A beaker contains a fluid of density ρ k g m 3 , specific heat S J k g o C and viscosity η . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area Q ˙ A by convection when beaker is put on a hot plate, a student proposes that it should depend on η , S Δ θ h and 1 ρ g when Δ θ ( i n o C ) is the difference in the temperature between the bo

Step-by-step solution

Q A = η x s ∆ θ h y 1 ρ g z . . . (1) Q A = M T - 3 , η = M L - 1 T - 1 s ∆ θ h = L T - 2 , 1 ρg = M - 1 L 2 T 2 M T - 3 = M x L - x T - x L y T - 2 y M - 2 L 2z T 2z M T - 3 = M x - z L - x + y + 2 z T - x - 2 y + 2 z So 1 = x - z . . . (2) - x + y + 2 z = 0 . . . (3) - x - 2 y + 2 z = - 3 . . . (4) from 2, 3, 4 x = 1 , y = 1 , z = 0 ,  from (1) so Q A = η s ∆ θ h