Heat is being transferred convectively from a cylindrical nuclear reactor fuel rod of $$50mm$$ diameter to water at $${70^ \circ }C$$, under steady state condition, the rate of heat generation within the fuel element is $$50 \times {10^6}\,\,W/{m^3}$$ and the convective heat transfer coefficient is $$1$$ $$kW/{m^2}K.$$ The outer surface temperature of the fuel element would be

Resistance spot welding of two steel sheets is carried out in lap joint configuration by using a welding current of $$3$$ $$KA$$ and a weld time of $$0.2s.$$ A molten weld nugget of volume $$20m{m^3}$$ is obtained. The effective contact resistance is $$200\mu \Omega .$$ The material properties of steel are given as (i) latent heat of melting $$1400$$ $$kJ/kg,$$ (ii) density $$8000$$ $$kg/{m^3},$$ (iii) melting temp $${1520^ \circ }C$$, (iv) specific heat $$0.5$$ $$kJ/kgC.$$ The ambient temp is $$20C.$$

Heat (Joules) dissipated to the base metal will be (neglecting all other heat losses)

Resistance spot welding of two steel sheets is carried out in lap joint configuration by using a welding current of $$3$$ $$KA$$ and a weld time of $$0.2s.$$ A molten weld nugget of volume $$20m{m^3}$$ is obtained. The effective contact resistance is $$200\mu \Omega .$$ The material properties of steel are given as (i) latent heat of melting $$1400$$ $$kJ/kg,$$ (ii) density $$8000$$ $$kg/{m^3},$$ (iii) melting temp $${1520^ \circ }C$$, (iv) specific heat $$0.5$$ $$kJ/kgC.$$ The ambient temp is $$20C.$$

Heat (in Joules) used for producing weld nugget will be (assuming $$100\% $$ heat transfer efficiency

Autogeneous gas tungsten arc welding of a steel plate is carried out with welding current of $$500A,$$ voltage of $$20V,$$ and weld speed of $$20mm/min.$$ Consider the heat transfer efficiency from the arc to the weld pool as $$90\% $$. The heat input per unit length (in $$kJ/mm$$) is