In a condenser, water enters at $${30^ \circ }C$$ and flows at the rate $$1500$$ $$Kg/hr.$$ The condensing steam is at a temperature of $${120^ \circ }C$$ and cooling water leaves the condenser at $${80^ \circ }C$$. Specific heat of water is $$4.187 kJ/kg$$ $$K.$$ If the overall heat transfer coefficient is $$2000$$ $$W/{m^2}K,$$ the heat transfer area is

A spherical thermocouple junction of diameter $$0.706 mm$$ is to be used for the measurement of temperature of a gas stream. The convective heat transfer co-efficient on the bead surface is $$400W/{m^2}K.$$ Thermo-physical properties of thermocouple material are
$$k = 20W/mK,$$ $$C = 400J/kgK$$ and $$\rho = 8500\,\,kg/{m^3}.$$ If the thermocouple initially at $${30^ \circ }C$$ is placed in a hot stream of $${300^ \circ }C$$ the time taken by the bead to reach $${298^ \circ }C$$, is

One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate $$'{q_g}',$$ can be written as

A company produces two types of toys: $$P$$ and $$Q.$$ Production time of $$Q$$ is twice that of $$P$$ and the company has a maximum of $$2000$$ time units per day. The supply of raw material is just sufficient to produce $$1500$$ toys (of any type) per day. Toy type $$Q$$ requires an electric switch which is available @ $$600$$ pieces per day only. The company makes a profit of Rs.$$3$$ and Rs.$$5$$ on type $$P$$ and $$Q$$ respectively. For maximization of profits, the daily production quantities of $$P$$ and $$Q$$ toys should respectively be