Question

pe the earth at a rate of around 30 watts per cubic kilometer. (A watt is a rate of heat production.) The heat then flows to the earth's surface where it is lost to space. Let F(x,y, z) denote the rate of flow of heat measured in watts per square kilometer. By definition, the flux of F across a surface is the quantity of heat flowing through the surface per unit of time. (a) Suppose that the actual heat generation is 32W/km3 What is the value of div F? div F = (Include units.) (b) Assume the heat flows outward symmetrically. Verify that F-ar, where is a suitable constant, satisfies the given conditions. Find a. xì +yj + zk and α α= (Include units.) (c) Let T(x, y, z) denote the temperature inside the earth. Heat flows according to the equation F--k grad T, where k is a constant. If T is in °C, then k = 32, 000°C/km. Assuming the earth is a sphere with radius 6400 km and surface temperature 20 ° C, what is the temperature at the center? (degrees C) 1

Answer 1

per 2000

T- 2 (32000 64,D00 660 c