Laminar natural convection heat transfer from vertical plate to power-law fluid

Summary Approximate solutions for laminar natural convection heat transfer between a vertical plate and a power-law fluid with high Prandtl number were obtained using an integral method for cases with various types of boundary conditions. The results were found in good agreement with available experimental evidence.Nomenclature a exponent defined by equations (28) and (29) - A, B, C, D, E constants defined by equations (15) to (19) - C₁, C₂, M₁, M₂ coefficients for Nusselt number expression defined by (32b), (33b) - f temperature difference, equal to T_s–T - f⁺ dimensionless temperature difference - g gravitational acceleration - Gr Grashof number defined by (25), (50) and (66), respectively - H heat flux at plate surface - h_x local heat transfer coefficient - K consistency index for Power-law fluid - k thermal conductivity of fluid - K₁, K₂ constants defined by (50) and (51) - L height of plate - n flow behavior index for Power-law fluid - P a quantity defined by (54a) - T temperature - T_s plate temperature - T temperature of the bulk of fluid - s constant given by (35) - u velocity component along x-direction - u_x maximum velocity induced by natural convection current, (10) - v velocity component along y-direction - x distance measured along direction parallel to that of gravitational force - x⁺ dimensionless quantity, defined as x/L - y distance measured away from plate - Nu_x local Nusselt number - Nu_av average Nusselt number - Pr Prandtl number defined by (24) - T temperature difference according to boundary conditions - thermal diffusivity of fluid - coefficient of thermal expression of fluid - boundary layer thickness - ⁺ dimensionless boundary layer thickness - dimensionless velocity profile - dimensionless variable, defined as y/ - dimensionless temperature difference