In a syringe as shown in the figure, a piston of $$1\,\,c{m^2}$$ cross section is pushed at a constant speed of $$10\,\,cm/s$$ to eject water through an outlet of $$1\,\,m{m^2}.$$ Determine the force required to move the piston. Neglecting losses.

The heat transfer process between a body and its ambient is governed by an internal conductive resistance $$\left( {{\rm I}CR} \right)$$ and an external convective resistance $$(ECR).$$ The body can be considered to be a lumped heat capacity system if

The total efficiency, $${\eta _t}$$ for a finned surface may be defined as the ratio of the total heat transferred by the combined area of the fins, $${A_r},$$ and the exposed surface to that by the total area, $$A$$, if it were maintained at the base temp, $${T_0}.$$ Assuming uniform heat transfer coefficient over the entire surface, derive an expression for the relationship between efficiency and effectiveness of the fin.

Two black plates, each one meter square, are placed parallel to each other in such a way that the radiation shape factor for the system is $$0.4.$$ If the plates are maintained at $${800^ \circ }C$$ and $${400^ \circ }C$$ respectively, determine the net radiant heat transfer between the plates. Also calculate the net heat exchange if the plates were infinite in size. Stephen Boltzmann constant $$ = 5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}$$