Analytical Solutions of Some Fully Developed Flows of Couple Stress Fluid between Concentric Cylinders with Slip Boundary Conditions

Table 1

Limiting solutions of (i) Poiseuille flow, (ii) Couette flow, and (iii) generalized Couette flow.

(i)	𝑤(𝑟)=𝑘(𝑘)(𝑟)𝑘𝛼+𝛼+𝑘lnln𝐺𝑘^24+𝐺𝑘𝛼2+𝐺𝛼2−𝐺4+−𝐺𝛼2+𝐺4𝛼ln𝑘+𝑘+𝛼𝐺𝑘^24+𝐺𝑘𝛼2−𝐺𝑟^24
(ii)	𝑤(𝑟)=𝛼+𝑘ln(𝑘/𝑟)𝛼+𝑘𝛼+𝑘ln(𝑘)
(iii)	𝑤(𝑟)=𝑘(𝑘)(𝑟)𝑘𝛼+𝛼+𝑘lnln𝐺𝑘^24+𝐺𝑘𝛼2+𝐺𝛼2−𝐺4−1+−𝐺𝛼2+𝐺4𝛼+1ln𝑘+𝑘+𝛼𝐺𝑘^24+𝐺𝑘𝛼2−𝐺𝑟^24