1-14 Calculate the radiation heat exchange in 1 day between two black planes having thearea of the surface of a 0.7-m-diameter sphere when the planes are maintained at70 K and 300 K.1-15 Two infinite black plates at 500 and 100C exchange heat by radiation. Calculatethe heat-transfer rate per unit area. If another perfectly black plate is placed betweenthe 500 and 100C plates, by how much is the heat transfer reduced? What is thetemperature of the center plate?1-21 If the radiant flux from the sun is 1350W/m2, what would be its equivalent blackbodytemperature?1-22 A 4.0-cm-diameter sphere is heated to a temperature of 200C and is enclosed in alarge room at 20C. Calculate the radiant heat loss if the surface emissivity is 0.6.1-23 A flat wall is exposed to an environmental temperature of 38C. The wall is coveredwith a layer of insulation 2.5 cm thick whose thermal conductivity is 1.4 W/m C,and the temperature of the wall on the inside of the insulation is 315C. The wall. loses heat to the environment by convection. Compute the value of the convectionheat-transfer coefficient that must be maintained on the outer surface of the insulationto ensure that the outer-surface temperature does not exceed 41C.1-24 Consider a wall heated by convection on one side and cooled by convection on theother side. Show that the heat-transfer rate through the wall isq= T1 T21/h1A+_x/kA+1/h2A4-3 What error would result from using the first four terms of Equation (4-3) to computethe temperature at =0 and x=L? (Note: temperature=Ti.)4-4 A solid body at some initial temperature T0 is suddenly placed in a room where theair temperature is T and the walls of the room are very large. The heat-transfercoefficient for the convection heat loss is h, and the surface of the solid may beassumed black. Assuming that the temperature in the solid is uniform at any instant,write the differential equation for the variation in temperature with time, consideringboth radiation and convection.4-3 What error would result from using the first four terms of Equation (4-3) to computethe temperature at =0 and x=L? (Note: temperature=Ti.)4-4 A solid body at some initial temperature T0 is suddenly placed in a room where the air temperature is T and the walls of the room are very large. The heat-transfercoefficient for the convection heat loss is h, and the surface of the solid may beassumed black. Assuming that the temperature in the solid is uniform at any instant,write the differential equation for the variation in temperature with time, consideringboth radiation and convection.5-3 Using the continuity relationux+ vy=0along with the velocity distributionuu= 32y 12y3and the expression for the boundary-layer thicknessx= 4.64 Rexderive an expression for the y component of velocity v as a function of x and y.Calculate the value of v at the outer edge of the boundary layer at distances of 6 and12 in from the leading edge for the conditions of Example 5-3.5-4 Repeat Problem 5-3 for the linear velocity profile of Problem 5-2.