8.50 g of ice in 10 min. Find the thermal conductivity k of the metal. 3.A long rod, insulated to prevent heat loss along its sides, is in perfect thermal contact with boiling water (at atmospheric pressure) at one end and with an ice-water mixture at the other end. The rod consists of 1 m long copper (one end in boiling water) joined end to end to a length L2 of steel (one end in ice-water). Both sections of the rod have cross-sectional areas of 4 cm2. The temperature of the copper-steel junction is 65oC after a steady state has been set-up. K cu = 385 W/m.K K steel = 50.2 W/m.K a) b) c) How much heat per second flows from the steam bath to the ice-water mixture? What is the length L2 of the steel section? Find the mass of ice melted in one hour. 4) An insulating wall consist of 4 cm of material of thermal conductivity K1 and a 2nd layer 8.0 cm thick whose conductivity K2 = 4K1. The innermost and outermost surfaces are kept at -10˚C and 76 ˚C respectively. Calculate the temperature of the interface. 5)The surface area of the sun has a temperature of about 5800 K. Taking the radius of the sun to be equal to be equal to 6.86 X 108 m, calculate the energy radiated by the sun each day. (Assume e = 1) 6) An aluminum kettle (K al = 238 W/m.C°) has a circular cross-section and is 8 cm in radius and 0.3 cm thick. It is placed on a hot plate and filled with 1 kg of water. If the bottom of the kettle is maintained at 101°C and the inside at 100°C, find (a) the rate of heat flow into the water and (b) the time it takes for all the water to boil away. (Neglect heat transferred from the sides.)